LMFDB - Embedded newform 309.6.a.c.1.11

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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-0.949926 q^{2} -9.00000 q^{3} -31.0976 q^{4} -46.7244 q^{5} +8.54933 q^{6} -212.784 q^{7} +59.9381 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-0.949926 q^{2} -9.00000 q^{3} -31.0976 q^{4} -46.7244 q^{5} +8.54933 q^{6} -212.784 q^{7} +59.9381 q^{8} +81.0000 q^{9} +44.3847 q^{10} +476.272 q^{11} +279.879 q^{12} +307.256 q^{13} +202.129 q^{14} +420.520 q^{15} +938.188 q^{16} +708.532 q^{17} -76.9440 q^{18} -168.011 q^{19} +1453.02 q^{20} +1915.06 q^{21} -452.423 q^{22} +3384.06 q^{23} -539.443 q^{24} -941.829 q^{25} -291.870 q^{26} -729.000 q^{27} +6617.10 q^{28} -158.650 q^{29} -399.463 q^{30} -6398.71 q^{31} -2809.23 q^{32} -4286.45 q^{33} -673.053 q^{34} +9942.23 q^{35} -2518.91 q^{36} -3307.07 q^{37} +159.598 q^{38} -2765.30 q^{39} -2800.57 q^{40} +817.716 q^{41} -1819.17 q^{42} -11667.5 q^{43} -14810.9 q^{44} -3784.68 q^{45} -3214.60 q^{46} +19290.8 q^{47} -8443.69 q^{48} +28470.2 q^{49} +894.668 q^{50} -6376.79 q^{51} -9554.92 q^{52} +4484.50 q^{53} +692.496 q^{54} -22253.5 q^{55} -12753.9 q^{56} +1512.10 q^{57} +150.706 q^{58} +13008.6 q^{59} -13077.2 q^{60} +17932.7 q^{61} +6078.30 q^{62} -17235.5 q^{63} -27353.5 q^{64} -14356.3 q^{65} +4071.81 q^{66} -18200.7 q^{67} -22033.7 q^{68} -30456.5 q^{69} -9444.38 q^{70} +50714.4 q^{71} +4854.98 q^{72} +4429.41 q^{73} +3141.47 q^{74} +8476.46 q^{75} +5224.74 q^{76} -101343. q^{77} +2626.83 q^{78} +31220.2 q^{79} -43836.3 q^{80} +6561.00 q^{81} -776.770 q^{82} -21886.7 q^{83} -59553.9 q^{84} -33105.8 q^{85} +11083.3 q^{86} +1427.85 q^{87} +28546.8 q^{88} -95042.8 q^{89} +3595.16 q^{90} -65379.2 q^{91} -105236. q^{92} +57588.4 q^{93} -18324.9 q^{94} +7850.21 q^{95} +25283.0 q^{96} +120350. q^{97} -27044.6 q^{98} +38578.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) $ 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.949926	−0.167925	−0.0839624	−	0.996469i	$-0.526758\pi$
$2$	−0.949926	−0.167925	−0.0839624	+	0.996469i	$0.526758\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−31.0976	−0.971801
$5$	−46.7244	−0.835832	−0.417916	−	0.908486i	$-0.637239\pi$
$5$	−46.7244	−0.835832	−0.417916	+	0.908486i	$0.637239\pi$
$6$	8.54933	0.0969514
$7$	−212.784	−1.64133	−0.820663	−	0.571412i	$-0.806396\pi$
$7$	−212.784	−1.64133	−0.820663	+	0.571412i	$0.806396\pi$
$8$	59.9381	0.331114
$9$	81.0000	0.333333
$10$	44.3847	0.140357
$11$	476.272	1.18679	0.593394	−	0.804912i	$-0.297787\pi$
$11$	476.272	1.18679	0.593394	+	0.804912i	$0.297787\pi$
$12$	279.879	0.561070
$13$	307.256	0.504245	0.252122	−	0.967695i	$-0.418871\pi$
$13$	307.256	0.504245	0.252122	+	0.967695i	$0.418871\pi$
$14$	202.129	0.275619
$15$	420.520	0.482568
$16$	938.188	0.916199
$17$	708.532	0.594617	0.297309	−	0.954781i	$-0.403911\pi$
$17$	708.532	0.594617	0.297309	+	0.954781i	$0.403911\pi$
$18$	−76.9440	−0.0559749
$19$	−168.011	−0.106771	−0.0533855	−	0.998574i	$-0.517001\pi$
$19$	−168.011	−0.106771	−0.0533855	+	0.998574i	$0.517001\pi$
$20$	1453.02	0.812262
$21$	1915.06	0.947620
$22$	−452.423	−0.199291
$23$	3384.06	1.33388	0.666942	−	0.745110i	$-0.267603\pi$
$23$	3384.06	1.33388	0.666942	+	0.745110i	$0.267603\pi$
$24$	−539.443	−0.191169
$25$	−941.829	−0.301385
$26$	−291.870	−0.0846752
$27$	−729.000	−0.192450
$28$	6617.10	1.59504
$29$	−158.650	−0.0350304	−0.0175152	−	0.999847i	$-0.505576\pi$
$29$	−158.650	−0.0350304	−0.0175152	+	0.999847i	$0.505576\pi$
$30$	−399.463	−0.0810351
$31$	−6398.71	−1.19588	−0.597941	−	0.801540i	$-0.704014\pi$
$31$	−6398.71	−1.19588	−0.597941	+	0.801540i	$0.704014\pi$
$32$	−2809.23	−0.484967
$33$	−4286.45	−0.685193
$34$	−673.053	−0.0998509
$35$	9942.23	1.37187
$36$	−2518.91	−0.323934
$37$	−3307.07	−0.397135	−0.198568	−	0.980087i	$-0.563629\pi$
$37$	−3307.07	−0.397135	−0.198568	+	0.980087i	$0.563629\pi$
$38$	159.598	0.0179295
$39$	−2765.30	−0.291126
$40$	−2800.57	−0.276756
$41$	817.716	0.0759701	0.0379851	−	0.999278i	$-0.487906\pi$
$41$	817.716	0.0759701	0.0379851	+	0.999278i	$0.487906\pi$
$42$	−1819.17	−0.159129
$43$	−11667.5	−0.962294	−0.481147	−	0.876640i	$-0.659780\pi$
$43$	−11667.5	−0.962294	−0.481147	+	0.876640i	$0.659780\pi$
$44$	−14810.9	−1.15332
$45$	−3784.68	−0.278611
$46$	−3214.60	−0.223992
$47$	19290.8	1.27381	0.636907	−	0.770941i	$-0.280213\pi$
$47$	19290.8	1.27381	0.636907	+	0.770941i	$0.280213\pi$
$48$	−8443.69	−0.528968
$49$	28470.2	1.69395
$50$	894.668	0.0506100
$51$	−6376.79	−0.343302
$52$	−9554.92	−0.490026
$53$	4484.50	0.219293	0.109646	−	0.993971i	$-0.465028\pi$
$53$	4484.50	0.219293	0.109646	+	0.993971i	$0.465028\pi$
$54$	692.496	0.0323171
$55$	−22253.5	−0.991956
$56$	−12753.9	−0.543466
$57$	1512.10	0.0616443
$58$	150.706	0.00588247
$59$	13008.6	0.486519	0.243259	−	0.969961i	$-0.421783\pi$
$59$	13008.6	0.486519	0.243259	+	0.969961i	$0.421783\pi$
$60$	−13077.2	−0.468960
$61$	17932.7	0.617051	0.308525	−	0.951216i	$-0.400165\pi$
$61$	17932.7	0.617051	0.308525	+	0.951216i	$0.400165\pi$
$62$	6078.30	0.200818
$63$	−17235.5	−0.547109
$64$	−27353.5	−0.834761
$65$	−14356.3	−0.421464
$66$	4071.81	0.115061
$67$	−18200.7	−0.495338	−0.247669	−	0.968845i	$-0.579665\pi$
$67$	−18200.7	−0.495338	−0.247669	+	0.968845i	$0.579665\pi$
$68$	−22033.7	−0.577850
$69$	−30456.5	−0.770118
$70$	−9444.38	−0.230371
$71$	50714.4	1.19395	0.596974	−	0.802260i	$-0.296369\pi$
$71$	50714.4	1.19395	0.596974	+	0.802260i	$0.296369\pi$
$72$	4854.98	0.110371
$73$	4429.41	0.0972834	0.0486417	−	0.998816i	$-0.484511\pi$
$73$	4429.41	0.0972834	0.0486417	+	0.998816i	$0.484511\pi$
$74$	3141.47	0.0666889
$75$	8476.46	0.174005
$76$	5224.74	0.103760
$77$	−101343.	−1.94791
$78$	2626.83	0.0488872
$79$	31220.2	0.562818	0.281409	−	0.959588i	$-0.409198\pi$
$79$	31220.2	0.562818	0.281409	+	0.959588i	$0.409198\pi$
$80$	−43836.3	−0.765788
$81$	6561.00	0.111111
$82$	−776.770	−0.0127573
$83$	−21886.7	−0.348727	−0.174364	−	0.984681i	$-0.555787\pi$
$83$	−21886.7	−0.348727	−0.174364	+	0.984681i	$0.555787\pi$
$84$	−59553.9	−0.920898
$85$	−33105.8	−0.497000
$86$	11083.3	0.161593
