LMFDB - Embedded newform 1045.6.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.34868 q^{2} -22.4542 q^{3} +8.30576 q^{4} +25.0000 q^{5} +142.555 q^{6} +214.893 q^{7} +150.427 q^{8} +261.192 q^{9} +O(q^{10})$	\(q-6.34868 q^{2} -22.4542 q^{3} +8.30576 q^{4} +25.0000 q^{5} +142.555 q^{6} +214.893 q^{7} +150.427 q^{8} +261.192 q^{9} -158.717 q^{10} +121.000 q^{11} -186.499 q^{12} -442.495 q^{13} -1364.29 q^{14} -561.355 q^{15} -1220.80 q^{16} -1314.46 q^{17} -1658.22 q^{18} +361.000 q^{19} +207.644 q^{20} -4825.25 q^{21} -768.191 q^{22} +2155.21 q^{23} -3377.72 q^{24} +625.000 q^{25} +2809.26 q^{26} -408.482 q^{27} +1784.85 q^{28} +5038.86 q^{29} +3563.87 q^{30} -436.198 q^{31} +2936.79 q^{32} -2716.96 q^{33} +8345.06 q^{34} +5372.33 q^{35} +2169.40 q^{36} +3960.63 q^{37} -2291.87 q^{38} +9935.87 q^{39} +3760.68 q^{40} +8185.36 q^{41} +30634.0 q^{42} +2467.24 q^{43} +1005.00 q^{44} +6529.79 q^{45} -13682.7 q^{46} +17130.2 q^{47} +27412.1 q^{48} +29372.0 q^{49} -3967.93 q^{50} +29515.1 q^{51} -3675.25 q^{52} -23996.2 q^{53} +2593.32 q^{54} +3025.00 q^{55} +32325.8 q^{56} -8105.97 q^{57} -31990.1 q^{58} -31353.1 q^{59} -4662.48 q^{60} +42578.9 q^{61} +2769.28 q^{62} +56128.3 q^{63} +20420.8 q^{64} -11062.4 q^{65} +17249.1 q^{66} +3535.51 q^{67} -10917.6 q^{68} -48393.5 q^{69} -34107.2 q^{70} -34547.2 q^{71} +39290.3 q^{72} +9028.46 q^{73} -25144.8 q^{74} -14033.9 q^{75} +2998.38 q^{76} +26002.1 q^{77} -63079.7 q^{78} +3140.13 q^{79} -30520.0 q^{80} -54297.5 q^{81} -51966.2 q^{82} -42776.4 q^{83} -40077.4 q^{84} -32861.4 q^{85} -15663.8 q^{86} -113144. q^{87} +18201.7 q^{88} +83224.0 q^{89} -41455.6 q^{90} -95089.0 q^{91} +17900.6 q^{92} +9794.47 q^{93} -108754. q^{94} +9025.00 q^{95} -65943.4 q^{96} -42553.9 q^{97} -186474. q^{98} +31604.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * 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 $

$2$	−6.34868	−1.12230	−0.561150	−	0.827714i	$-0.689641\pi$
$2$	−6.34868	−1.12230	−0.561150	+	0.827714i	$0.689641\pi$
$3$	−22.4542	−1.44044	−0.720219	−	0.693746i	$-0.755959\pi$
$3$	−22.4542	−1.44044	−0.720219	+	0.693746i	$0.755959\pi$
$4$	8.30576	0.259555
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	142.555	1.61660
$7$	214.893	1.65759	0.828795	−	0.559552i	$-0.189027\pi$
$7$	214.893	1.65759	0.828795	+	0.559552i	$0.189027\pi$
$8$	150.427	0.831001
$9$	261.192	1.07486
$10$	−158.717	−0.501907
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−186.499	−0.373873
$13$	−442.495	−0.726189	−0.363094	−	0.931752i	$-0.618280\pi$
$13$	−442.495	−0.726189	−0.363094	+	0.931752i	$0.618280\pi$
$14$	−1364.29	−1.86031
$15$	−561.355	−0.644184
$16$	−1220.80	−1.19219
$17$	−1314.46	−1.10312	−0.551561	−	0.834134i	$-0.685968\pi$
$17$	−1314.46	−1.10312	−0.551561	+	0.834134i	$0.685968\pi$
$18$	−1658.22	−1.20632
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	207.644	0.116077
$21$	−4825.25	−2.38766
$22$	−768.191	−0.338386
$23$	2155.21	0.849512	0.424756	−	0.905308i	$-0.360360\pi$
$23$	2155.21	0.849512	0.424756	+	0.905308i	$0.360360\pi$
$24$	−3377.72	−1.19701
$25$	625.000	0.200000
$26$	2809.26	0.815001
$27$	−408.482	−0.107836
$28$	1784.85	0.430236
$29$	5038.86	1.11260	0.556298	−	0.830983i	$-0.312221\pi$
$29$	5038.86	1.11260	0.556298	+	0.830983i	$0.312221\pi$
$30$	3563.87	0.722967