$87$	1427.85	0.0202248
$88$	28546.8	0.392963
$89$	−95042.8	−1.27187	−0.635937	−	0.771741i	$-0.719386\pi$
$89$	−95042.8	−1.27187	−0.635937	+	0.771741i	$0.719386\pi$
$90$	3595.16	0.0467856
$91$	−65379.2	−0.827630
$92$	−105236.	−1.29627
$93$	57588.4	0.690443
$94$	−18324.9	−0.213905
$95$	7850.21	0.0892426
$96$	25283.0	0.279996
$97$	120350.	1.29872	0.649361	−	0.760480i	$-0.275036\pi$
$97$	120350.	1.29872	0.649361	+	0.760480i	$0.275036\pi$
$98$	−27044.6	−0.284456
$99$	38578.0	0.395596
$100$	29288.7	0.292887
$101$	6840.28	0.0667222	0.0333611	−	0.999443i	$-0.489379\pi$
$101$	6840.28	0.0667222	0.0333611	+	0.999443i	$0.489379\pi$
$102$	6057.48	0.0576490
$103$	−10609.0	−0.0985329
$103$	−10609.0	−0.0985329
$104$	18416.3	0.166963
$105$	−89480.1	−0.792051
$106$	−4259.94	−0.0368247
$107$	−77404.8	−0.653595	−0.326797	−	0.945094i	$-0.605970\pi$
$107$	−77404.8	−0.653595	−0.326797	+	0.945094i	$0.605970\pi$
$108$	22670.2	0.187023
$109$	−6408.21	−0.0516619	−0.0258310	−	0.999666i	$-0.508223\pi$
$109$	−6408.21	−0.0516619	−0.0258310	+	0.999666i	$0.508223\pi$
$110$	21139.2	0.166574
$111$	29763.6	0.229286
$112$	−199632.	−1.50378
$113$	91604.1	0.674868	0.337434	−	0.941349i	$-0.390441\pi$
$113$	91604.1	0.674868	0.337434	+	0.941349i	$0.390441\pi$
$114$	−1436.38	−0.0103516
$115$	−158118.	−1.11490
$116$	4933.64	0.0340426
$117$	24887.7	0.168082
$118$	−12357.2	−0.0816986
$119$	−150765.	−0.975961
$120$	25205.1	0.159785
$121$	65784.1	0.408468
$122$	−17034.7	−0.103618
$123$	−7359.44	−0.0438614
$124$	198985.	1.16216
$125$	190020.	1.08774
$126$	16372.5	0.0918731
$127$	−175926.	−0.967880	−0.483940	−	0.875101i	$-0.660795\pi$
$127$	−175926.	−0.967880	−0.483940	+	0.875101i	$0.660795\pi$
$128$	115879.	0.625144
$129$	105008.	0.555581
$130$	13637.5	0.0707742
$131$	25512.8	0.129891	0.0649457	−	0.997889i	$-0.479313\pi$
$131$	25512.8	0.129891	0.0649457	+	0.997889i	$0.479313\pi$
$132$	133298.	0.665871
$133$	35750.1	0.175246
$134$	17289.3	0.0831796
$135$	34062.1	0.160856
$136$	42468.1	0.196886
$137$	−300890.	−1.36964	−0.684820	−	0.728712i	$-0.740119\pi$
$137$	−300890.	−1.36964	−0.684820	+	0.728712i	$0.740119\pi$
$138$	28931.4	0.129322
$139$	−443321.	−1.94617	−0.973086	−	0.230443i	$-0.925982\pi$
$139$	−443321.	−1.94617	−0.973086	+	0.230443i	$0.925982\pi$
$140$	−309180.	−1.33319
$141$	−173617.	−0.735437
$142$	−48174.9	−0.200494
$143$	146337.	0.598432
$144$	75993.2	0.305400
$145$	7412.83	0.0292795
$146$	−4207.61	−0.0163363
$147$	−256232.	−0.978003
$148$	102842.	0.385937
$149$	−338826.	−1.25029	−0.625145	−	0.780509i	$-0.714960\pi$
$149$	−338826.	−1.25029	−0.625145	+	0.780509i	$0.714960\pi$
$150$	−8052.01	−0.0292197
$151$	−52739.4	−0.188232	−0.0941158	−	0.995561i	$-0.530002\pi$
$151$	−52739.4	−0.188232	−0.0941158	+	0.995561i	$0.530002\pi$
$152$	−10070.2	−0.0353534
$153$	57391.1	0.198206
$154$	96268.6	0.327102
$155$	298976.	0.999557
$156$	85994.3	0.282916
$157$	256748.	0.831302	0.415651	−	0.909524i	$-0.363554\pi$
$157$	256748.	0.831302	0.415651	+	0.909524i	$0.363554\pi$
$158$	−29656.9	−0.0945111
$159$	−40360.5	−0.126609
$160$	131260.	0.405351
$161$	−720075.	−2.18934
$162$	−6232.46	−0.0186583
$163$	317322.	0.935473	0.467736	−	0.883868i	$-0.345070\pi$
$163$	317322.	0.935473	0.467736	+	0.883868i	$0.345070\pi$
$164$	−25429.0	−0.0738279
$165$	200282.	0.572706
$166$	20790.8	0.0585599
$167$	−490351.	−1.36055	−0.680277	−	0.732955i	$-0.738141\pi$
$167$	−490351.	−1.36055	−0.680277	+	0.732955i	$0.738141\pi$
$168$	114785.	0.313771
$169$	−276887.	−0.745737
$170$	31448.0	0.0834586
$171$	−13608.9	−0.0355903
$172$	362833.	0.935159
$173$	396872.	1.00817	0.504086	−	0.863653i	$-0.331829\pi$
$173$	396872.	1.00817	0.504086	+	0.863653i	$0.331829\pi$
$174$	−1356.35	−0.00339625
$175$	200407.	0.494671
$176$	446833.	1.08733
$177$	−117077.	−0.280892
$178$	90283.7	0.213579
$179$	337387.	0.787038	0.393519	−	0.919317i	$-0.371258\pi$
$179$	337387.	0.787038	0.393519	+	0.919317i	$0.371258\pi$
$180$	117695.	0.270754
$181$	−547542.	−1.24228	−0.621142	−	0.783698i	$-0.713331\pi$
$181$	−547542.	−1.24228	−0.621142	+	0.783698i	$0.713331\pi$
$182$	62105.4	0.138980
$183$	−161394.	−0.356254
$184$	202834.	0.441668
$185$	154521.	0.331938
$186$	−54704.7	−0.115942
$187$	337454.	0.705685
$188$	−599899.	−1.23789
$189$	155120.	0.315873
$190$	−7457.12	−0.0149860
$191$	−521773.	−1.03490	−0.517450	−	0.855713i	$-0.673119\pi$
$191$	−521773.	−1.03490	−0.517450	+	0.855713i	$0.673119\pi$
$192$	246181.	0.481950
$193$	282342.	0.545610	0.272805	−	0.962069i	$-0.412049\pi$
$193$	282342.	0.545610	0.272805	+	0.962069i	$0.412049\pi$
$194$	−114323.	−0.218088
$195$	129207.	0.243332
$196$	−885357.	−1.64618
$197$	423695.	0.777836	0.388918	−	0.921272i	$-0.372849\pi$
$197$	423695.	0.777836	0.388918	+	0.921272i	$0.372849\pi$
$198$	−36646.3	−0.0664304
$199$	−43991.4	−0.0787472	−0.0393736	−	0.999225i	$-0.512536\pi$
$199$	−43991.4	−0.0787472	−0.0393736	+	0.999225i	$0.512536\pi$
$200$	−56451.4	−0.0997929
$201$	163807.	0.285984
$202$	−6497.76	−0.0112043
$203$	33758.2	0.0574963
$204$	198303.	0.333622
$205$	−38207.3	−0.0634982
$206$	10077.8	0.0165461
$207$	274109.	0.444628
$208$	288263.	0.461989
$209$	−80018.9	−0.126715
$210$	84999.4	0.133005
$211$	1.15113e6	1.77999	0.889995	−	0.455970i	$-0.150707\pi$
$211$	1.15113e6	1.77999	0.889995	+	0.455970i	$0.150707\pi$
$212$	−139457.	−0.213109
$213$	−456430.	−0.689327
$214$	73528.9	0.109755
$215$	545159.	0.804316
$216$	−43694.9	−0.0637230
$217$	1.36155e6	1.96283
$218$	6087.33	0.00867532
$219$	−39864.7	−0.0561666
$220$	692032.	0.963984
$221$	217701.	0.299833
$222$	−28273.2	−0.0385028
$223$	238784.	0.321547	0.160773	−	0.986991i	$-0.448601\pi$
$223$	238784.	0.321547	0.160773	+	0.986991i	$0.448601\pi$
$224$	597760.	0.795989
$225$	−76288.1	−0.100462
$226$	−87017.1	−0.113327
$227$	−565264.	−0.728093	−0.364046	−	0.931381i	$-0.618605\pi$
$227$	−565264.	−0.728093	−0.364046	+	0.931381i	$0.618605\pi$
$228$	−47022.7	−0.0599060
$229$	905491.	1.14103	0.570513	−	0.821289i	$-0.306745\pi$
$229$	905491.	1.14103	0.570513	+	0.821289i	$0.306745\pi$
$230$	150200.	0.187220
$231$	912090.	1.12462
$232$	−9509.17	−0.0115991
$233$	1.09030e6	1.31569	0.657847	−	0.753151i	$-0.271467\pi$
$233$	1.09030e6	1.31569	0.657847	+	0.753151i	$0.271467\pi$
$234$	−23641.5	−0.0282251
$235$	−901352.	−1.06469
$236$	−404536.	−0.472800
$237$	−280982.	−0.324943
$238$	143215.	0.163888
$239$	−941366.	−1.06602	−0.533008	−	0.846110i	$-0.678938\pi$
$239$	−941366.	−1.06602	−0.533008	+	0.846110i	$0.678938\pi$
$240$	394526.	0.442128
$241$	162234.	0.179928	0.0899641	−	0.995945i	$-0.471325\pi$
$241$	162234.	0.179928	0.0899641	+	0.995945i	$0.471325\pi$
$242$	−62490.0	−0.0685918
$243$	−59049.0	−0.0641500
$244$	−557664.	−0.599651
$245$	−1.33026e6	−1.41586
$246$	6990.93	0.00736541
$247$	−51622.3	−0.0538387
$248$	−383527.	−0.395974
$249$	196981.	0.201338
$250$	−180505.	−0.182658
$251$	−1.47199e6	−1.47476	−0.737381	−	0.675477i	$-0.763938\pi$
$251$	−1.47199e6	−1.47476	−0.737381	+	0.675477i	$0.763938\pi$
$252$	535985.	0.531681
$253$	1.61173e6	1.58304
$254$	167117.	0.162531
$255$	297952.	0.286943
$256$	765234.	0.729784
$257$	−1.98601e6	−1.87564	−0.937819	−	0.347126i	$-0.887158\pi$
$257$	−1.98601e6	−1.87564	−0.937819	+	0.347126i	$0.887158\pi$
$258$	−99749.6	−0.0932958
$259$	703693.	0.651829
$260$	446448.	0.409579
$261$	−12850.6	−0.0116768
$262$	−24235.3	−0.0218120
$263$	−237448.	−0.211680	−0.105840	−	0.994383i	$-0.533753\pi$
$263$	−237448.	−0.211680	−0.105840	+	0.994383i	$0.533753\pi$
$264$	−256922.	−0.226877
$265$	−209535.	−0.183292
$266$	−33960.0	−0.0294282
$267$	855386.	0.734317
$268$	566000.	0.481370
$269$	−152684.	−0.128651	−0.0643255	−	0.997929i	$-0.520490\pi$
$269$	−152684.	−0.128651	−0.0643255	+	0.997929i	$0.520490\pi$
$270$	−32356.5	−0.0270117
$271$	−2.17992e6	−1.80309	−0.901546	−	0.432684i	$-0.857567\pi$
$271$	−2.17992e6	−1.80309	−0.901546	+	0.432684i	$0.857567\pi$
$272$	664736.	0.544788
$273$	588413.	0.477832
$274$	285823.	0.229997
$275$	−448567.	−0.357681
$276$	947126.	0.748402
$277$	661610.	0.518087	0.259043	−	0.965866i	$-0.416593\pi$
$277$	661610.	0.518087	0.259043	+	0.965866i	$0.416593\pi$
$278$	421122.	0.326810
$279$	−518296.	−0.398628
$280$	595918.	0.454247
$281$	1.29032e6	0.974838	0.487419	−	0.873168i	$-0.337938\pi$
$281$	1.29032e6	0.974838	0.487419	+	0.873168i	$0.337938\pi$
$282$	164924.	0.123498
$283$	−279351.	−0.207340	−0.103670	−	0.994612i	$-0.533059\pi$
$283$	−279351.	−0.207340	−0.103670	+	0.994612i	$0.533059\pi$
$284$	−1.57710e6	−1.16028
$285$	−70651.9	−0.0515242
$286$	−139010.	−0.100492
$287$	−173997.	−0.124692
$288$	−227547.	−0.161656
$289$	−917839.	−0.646431
$290$	−7041.64	−0.00491675
$291$	−1.08315e6	−0.749817
$292$	−137744.	−0.0945402
$293$	−998717.	−0.679631	−0.339816	−	0.940492i	$-0.610365\pi$
$293$	−998717.	−0.679631	−0.339816	+	0.940492i	$0.610365\pi$
$294$	243402.	0.164231
$295$	−607818.	−0.406648
$296$	−198219.	−0.131497
$297$	−347202.	−0.228398
$298$	321859.	0.209955
$299$	1.03977e6	0.672604
$300$	−263598.	−0.169098
$301$	2.48267e6	1.57944
$302$	50098.5	0.0316088
$303$	−61562.5	−0.0385221
$304$	−157626.	−0.0978235
$305$	−837894.	−0.515751
$306$	−54517.3	−0.0332836
$307$	324599.	0.196563	0.0982813	−	0.995159i	$-0.468666\pi$
$307$	324599.	0.196563	0.0982813	+	0.995159i	$0.468666\pi$
$308$	3.15154e6	1.89298
$309$	95481.0	0.0568880
$310$	−284005.	−0.167850
$311$	945199.	0.554143	0.277072	−	0.960849i	$-0.410636\pi$
$311$	945199.	0.554143	0.277072	+	0.960849i	$0.410636\pi$
$312$	−165747.	−0.0963959
$313$	2.67846e6	1.54534	0.772671	−	0.634807i	$-0.218920\pi$
$313$	2.67846e6	1.54534	0.772671	+	0.634807i	$0.218920\pi$
$314$	−243892.	−0.139596
$315$	805321.	0.457291
$316$	−970875.	−0.546947
$317$	813684.	0.454787	0.227393	−	0.973803i	$-0.426980\pi$
$317$	813684.	0.454787	0.227393	+	0.973803i	$0.426980\pi$
$318$	38339.5	0.0212607
$319$	−75560.5	−0.0415737
$320$	1.27807e6	0.697720
$321$	696644.	0.377353
$322$	684018.	0.367644
$323$	−119041.	−0.0634879
$324$	−204032.	−0.107978
$325$	−289382.	−0.151972
$326$	−301432.	−0.157089
$327$	57673.9	0.0298270
$328$	49012.3	0.0251548
$329$	−4.10479e6	−2.09074
$330$	−190253.	−0.0961715
$331$	3.27560e6	1.64332	0.821658	−	0.569981i	$-0.193049\pi$
$331$	3.27560e6	1.64332	0.821658	+	0.569981i	$0.193049\pi$
$332$	680626.	0.338894
$333$	−267872.	−0.132378
$334$	465797.	0.228471
$335$	850419.	0.414019
$336$	1.79669e6	0.868209
$337$	−3.24455e6	−1.55625	−0.778126	−	0.628108i	$-0.783830\pi$
$337$	−3.24455e6	−1.55625	−0.778126	+	0.628108i	$0.783830\pi$
$338$	263022.	0.125228
$339$	−824437.	−0.389635
$340$	1.02951e6	0.482985
$341$	−3.04753e6	−1.41926
$342$	12927.4	0.00597650
$343$	−2.48176e6	−1.13900
$344$	−699330.	−0.318629
$345$	1.42306e6	0.643689
$346$	−376999.	−0.169297
$347$	−1.78377e6	−0.795272	−0.397636	−	0.917543i	$-0.630169\pi$
$347$	−1.78377e6	−0.795272	−0.397636	+	0.917543i	$0.630169\pi$
$348$	−44402.7	−0.0196545
$349$	−1.86255e6	−0.818551	−0.409275	−	0.912411i	$-0.634218\pi$
$349$	−1.86255e6	−0.818551	−0.409275	+	0.912411i	$0.634218\pi$
$350$	−190371.	−0.0830676
$351$	−223989.	−0.0970420
$352$	−1.33796e6	−0.575553
$353$	359677.	0.153630	0.0768149	−	0.997045i	$-0.475525\pi$
$353$	359677.	0.153630	0.0768149	+	0.997045i	$0.475525\pi$
$354$	111215.	0.0471687
$355$	−2.36960e6	−0.997940
$356$	2.95561e6	1.23601
$357$	1.35688e6	0.563471
$358$	−320492.	−0.132163
$359$	−2.35983e6	−0.966372	−0.483186	−	0.875518i	$-0.660521\pi$
$359$	−2.35983e6	−0.966372	−0.483186	+	0.875518i	$0.660521\pi$
$360$	−226846.	−0.0922519
$361$	−2.44787e6	−0.988600
$362$	520124.	0.208610
$363$	−592057.	−0.235829
$364$	2.03314e6	0.804292
$365$	−206962.	−0.0813126
$366$	153313.	0.0598239
$367$	−2.66771e6	−1.03389	−0.516944	−	0.856019i	$-0.672931\pi$
$367$	−2.66771e6	−1.03389	−0.516944	+	0.856019i	$0.672931\pi$
$368$	3.17488e6	1.22210
$369$	66235.0	0.0253234
$370$	−146783.	−0.0557407
$371$	−954231.	−0.359931
$372$	−1.79086e6	−0.670973
$373$	−3.00041e6	−1.11663	−0.558313	−	0.829630i	$-0.688551\pi$
$373$	−3.00041e6	−1.11663	−0.558313	+	0.829630i	$0.688551\pi$
$374$	−320556.	−0.118502
$375$	−1.71018e6	−0.628006
$376$	1.15625e6	0.421778
$377$	−48746.1	−0.0176639
$378$	−147352.	−0.0530430
$379$	−2.21390e6	−0.791698	−0.395849	−	0.918316i	$-0.629550\pi$
$379$	−2.21390e6	−0.791698	−0.395849	+	0.918316i	$0.629550\pi$
$380$	−244123.	−0.0867261
$381$	1.58334e6	0.558806
$382$	495646.	0.173785
$383$	−1.53616e6	−0.535105	−0.267552	−	0.963543i	$-0.586215\pi$
$383$	−1.53616e6	−0.535105	−0.267552	+	0.963543i	$0.586215\pi$
$384$	−1.04291e6	−0.360927
$385$	4.73521e6	1.62812
$386$	−268204.	−0.0916215
$387$	−945070.	−0.320765
$388$	−3.74260e6	−1.26210
$389$	964641.	0.323215	0.161608	−	0.986855i	$-0.448332\pi$
$389$	964641.	0.323215	0.161608	+	0.986855i	$0.448332\pi$
$390$	−122737.	−0.0408615
$391$	2.39771e6	0.793150
$392$	1.70645e6	0.560891
$393$	−229616.	−0.0749929
$394$	−402479.	−0.130618
$395$	−1.45875e6	−0.470421
$396$	−1.19969e6	−0.384441
$397$	−5.71731e6	−1.82060	−0.910301	−	0.413946i	$-0.864150\pi$
$397$	−5.71731e6	−1.82060	−0.910301	+	0.413946i	$0.864150\pi$
$398$	41788.6	0.0132236
$399$	−321751.	−0.101178
$400$	−883612.	−0.276129
$401$	−4.12876e6	−1.28221	−0.641104	−	0.767454i	$-0.721523\pi$
$401$	−4.12876e6	−1.28221	−0.641104	+	0.767454i	$0.721523\pi$
$402$	−155604.	−0.0480237
$403$	−1.96604e6	−0.603018
$404$	−212717.	−0.0648407
$405$	−306559.	−0.0928702
$406$	−32067.8	−0.00965505
$407$	−1.57506e6	−0.471316
$408$	−382213.	−0.113672
$409$	−2.64369e6	−0.781451	−0.390725	−	0.920507i	$-0.627776\pi$
$409$	−2.64369e6	−0.781451	−0.390725	+	0.920507i	$0.627776\pi$
$410$	36294.1	0.0106629
$411$	2.70801e6	0.790762
$412$	329915.	0.0957544
$413$	−2.76802e6	−0.798536
$414$	−260383.	−0.0746640
$415$	1.02265e6	0.291477
$416$	−863151.	−0.244542
$417$	3.98989e6	1.12362
$418$	76012.0	0.0212785
$419$	890223.	0.247722	0.123861	−	0.992300i	$-0.460472\pi$
$419$	890223.	0.247722	0.123861	+	0.992300i	$0.460472\pi$
$420$	2.78262e6	0.769716
$421$	4.22387e6	1.16146	0.580732	−	0.814095i	$-0.302767\pi$
$421$	4.22387e6	1.16146	0.580732	+	0.814095i	$0.302767\pi$
$422$	−1.09349e6	−0.298905
$423$	1.56256e6	0.424605
$424$	268792.	0.0726109
$425$	−667316.	−0.179209
$426$	433575.	0.115755
$427$	−3.81580e6	−1.01278
$428$	2.40711e6	0.635164
$429$	−1.31704e6	−0.345505
$430$	−517860.	−0.135065
$431$	659756.	0.171076	0.0855382	−	0.996335i	$-0.472739\pi$
$431$	659756.	0.171076	0.0855382	+	0.996335i	$0.472739\pi$
$432$	−683939.	−0.176323
$433$	−331652.	−0.0850087	−0.0425043	−	0.999096i	$-0.513534\pi$
$433$	−331652.	−0.0850087	−0.0425043	+	0.999096i	$0.513534\pi$
$434$	−1.29337e6	−0.329608
$435$	−66715.4	−0.0169045
$436$	199280.	0.0502051
$437$	−568558.	−0.142420
$438$	37868.5	0.00943177
$439$	−5.31184e6	−1.31548	−0.657739	−	0.753246i	$-0.728487\pi$
$439$	−5.31184e6	−1.31548	−0.657739	+	0.753246i	$0.728487\pi$
$440$	−1.33383e6	−0.328451
$441$	2.30609e6	0.564650
$442$	−206799.	−0.0503493
$443$	−2.19910e6	−0.532398	−0.266199	−	0.963918i	$-0.585768\pi$
$443$	−2.19910e6	−0.532398	−0.266199	+	0.963918i	$0.585768\pi$
$444$	−925578.	−0.222821
$445$	4.44082e6	1.06307
$446$	−226827.	−0.0539956
$447$	3.04943e6	0.721855
$448$	5.82039e6	1.37012
$449$	−362358.	−0.0848246	−0.0424123	−	0.999100i	$-0.513504\pi$
$449$	−362358.	−0.0848246	−0.0424123	+	0.999100i	$0.513504\pi$
$450$	72468.1	0.0168700
$451$	389455.	0.0901605
$452$	−2.84867e6	−0.655838
$453$	474654.	0.108676
$454$	536959.	0.122265
$455$	3.05481e6	0.691760
$456$	90632.2	0.0204113
$457$	5.78899e6	1.29662	0.648310	−	0.761377i	$-0.275476\pi$
$457$	5.78899e6	1.29662	0.648310	+	0.761377i	$0.275476\pi$
$458$	−860149.	−0.191606
$459$	−516520.	−0.114434
$460$	4.91710e6	1.08346
$461$	−5.08649e6	−1.11472	−0.557360	−	0.830271i	$-0.688186\pi$
$461$	−5.08649e6	−1.11472	−0.557360	+	0.830271i	$0.688186\pi$
$462$	−866418.	−0.188852
$463$	7.80925e6	1.69300	0.846500	−	0.532389i	$-0.178705\pi$
$463$	7.80925e6	1.69300	0.846500	+	0.532389i	$0.178705\pi$
$464$	−148843.	−0.0320948
$465$	−2.69079e6	−0.577094
$466$	−1.03570e6	−0.220938
$467$	−211359.	−0.0448464	−0.0224232	−	0.999749i	$-0.507138\pi$
$467$	−211359.	−0.0448464	−0.0224232	+	0.999749i	$0.507138\pi$
$468$	−773949.	−0.163342
$469$	3.87283e6	0.813012
$470$	856218.	0.178789
$471$	−2.31074e6	−0.479952
$472$	779709.	0.161093
$473$	−5.55692e6	−1.14204
$474$	266912.	0.0545660
$475$	158237.	0.0321792
$476$	4.68843e6	0.948440
$477$	363244.	0.0730975
$478$	894228.	0.179011
$479$	5.25733e6	1.04695	0.523476	−	0.852041i	$-0.324635\pi$
$479$	5.25733e6	1.04695	0.523476	+	0.852041i	$0.324635\pi$
$480$	−1.18134e6	−0.234029
$481$	−1.01611e6	−0.200253
$482$	−154110.	−0.0302144
$483$	6.48067e6	1.26402
$484$	−2.04573e6	−0.396949
$485$	−5.62328e6	−1.08551
$486$	56092.2	0.0107724
$487$	−5.09439e6	−0.973352	−0.486676	−	0.873582i	$-0.661791\pi$
$487$	−5.09439e6	−0.973352	−0.486676	+	0.873582i	$0.661791\pi$
$488$	1.07485e6	0.204314
$489$	−2.85590e6	−0.540096
$490$	1.26364e6	0.237758
$491$	−5.35096e6	−1.00168	−0.500839	−	0.865541i	$-0.666975\pi$
$491$	−5.35096e6	−1.00168	−0.500839	+	0.865541i	$0.666975\pi$
$492$	228861.	0.0426245
$493$	−112409.	−0.0208297
$494$	49037.3	0.00904085
$495$	−1.80254e6	−0.330652
$496$	−6.00320e6	−1.09567
$497$	−1.07912e7	−1.95966
$498$	−187117.	−0.0338096
$499$	−3.93333e6	−0.707145	−0.353573	−	0.935407i	$-0.615033\pi$
$499$	−3.93333e6	−0.707145	−0.353573	+	0.935407i	$0.615033\pi$
$500$	−5.90918e6	−1.05707
$501$	4.41316e6	0.785517
$502$	1.39829e6	0.247649
$503$	6.37584e6	1.12361	0.561807	−	0.827268i	$-0.310106\pi$
$503$	6.37584e6	1.12361	0.561807	+	0.827268i	$0.310106\pi$
$504$	−1.03307e6	−0.181155
$505$	−319608.	−0.0557686
$506$	−1.53103e6	−0.265831
$507$	2.49198e6	0.430552
$508$	5.47089e6	0.940587
$509$	8.50777e6	1.45553	0.727765	−	0.685827i	$-0.240559\pi$
$509$	8.50777e6	1.45553	0.727765	+	0.685827i	$0.240559\pi$
$510$	−283032.	−0.0481848
$511$	−942510.	−0.159674
$512$	−4.43504e6	−0.747693
$513$	122480.	0.0205481
$514$	1.88656e6	0.314966
$515$	495699.	0.0823570
$516$	−3.26550e6	−0.539914
$517$	9.18768e6	1.51175
$518$	−668456.	−0.109458
$519$	−3.57185e6	−0.582069
$520$	−860491.	−0.139553
$521$	−7.30246e6	−1.17862	−0.589312	−	0.807906i	$-0.700601\pi$
$521$	−7.30246e6	−1.17862	−0.589312	+	0.807906i	$0.700601\pi$
$522$	12207.2	0.00196082
$523$	−4.01445e6	−0.641758	−0.320879	−	0.947120i	$-0.603978\pi$
$523$	−4.01445e6	−0.641758	−0.320879	+	0.947120i	$0.603978\pi$
$524$	−793389.	−0.126229
$525$	−1.80366e6	−0.285599
$526$	225558.	0.0355462
$527$	−4.53370e6	−0.711092
$528$	−4.02149e6	−0.627773
$529$	5.01549e6	0.779246
$530$	199043.	0.0307792
$531$	1.05369e6	0.162173
$532$	−1.11174e6	−0.170304
$533$	251248.	0.0383075
$534$	−812553.	−0.123310
$535$	3.61670e6	0.546295
$536$	−1.09092e6	−0.164014
$537$	−3.03648e6	−0.454396
$538$	145039.	0.0216037
$539$	1.35596e7	2.01036
$540$	−1.05925e6	−0.156320
$541$	−5.06792e6	−0.744452	−0.372226	−	0.928142i	$-0.621405\pi$
$541$	−5.06792e6	−0.744452	−0.372226	+	0.928142i	$0.621405\pi$
$542$	2.07076e6	0.302784
$543$	4.92788e6	0.717233
$544$	−1.99043e6	−0.288370
$545$	299420.	0.0431807
$546$	−558949.	−0.0802399
$547$	4.35235e6	0.621950	0.310975	−	0.950418i	$-0.399344\pi$
$547$	4.35235e6	0.621950	0.310975	+	0.950418i	$0.399344\pi$
$548$	9.35698e6	1.33102
$549$	1.45255e6	0.205684
$550$	426105.	0.0600634
$551$	26654.9	0.00374023
$552$	−1.82550e6	−0.254997
$553$	−6.64318e6	−0.923768
$554$	−628480.	−0.0869996
$555$	−1.39069e6	−0.191645
$556$	1.37862e7	1.89129
$557$	4.65184e6	0.635312	0.317656	−	0.948206i	$-0.397104\pi$
$557$	4.65184e6	0.635312	0.317656	+	0.948206i	$0.397104\pi$
$558$	492343.	0.0669394
$559$	−3.58492e6	−0.485232
$560$	9.32768e6	1.25691
$561$	−3.03709e6	−0.407427
$562$	−1.22571e6	−0.163699
$563$	−2.19998e6	−0.292514	−0.146257	−	0.989247i	$-0.546723\pi$
$563$	−2.19998e6	−0.292514	−0.146257	+	0.989247i	$0.546723\pi$
$564$	5.39909e6	0.714699
$565$	−4.28015e6	−0.564076
$566$	265362.	0.0348175
$567$	−1.39608e6	−0.182370
$568$	3.03973e6	0.395333
$569$	1.48499e7	1.92284	0.961422	−	0.275078i	$-0.0887038\pi$
$569$	1.48499e7	1.92284	0.961422	+	0.275078i	$0.0887038\pi$
$570$	67114.1	0.00865220
$571$	−1.25792e7	−1.61459	−0.807297	−	0.590145i	$-0.799071\pi$
$571$	−1.25792e7	−1.61459	−0.807297	+	0.590145i	$0.799071\pi$
$572$	−4.55074e6	−0.581557
$573$	4.69596e6	0.597500
$574$	165285.	0.0209388
$575$	−3.18720e6	−0.402013
$576$	−2.21563e6	−0.278254
$577$	7.42266e6	0.928154	0.464077	−	0.885795i	$-0.346386\pi$
$577$	7.42266e6	0.928154	0.464077	+	0.885795i	$0.346386\pi$
$578$	871879.	0.108552
$579$	−2.54108e6	−0.315008
$580$	−230521.	−0.0284539
$581$	4.65716e6	0.572375
$582$	1.02891e6	0.125913
$583$	2.13584e6	0.260254
$584$	265490.	0.0322119
$585$	−1.16286e6	−0.140488
$586$	948707.	0.114127
$587$	−1.66388e6	−0.199309	−0.0996547	−	0.995022i	$-0.531774\pi$
$587$	−1.66388e6	−0.199309	−0.0996547	+	0.995022i	$0.531774\pi$
$588$	7.96822e6	0.950425
$589$	1.07505e6	0.127686
$590$	577382.	0.0682863
$591$	−3.81326e6	−0.449084
$592$	−3.10265e6	−0.363855
$593$	−4.35070e6	−0.508069	−0.254035	−	0.967195i	$-0.581758\pi$
$593$	−4.35070e6	−0.508069	−0.254035	+	0.967195i	$0.581758\pi$
$594$	329817.	0.0383536
$595$	7.04439e6	0.815739
$596$	1.05367e7	1.21503
$597$	395923.	0.0454647
$598$	−987705.	−0.112947
$599$	1.25200e7	1.42573	0.712864	−	0.701303i	$-0.247398\pi$
$599$	1.25200e7	1.42573	0.712864	+	0.701303i	$0.247398\pi$
$600$	508063.	0.0576155
$601$	−1.27442e7	−1.43922	−0.719608	−	0.694380i	$-0.755679\pi$
$601$	−1.27442e7	−1.43922	−0.719608	+	0.694380i	$0.755679\pi$
$602$	−2.35835e6	−0.265227
$603$	−1.47426e6	−0.165113
$604$	1.64007e6	0.182924
$605$	−3.07372e6	−0.341410
$606$	58479.8	0.00646881
$607$	768639.	0.0846741	0.0423371	−	0.999103i	$-0.486520\pi$
$607$	768639.	0.0846741	0.0423371	+	0.999103i	$0.486520\pi$
$608$	471981.	0.0517804
$609$	−303824.	−0.0331955
$610$	795938.	0.0866073
$611$	5.92721e6	0.642314
$612$	−1.78473e6	−0.192617
$613$	8.70191e6	0.935327	0.467663	−	0.883907i	$-0.345096\pi$
$613$	8.70191e6	0.935327	0.467663	+	0.883907i	$0.345096\pi$
$614$	−308345.	−0.0330077
$615$	343866.	0.0366607
$616$	−6.07432e6	−0.644980
$617$	1.40382e7	1.48457	0.742283	−	0.670086i	$-0.233743\pi$
$617$	1.40382e7	1.48457	0.742283	+	0.670086i	$0.233743\pi$
$618$	−90699.9	−0.00955291
$619$	7.07826e6	0.742506	0.371253	−	0.928532i	$-0.378928\pi$
$619$	7.07826e6	0.742506	0.371253	+	0.928532i	$0.378928\pi$
$620$	−9.29746e6	−0.971370
$621$	−2.46698e6	−0.256706
$622$	−897869.	−0.0930544
$623$	2.02236e7	2.08756
$624$	−2.59437e6	−0.266729
$625$	−5.93537e6	−0.607782
$626$	−2.54434e6	−0.259501
$627$	720170.	0.0731587
$628$	−7.98427e6	−0.807860
$629$	−2.34316e6	−0.236144
$630$	−764995.	−0.0767905
$631$	6.57994e6	0.657883	0.328941	−	0.944350i	$-0.393308\pi$
$631$	6.57994e6	0.657883	0.328941	+	0.944350i	$0.393308\pi$
$632$	1.87128e6	0.186357
$633$	−1.03602e7	−1.02768
$634$	−772940.	−0.0763699
$635$	8.22006e6	0.808985
$636$	1.25512e6	0.123038
$637$	8.74764e6	0.854166
$638$	71776.9	0.00698125
$639$	4.10787e6	0.397983
$640$	−5.41438e6	−0.522515
$641$	1.31644e7	1.26549	0.632743	−	0.774362i	$-0.281929\pi$
$641$	1.31644e7	1.26549	0.632743	+	0.774362i	$0.281929\pi$
$642$	−661760.	−0.0633669
$643$	−1.01170e7	−0.964998	−0.482499	−	0.875897i	$-0.660271\pi$
$643$	−1.01170e7	−0.964998	−0.482499	+	0.875897i	$0.660271\pi$
$644$	2.23926e7	2.12760
$645$	−4.90643e6	−0.464372
$646$	113080.	0.0106612
$647$	5.15776e6	0.484396	0.242198	−	0.970227i	$-0.422132\pi$
$647$	5.15776e6	0.484396	0.242198	+	0.970227i	$0.422132\pi$
$648$	393254.	0.0367905
$649$	6.19562e6	0.577395
$650$	274892.	0.0255198
$651$	−1.22539e7	−1.13324
$652$	−9.86797e6	−0.909094
$653$	−7.30728e6	−0.670615	−0.335307	−	0.942109i	$-0.608840\pi$
$653$	−7.30728e6	−0.670615	−0.335307	+	0.942109i	$0.608840\pi$
$654$	−54785.9	−0.00500870
$655$	−1.19207e6	−0.108567
$656$	767171.	0.0696038
$657$	358782.	0.0324278
$658$	3.89924e6	0.351088
$659$	−2.51752e6	−0.225819	−0.112909	−	0.993605i	$-0.536017\pi$
$659$	−2.51752e6	−0.225819	−0.112909	+	0.993605i	$0.536017\pi$
$660$	−6.22829e6	−0.556556
$661$	−9.77730e6	−0.870392	−0.435196	−	0.900336i	$-0.643321\pi$
$661$	−9.77730e6	−0.870392	−0.435196	+	0.900336i	$0.643321\pi$
$662$	−3.11158e6	−0.275953
$663$	−1.95930e6	−0.173108
$664$	−1.31185e6	−0.115469
$665$	−1.67040e6	−0.146476
$666$	254459.	0.0222296
$667$	−536880.	−0.0467265
$668$	1.52488e7	1.32219
$669$	−2.14906e6	−0.185645
$670$	−807835.	−0.0695241
$671$	8.54084e6	0.732309
$672$	−5.37984e6	−0.459564
$673$	−1.77895e7	−1.51400	−0.757002	−	0.653413i	$-0.773337\pi$
$673$	−1.77895e7	−1.51400	−0.757002	+	0.653413i	$0.773337\pi$
$674$	3.08209e6	0.261333
$675$	686593.	0.0580016
$676$	8.61053e6	0.724708
$677$	1.33517e7	1.11960	0.559802	−	0.828627i	$-0.310877\pi$
$677$	1.33517e7	1.11960	0.559802	+	0.828627i	$0.310877\pi$
$678$	783154.	0.0654294
$679$	−2.56086e7	−2.13163
$680$	−1.98430e6	−0.164564
$681$	5.08738e6	0.420365
$682$	2.89493e6	0.238329
$683$	468129.	0.0383985	0.0191992	−	0.999816i	$-0.493888\pi$
$683$	468129.	0.0383985	0.0191992	+	0.999816i	$0.493888\pi$
$684$	423204.	0.0345867
$685$	1.40589e7	1.14479
$686$	2.35749e6	0.191266
$687$	−8.14941e6	−0.658771
$688$	−1.09463e7	−0.881653
$689$	1.37789e6	0.110577
$690$	−1.35180e6	−0.108091
$691$	−1.81330e7	−1.44469	−0.722344	−	0.691534i	$-0.756935\pi$
$691$	−1.81330e7	−1.44469	−0.722344	+	0.691534i	$0.756935\pi$
$692$	−1.23418e7	−0.979743
$693$	−8.20881e6	−0.649302
$694$	1.69445e6	0.133546
$695$	2.07139e7	1.62667
$696$	85582.6	0.00669672
$697$	579378.	0.0451731
$698$	1.76929e6	0.137455
$699$	−9.81267e6	−0.759617
$700$	−6.23217e6	−0.480722
$701$	1.45790e7	1.12055	0.560277	−	0.828305i	$-0.310695\pi$
$701$	1.45790e7	1.12055	0.560277	+	0.828305i	$0.310695\pi$
$702$	212773.	0.0162957
$703$	555623.	0.0424026
$704$	−1.30277e7	−0.990685
$705$	8.11217e6	0.614702
$706$	−341666.	−0.0257983
$707$	−1.45551e6	−0.109513
$708$	3.64082e6	0.272971
$709$	2.38968e7	1.78535	0.892677	−	0.450696i	$-0.148824\pi$
$709$	2.38968e7	1.78535	0.892677	+	0.450696i	$0.148824\pi$
$710$	2.25095e6	0.167579
$711$	2.52884e6	0.187606
$712$	−5.69669e6	−0.421136
$713$	−2.16536e7	−1.59517
$714$	−1.28894e6	−0.0946207
$715$	−6.83752e6	−0.500189
$716$	−1.04919e7	−0.764844
$717$	8.47229e6	0.615465
$718$	2.24166e6	0.162278
$719$	−1.02322e7	−0.738150	−0.369075	−	0.929400i	$-0.620326\pi$
$719$	−1.02322e7	−0.738150	−0.369075	+	0.929400i	$0.620326\pi$
$720$	−3.55074e6	−0.255263
$721$	2.25743e6	0.161725
$722$	2.32530e6	0.166010
$723$	−1.46011e6	−0.103882
$724$	1.70273e7	1.20725
$725$	149421.	0.0105576
$726$	562410.	0.0396015
$727$	1.40418e7	0.985344	0.492672	−	0.870215i	$-0.336020\pi$
$727$	1.40418e7	0.985344	0.492672	+	0.870215i	$0.336020\pi$
$728$	−3.91871e6	−0.274040
$729$	531441.	0.0370370
$730$	196598.	0.0136544
$731$	−8.26683e6	−0.572197
$732$	5.01898e6	0.346208
$733$	1.10851e7	0.762045	0.381022	−	0.924566i	$-0.375572\pi$
$733$	1.10851e7	0.762045	0.381022	+	0.924566i	$0.375572\pi$
$734$	2.53413e6	0.173616
$735$	1.19723e7	0.817446
$736$	−9.50658e6	−0.646889
$737$	−8.66850e6	−0.587862
$738$	−62918.3	−0.00425242
$739$	−1.66017e7	−1.11826	−0.559130	−	0.829080i	$-0.688865\pi$
$739$	−1.66017e7	−1.11826	−0.559130	+	0.829080i	$0.688865\pi$
$740$	−4.80523e6	−0.322578
$741$	464600.	0.0310838
$742$	906449.	0.0604413
$743$	−4.71201e6	−0.313137	−0.156568	−	0.987667i	$-0.550043\pi$
$743$	−4.71201e6	−0.313137	−0.156568	+	0.987667i	$0.550043\pi$
$744$	3.45174e6	0.228616
$745$	1.58314e7	1.04503
$746$	2.85016e6	0.187509
$747$	−1.77283e6	−0.116242
$748$	−1.04940e7	−0.685785
$749$	1.64706e7	1.07276
$750$	1.62455e6	0.105458
$751$	−1.67562e7	−1.08411	−0.542057	−	0.840342i	$-0.682354\pi$
$751$	−1.67562e7	−1.08411	−0.542057	+	0.840342i	$0.682354\pi$
$752$	1.80984e7	1.16707
$753$	1.32480e7	0.851454
$754$	46305.2	0.00296620
$755$	2.46422e6	0.157330
$756$	−4.82386e6	−0.306966
$757$	2.17010e6	0.137638	0.0688192	−	0.997629i	$-0.478077\pi$
$757$	2.17010e6	0.137638	0.0688192	+	0.997629i	$0.478077\pi$
$758$	2.10304e6	0.132946
$759$	−1.45056e7	−0.913968
$760$	470527.	0.0295495
$761$	−2.10797e7	−1.31948	−0.659740	−	0.751494i	$-0.729334\pi$
$761$	−2.10797e7	−1.31948	−0.659740	+	0.751494i	$0.729334\pi$
$762$	−1.50405e6	−0.0938373
$763$	1.36357e6	0.0847941
$764$	1.62259e7	1.00572
$765$	−2.68157e6	−0.165667
$766$	1.45924e6	0.0898573
$767$	3.99696e6	0.245325
$768$	−6.88711e6	−0.421341
$769$	−3.19762e6	−0.194989	−0.0974947	−	0.995236i	$-0.531083\pi$
$769$	−3.19762e6	−0.194989	−0.0974947	+	0.995236i	$0.531083\pi$
$770$	−4.49810e6	−0.273402
$771$	1.78741e7	1.08290
$772$	−8.78017e6	−0.530225
$773$	1.36941e7	0.824300	0.412150	−	0.911116i	$-0.364778\pi$
$773$	1.36941e7	0.824300	0.412150	+	0.911116i	$0.364778\pi$
$774$	897747.	0.0538644
$775$	6.02649e6	0.360421
$776$	7.21354e6	0.430025
$777$	−6.33323e6	−0.376334
$778$	−916338.	−0.0542758
$779$	−137385.	−0.00811141
$780$	−4.01803e6	−0.236471
$781$	2.41539e7	1.41696
$782$	−2.27765e6	−0.133190
$783$	115656.	0.00674160
$784$	2.67104e7	1.55200
$785$	−1.19964e7	−0.694828
$786$	218118.	0.0125932
$787$	−1.53826e7	−0.885307	−0.442653	−	0.896693i	$-0.645963\pi$
$787$	−1.53826e7	−0.885307	−0.442653	+	0.896693i	$0.645963\pi$
$788$	−1.31759e7	−0.755902
$789$	2.13703e6	0.122213
$790$	1.38570e6	0.0789954
$791$	−1.94919e7	−1.10768
$792$	2.31229e6	0.130988
$793$	5.50992e6	0.311145
$794$	5.43102e6	0.305724
$795$	1.88582e6	0.105824
$796$	1.36803e6	0.0765267
$797$	−7.35228e6	−0.409993	−0.204996	−	0.978763i	$-0.565718\pi$
$797$	−7.35228e6	−0.409993	−0.204996	+	0.978763i	$0.565718\pi$
$798$	305640.	0.0169904
$799$	1.36682e7	0.757432
$800$	2.64581e6	0.146162
$801$	−7.69847e6	−0.423958
$802$	3.92201e6	0.215314
$803$	2.10961e6	0.115455
$804$	−5.09400e6	−0.277919
$805$	3.36451e7	1.82992
$806$	1.86759e6	0.101262
$807$	1.37416e6	0.0742767
$808$	409993.	0.0220927
$809$	2.22060e6	0.119289	0.0596444	−	0.998220i	$-0.481003\pi$
$809$	2.22060e6	0.119289	0.0596444	+	0.998220i	$0.481003\pi$
$810$	291208.	0.0155952
$811$	−2.87697e7	−1.53597	−0.767985	−	0.640467i	$-0.778741\pi$
$811$	−2.87697e7	−1.53597	−0.767985	+	0.640467i	$0.778741\pi$
$812$	−1.04980e6	−0.0558750
$813$	1.96193e7	1.04102
$814$	1.49619e6	0.0791456
$815$	−1.48267e7	−0.781898
$816$	−5.98263e6	−0.314533
$817$	1.96027e6	0.102745
$818$	2.51131e6	0.131225
$819$	−5.29572e6	−0.275877
$820$	1.18816e6	0.0617077
$821$	2.15788e7	1.11730	0.558649	−	0.829404i	$-0.311320\pi$
$821$	2.15788e7	1.11730	0.558649	+	0.829404i	$0.311320\pi$
$822$	−2.57241e6	−0.132789
$823$	−3.49771e7	−1.80005	−0.900024	−	0.435840i	$-0.856451\pi$
$823$	−3.49771e7	−1.80005	−0.900024	+	0.435840i	$0.856451\pi$
$824$	−635883.	−0.0326257
$825$	4.03710e6	0.206507
$826$	2.62942e6	0.134094
$827$	−1.13723e7	−0.578211	−0.289106	−	0.957297i	$-0.593358\pi$
$827$	−1.13723e7	−0.578211	−0.289106	+	0.957297i	$0.593358\pi$
$828$	−8.52413e6	−0.432090
$829$	2.21208e7	1.11793	0.558965	−	0.829192i	$-0.311199\pi$
$829$	2.21208e7	1.11793	0.558965	+	0.829192i	$0.311199\pi$
$830$	−971437.	−0.0489463
$831$	−5.95449e6	−0.299118
$832$	−8.40450e6	−0.420924
$833$	2.01721e7	1.00725
$834$	−3.79010e6	−0.188684
$835$	2.29114e7	1.13719
$836$	2.48840e6	0.123141
$837$	4.66466e6	0.230148
$838$	−845646.	−0.0415986
$839$	−1.02090e6	−0.0500701	−0.0250351	−	0.999687i	$-0.507970\pi$
$839$	−1.02090e6	−0.0500701	−0.0250351	+	0.999687i	$0.507970\pi$
$840$	−5.36326e6	−0.262259
$841$	−2.04860e7	−0.998773
$842$	−4.01237e6	−0.195038
$843$	−1.16129e7	−0.562823
$844$	−3.57974e7	−1.72980
$845$	1.29374e7	0.623311
$846$	−1.48431e6	−0.0713017
$847$	−1.39978e7	−0.670429
$848$	4.20730e6	0.200916
$849$	2.51415e6	0.119708
$850$	633901.	0.0300936
$851$	−1.11913e7	−0.529733
$852$	1.41939e7	0.669888
$853$	3.61069e6	0.169910	0.0849548	−	0.996385i	$-0.472925\pi$
$853$	3.61069e6	0.169910	0.0849548	+	0.996385i	$0.472925\pi$
$854$	3.62473e6	0.170071
$855$	635867.	0.0297475
$856$	−4.63950e6	−0.216415
$857$	−3.66828e7	−1.70612	−0.853061	−	0.521811i	$-0.825257\pi$
$857$	−3.66828e7	−1.70612	−0.853061	+	0.521811i	$0.825257\pi$
$858$	1.25109e6	0.0580188
$859$	4.14459e7	1.91645	0.958227	−	0.286009i	$-0.0923287\pi$
$859$	4.14459e7	1.91645	0.958227	+	0.286009i	$0.0923287\pi$
$860$	−1.69532e7	−0.781636
$861$	1.56598e6	0.0719908
$862$	−626720.	−0.0287280
$863$	1.99646e7	0.912500	0.456250	−	0.889852i	$-0.349192\pi$
$863$	1.99646e7	0.912500	0.456250	+	0.889852i	$0.349192\pi$
$864$	2.04793e6	0.0933319
$865$	−1.85436e7	−0.842663
$866$	315045.	0.0142751
$867$	8.26055e6	0.373217
$868$	−4.23409e7	−1.90748
$869$	1.48693e7	0.667946
$870$	63374.7	0.00283869
$871$	−5.59228e6	−0.249772
$872$	−384096.	−0.0171060
$873$	9.74834e6	0.432907
$874$	540088.	0.0239159
$875$	−4.04334e7	−1.78533
$876$	1.23970e6	0.0545828
$877$	−3.43090e7	−1.50629	−0.753145	−	0.657854i	$-0.771464\pi$
$877$	−3.43090e7	−1.50629	−0.753145	+	0.657854i	$0.771464\pi$
$878$	5.04586e6	0.220901
$879$	8.98845e6	0.392385
$880$	−2.08780e7	−0.908829
$881$	−1.67289e7	−0.726151	−0.363076	−	0.931760i	$-0.618273\pi$
$881$	−1.67289e7	−0.726151	−0.363076	+	0.931760i	$0.618273\pi$
$882$	−2.19061e6	−0.0948188
$883$	−2.86422e7	−1.23625	−0.618123	−	0.786082i	$-0.712107\pi$
$883$	−2.86422e7	−1.23625	−0.618123	+	0.786082i	$0.712107\pi$
$884$	−6.76997e6	−0.291378
$885$	5.47036e6	0.234778
$886$	2.08899e6	0.0894028
$887$	−1.83721e7	−0.784063	−0.392031	−	0.919952i	$-0.628228\pi$
$887$	−1.83721e7	−0.784063	−0.392031	+	0.919952i	$0.628228\pi$
$888$	1.78397e6	0.0759200
$889$	3.74344e7	1.58861
$890$	−4.21845e6	−0.178516
$891$	3.12482e6	0.131865
$892$	−7.42563e6	−0.312479
$893$	−3.24107e6	−0.136006
$894$	−2.89673e6	−0.121217
$895$	−1.57642e7	−0.657831
$896$	−2.46573e7	−1.02606
$897$	−9.35793e6	−0.388328
$898$	344213.	0.0142441
$899$	1.01516e6	0.0418922
$900$	2.37238e6	0.0976289
$901$	3.17741e6	0.130395
$902$	−369954.	−0.0151402
$903$	−2.23440e7	−0.911890
$904$	5.49058e6	0.223458
$905$	2.55836e7	1.03834
$906$	−450886.	−0.0182493
$907$	−3.18005e6	−0.128356	−0.0641779	−	0.997938i	$-0.520442\pi$
$907$	−3.18005e6	−0.128356	−0.0641779	+	0.997938i	$0.520442\pi$
$908$	1.75784e7	0.707561
$909$	554063.	0.0222407
$910$	−2.90184e6	−0.116164
$911$	−3.48303e7	−1.39047	−0.695235	−	0.718782i	$-0.744700\pi$
$911$	−3.48303e7	−1.39047	−0.695235	+	0.718782i	$0.744700\pi$
$912$	1.41863e6	0.0564784
$913$	−1.04240e7	−0.413866
$914$	−5.49912e6	−0.217735
$915$	7.54105e6	0.297769
$916$	−2.81586e7	−1.10885
$917$	−5.42874e6	−0.213194
$918$	490656.	0.0192163
$919$	−2.12338e7	−0.829353	−0.414677	−	0.909969i	$-0.636105\pi$
$919$	−2.12338e7	−0.829353	−0.414677	+	0.909969i	$0.636105\pi$
$920$	−9.47729e6	−0.369160
$921$	−2.92139e6	−0.113485
$922$	4.83179e6	0.187189
$923$	1.55823e7	0.602042
$924$	−2.83638e7	−1.09291
$925$	3.11469e6	0.119691
$926$	−7.41821e6	−0.284297
$927$	−859329.	−0.0328443
$928$	445684.	0.0169886
$929$	−3.74975e7	−1.42549	−0.712744	−	0.701425i	$-0.752548\pi$
$929$	−3.74975e7	−1.42549	−0.712744	+	0.701425i	$0.752548\pi$
$930$	2.55605e6	0.0969084
$931$	−4.78331e6	−0.180865
$932$	−3.39057e7	−1.27859
$933$	−8.50679e6	−0.319935
$934$	200775.	0.00753082
$935$	−1.57674e7	−0.589834
$936$	1.49172e6	0.0556542
$937$	−2.74426e7	−1.02112	−0.510559	−	0.859843i	$-0.670562\pi$
$937$	−2.74426e7	−1.02112	−0.510559	+	0.859843i	$0.670562\pi$
$938$	−3.67890e6	−0.136525
$939$	−2.41062e7	−0.892203
$940$	2.80299e7	1.03467
$941$	6.59743e6	0.242885	0.121442	−	0.992598i	$-0.461248\pi$
$941$	6.59743e6	0.242885	0.121442	+	0.992598i	$0.461248\pi$
$942$	2.19503e6	0.0805959
$943$	2.76720e6	0.101335
$944$	1.22045e7	0.445748
$945$	−7.24789e6	−0.264017
$946$	5.27866e6	0.191777
$947$	−3.06999e7	−1.11240	−0.556201	−	0.831048i	$-0.687741\pi$
$947$	−3.06999e7	−1.11240	−0.556201	+	0.831048i	$0.687741\pi$
$948$	8.73787e6	0.315780
$949$	1.36096e6	0.0490547
$950$	−150314.	−0.00540369
$951$	−7.32316e6	−0.262571
$952$	−9.03655e6	−0.323154
$953$	4.31886e7	1.54041	0.770206	−	0.637796i	$-0.220154\pi$
$953$	4.31886e7	1.54041	0.770206	+	0.637796i	$0.220154\pi$
$954$	−345055.	−0.0122749
$955$	2.43796e7	0.865003
$956$	2.92743e7	1.03596
$957$	680045.	0.0240026
$958$	−4.99407e6	−0.175809
$959$	6.40248e7	2.24803
$960$	−1.15027e7	−0.402829
$961$	1.23144e7	0.430135
$962$	965234.	0.0336275
$963$	−6.26979e6	−0.217865
$964$	−5.04510e6	−0.174855
$965$	−1.31923e7	−0.456038
$966$	−6.15616e6	−0.212259
$967$	824522.	0.0283554	0.0141777	−	0.999899i	$-0.495487\pi$
$967$	824522.	0.0283554	0.0141777	+	0.999899i	$0.495487\pi$
$968$	3.94297e6	0.135249
$969$	1.07137e6	0.0366547
$970$	5.34169e6	0.182284
$971$	−3.50049e7	−1.19146	−0.595732	−	0.803184i	$-0.703138\pi$
$971$	−3.50049e7	−1.19146	−0.595732	+	0.803184i	$0.703138\pi$
$972$	1.83628e6	0.0623411
$973$	9.43318e7	3.19430
$974$	4.83930e6	0.163450
$975$	2.60444e6	0.0877410
$976$	1.68242e7	0.565341
$977$	4.80689e7	1.61112	0.805560	−	0.592514i	$-0.201864\pi$
$977$	4.80689e7	1.61112	0.805560	+	0.592514i	$0.201864\pi$
$978$	2.71289e6	0.0906954
$979$	−4.52663e7	−1.50945
$980$	4.13678e7	1.37593
$981$	−519065.	−0.0172206
$982$	5.08302e6	0.168206
$983$	−1.45471e7	−0.480168	−0.240084	−	0.970752i	$-0.577175\pi$
$983$	−1.45471e7	−0.480168	−0.240084	+	0.970752i	$0.577175\pi$
$984$	−441111.	−0.0145231
$985$	−1.97969e7	−0.650140
$986$	106780.	0.00349782
$987$	3.69431e7	1.20709
$988$	1.60533e6	0.0523205
$989$	−3.94836e7	−1.28359
$990$	1.71228e6	0.0555246
$991$	4.07841e7	1.31919	0.659594	−	0.751622i	$-0.270728\pi$
$991$	4.07841e7	1.31919	0.659594	+	0.751622i	$0.270728\pi$
$992$	1.79754e7	0.579963
$993$	−2.94804e7	−0.948769
$994$	1.02509e7	0.329075
$995$	2.05547e6	0.0658194
$996$	−6.12563e6	−0.195660
$997$	4.96531e7	1.58201	0.791004	−	0.611811i	$-0.209559\pi$
$997$	4.96531e7	1.58201	0.791004	+	0.611811i	$0.209559\pi$
$998$	3.73637e6	0.118747
$999$	2.41085e6	0.0764288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.6.a.c.1.11	✓	22
3.2	odd	2		927.6.a.d.1.12		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.6.a.c.1.11	✓	22	1.1	even	1	trivial
927.6.a.d.1.12		22	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)

\(f(q)\)	\(=\)	\(q-0.949926 q^{2} -9.00000 q^{3} -31.0976 q^{4} -46.7244 q^{5} +8.54933 q^{6} -212.784 q^{7} +59.9381 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-0.949926 q^{2} -9.00000 q^{3} -31.0976 q^{4} -46.7244 q^{5} +8.54933 q^{6} -212.784 q^{7} +59.9381 q^{8} +81.0000 q^{9} +44.3847 q^{10} +476.272 q^{11} +279.879 q^{12} +307.256 q^{13} +202.129 q^{14} +420.520 q^{15} +938.188 q^{16} +708.532 q^{17} -76.9440 q^{18} -168.011 q^{19} +1453.02 q^{20} +1915.06 q^{21} -452.423 q^{22} +3384.06 q^{23} -539.443 q^{24} -941.829 q^{25} -291.870 q^{26} -729.000 q^{27} +6617.10 q^{28} -158.650 q^{29} -399.463 q^{30} -6398.71 q^{31} -2809.23 q^{32} -4286.45 q^{33} -673.053 q^{34} +9942.23 q^{35} -2518.91 q^{36} -3307.07 q^{37} +159.598 q^{38} -2765.30 q^{39} -2800.57 q^{40} +817.716 q^{41} -1819.17 q^{42} -11667.5 q^{43} -14810.9 q^{44} -3784.68 q^{45} -3214.60 q^{46} +19290.8 q^{47} -8443.69 q^{48} +28470.2 q^{49} +894.668 q^{50} -6376.79 q^{51} -9554.92 q^{52} +4484.50 q^{53} +692.496 q^{54} -22253.5 q^{55} -12753.9 q^{56} +1512.10 q^{57} +150.706 q^{58} +13008.6 q^{59} -13077.2 q^{60} +17932.7 q^{61} +6078.30 q^{62} -17235.5 q^{63} -27353.5 q^{64} -14356.3 q^{65} +4071.81 q^{66} -18200.7 q^{67} -22033.7 q^{68} -30456.5 q^{69} -9444.38 q^{70} +50714.4 q^{71} +4854.98 q^{72} +4429.41 q^{73} +3141.47 q^{74} +8476.46 q^{75} +5224.74 q^{76} -101343. q^{77} +2626.83 q^{78} +31220.2 q^{79} -43836.3 q^{80} +6561.00 q^{81} -776.770 q^{82} -21886.7 q^{83} -59553.9 q^{84} -33105.8 q^{85} +11083.3 q^{86} +1427.85 q^{87} +28546.8 q^{88} -95042.8 q^{89} +3595.16 q^{90} -65379.2 q^{91} -105236. q^{92} +57588.4 q^{93} -18324.9 q^{94} +7850.21 q^{95} +25283.0 q^{96} +120350. q^{97} -27044.6 q^{98} +38578.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9}+O(q^{10}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9	\( 22 q - 8 q^{2} - 198 q^{3} + 342 q^{4} - 53 q^{5} + 72 q^{6} + 10 q^{7} - 264 q^{8} + 1782 q^{9} - 355 q^{10} - 708 q^{11} - 3078 q^{12} - 133 q^{13} - 2748 q^{14} + 477 q^{15} + 3678 q^{16} - 2006 q^{17} - 648 q^{18} - 4788 q^{19} - 2785 q^{20} - 90 q^{21} + 3609 q^{22} - 5695 q^{23} + 2376 q^{24} + 18477 q^{25} + 2432 q^{26} - 16038 q^{27} + 7635 q^{28} - 978 q^{29} + 3195 q^{30} - 6009 q^{31} + 22809 q^{32} + 6372 q^{33} - 4078 q^{34} - 22822 q^{35} + 27702 q^{36} + 13640 q^{37} - 5454 q^{38} + 1197 q^{39} - 13351 q^{40} - 24618 q^{41} + 24732 q^{42} + 1257 q^{43} - 65465 q^{44} - 4293 q^{45} - 6175 q^{46} - 63834 q^{47} - 33102 q^{48} + 18022 q^{49} - 41643 q^{50} + 18054 q^{51} - 40853 q^{52} - 13316 q^{53} + 5832 q^{54} - 35934 q^{55} - 251195 q^{56} + 43092 q^{57} - 103895 q^{58} - 138587 q^{59} + 25065 q^{60} - 53985 q^{61} - 218186 q^{62} + 810 q^{63} + 23758 q^{64} - 114073 q^{65} - 32481 q^{66} - 102785 q^{67} - 338669 q^{68} + 51255 q^{69} - 104184 q^{70} - 108740 q^{71} - 21384 q^{72} + 69762 q^{73} - 221377 q^{74} - 166293 q^{75} - 223267 q^{76} - 140360 q^{77} - 21888 q^{78} - 238938 q^{79} - 864251 q^{80} + 144342 q^{81} - 660293 q^{82} - 305455 q^{83} - 68715 q^{84} - 201204 q^{85} - 794679 q^{86} + 8802 q^{87} - 420823 q^{88} - 438448 q^{89} - 28755 q^{90} - 294186 q^{91} - 1251930 q^{92} + 54081 q^{93} - 826416 q^{94} - 652572 q^{95} - 205281 q^{96} - 284729 q^{97} - 887529 q^{98} - 57348 q^{99}+O(q^{100}) \) 22 * q - 8 * q^2 - 198 * q^3 + 342 * q^4 - 53 * q^5 + 72 * q^6 + 10 * q^7 - 264 * q^8 + 1782 * q^9 - 355 * q^10 - 708 * q^11 - 3078 * q^12 - 133 * q^13 - 2748 * q^14 + 477 * q^15 + 3678 * q^16 - 2006 * q^17 - 648 * q^18 - 4788 * q^19 - 2785 * q^20 - 90 * q^21 + 3609 * q^22 - 5695 * q^23 + 2376 * q^24 + 18477 * q^25 + 2432 * q^26 - 16038 * q^27 + 7635 * q^28 - 978 * q^29 + 3195 * q^30 - 6009 * q^31 + 22809 * q^32 + 6372 * q^33 - 4078 * q^34 - 22822 * q^35 + 27702 * q^36 + 13640 * q^37 - 5454 * q^38 + 1197 * q^39 - 13351 * q^40 - 24618 * q^41 + 24732 * q^42 + 1257 * q^43 - 65465 * q^44 - 4293 * q^45 - 6175 * q^46 - 63834 * q^47 - 33102 * q^48 + 18022 * q^49 - 41643 * q^50 + 18054 * q^51 - 40853 * q^52 - 13316 * q^53 + 5832 * q^54 - 35934 * q^55 - 251195 * q^56 + 43092 * q^57 - 103895 * q^58 - 138587 * q^59 + 25065 * q^60 - 53985 * q^61 - 218186 * q^62 + 810 * q^63 + 23758 * q^64 - 114073 * q^65 - 32481 * q^66 - 102785 * q^67 - 338669 * q^68 + 51255 * q^69 - 104184 * q^70 - 108740 * q^71 - 21384 * q^72 + 69762 * q^73 - 221377 * q^74 - 166293 * q^75 - 223267 * q^76 - 140360 * q^77 - 21888 * q^78 - 238938 * q^79 - 864251 * q^80 + 144342 * q^81 - 660293 * q^82 - 305455 * q^83 - 68715 * q^84 - 201204 * q^85 - 794679 * q^86 + 8802 * q^87 - 420823 * q^88 - 438448 * q^89 - 28755 * q^90 - 294186 * q^91 - 1251930 * q^92 + 54081 * q^93 - 826416 * q^94 - 652572 * q^95 - 205281 * q^96 - 284729 * q^97 - 887529 * q^98 - 57348 * q^99

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