$31$	−436.198	−0.0815228	−0.0407614	−	0.999169i	$-0.512978\pi$
$31$	−436.198	−0.0815228	−0.0407614	+	0.999169i	$0.512978\pi$
$32$	2936.79	0.506989
$33$	−2716.96	−0.434309
$34$	8345.06	1.23803
$35$	5372.33	0.741297
$36$	2169.40	0.278986
$37$	3960.63	0.475620	0.237810	−	0.971312i	$-0.423570\pi$
$37$	3960.63	0.475620	0.237810	+	0.971312i	$0.423570\pi$
$38$	−2291.87	−0.257473
$39$	9935.87	1.04603
$40$	3760.68	0.371635
$41$	8185.36	0.760463	0.380231	−	0.924891i	$-0.375844\pi$
$41$	8185.36	0.760463	0.380231	+	0.924891i	$0.375844\pi$
$42$	30634.0	2.67967
$43$	2467.24	0.203489	0.101745	−	0.994811i	$-0.467558\pi$
$43$	2467.24	0.203489	0.101745	+	0.994811i	$0.467558\pi$
$44$	1005.00	0.0782588
$45$	6529.79	0.480693
$46$	−13682.7	−0.953407
$47$	17130.2	1.13114	0.565572	−	0.824699i	$-0.308656\pi$
$47$	17130.2	1.13114	0.565572	+	0.824699i	$0.308656\pi$
$48$	27412.1	1.71727
$49$	29372.0	1.74761
$50$	−3967.93	−0.224460
$51$	29515.1	1.58898
$52$	−3675.25	−0.188486
$53$	−23996.2	−1.17342	−0.586709	−	0.809798i	$-0.699577\pi$
$53$	−23996.2	−1.17342	−0.586709	+	0.809798i	$0.699577\pi$
$54$	2593.32	0.121024
$55$	3025.00	0.134840
$56$	32325.8	1.37746
$57$	−8105.97	−0.330459
$58$	−31990.1	−1.24866
$59$	−31353.1	−1.17260	−0.586301	−	0.810094i	$-0.699416\pi$
$59$	−31353.1	−1.17260	−0.586301	+	0.810094i	$0.699416\pi$
$60$	−4662.48	−0.167201
$61$	42578.9	1.46511	0.732555	−	0.680708i	$-0.238328\pi$
$61$	42578.9	1.46511	0.732555	+	0.680708i	$0.238328\pi$
$62$	2769.28	0.0914929
$63$	56128.3	1.78168
$64$	20420.8	0.623193
$65$	−11062.4	−0.324761
$66$	17249.1	0.487424
$67$	3535.51	0.0962199	0.0481100	−	0.998842i	$-0.484680\pi$
$67$	3535.51	0.0962199	0.0481100	+	0.998842i	$0.484680\pi$
$68$	−10917.6	−0.286321
$69$	−48393.5	−1.22367
$70$	−34107.2	−0.831957
$71$	−34547.2	−0.813330	−0.406665	−	0.913577i	$-0.633308\pi$
$71$	−34547.2	−0.813330	−0.406665	+	0.913577i	$0.633308\pi$
$72$	39290.3	0.893212
$73$	9028.46	0.198293	0.0991464	−	0.995073i	$-0.468389\pi$
$73$	9028.46	0.198293	0.0991464	+	0.995073i	$0.468389\pi$
$74$	−25144.8	−0.533788
$75$	−14033.9	−0.288088
$76$	2998.38	0.0595460
$77$	26002.1	0.499782
$78$	−63079.7	−1.17396
$79$	3140.13	0.0566083	0.0283042	−	0.999599i	$-0.490989\pi$
$79$	3140.13	0.0566083	0.0283042	+	0.999599i	$0.490989\pi$
$80$	−30520.0	−0.533162
$81$	−54297.5	−0.919532
$82$	−51966.2	−0.853467
$83$	−42776.4	−0.681568	−0.340784	−	0.940142i	$-0.610692\pi$
$83$	−42776.4	−0.681568	−0.340784	+	0.940142i	$0.610692\pi$
$84$	−40077.4	−0.619729
$85$	−32861.4	−0.493331
$86$	−15663.8	−0.228376
$87$	−113144.	−1.60263
$88$	18201.7	0.250556
$89$	83224.0	1.11371	0.556857	−	0.830608i	$-0.312007\pi$
$89$	83224.0	1.11371	0.556857	+	0.830608i	$0.312007\pi$
$90$	−41455.6	−0.539482
$91$	−95089.0	−1.20372
$92$	17900.6	0.220495
$93$	9794.47	0.117429
$94$	−108754.	−1.26948
$95$	9025.00	0.102598
$96$	−65943.4	−0.730286
$97$	−42553.9	−0.459209	−0.229604	−	0.973284i	$-0.573743\pi$
$97$	−42553.9	−0.459209	−0.229604	+	0.973284i	$0.573743\pi$
$98$	−186474.	−1.96134
$99$	31604.2	0.324083
$100$	5191.10	0.0519110
$101$	107041.	1.04411	0.522054	−	0.852913i	$-0.325166\pi$
$101$	107041.	1.04411	0.522054	+	0.852913i	$0.325166\pi$
$102$	−187382.	−1.78331
$103$	−79882.8	−0.741925	−0.370963	−	0.928648i	$-0.620972\pi$
$103$	−79882.8	−0.741925	−0.370963	+	0.928648i	$0.620972\pi$
$104$	−66563.2	−0.603463
$105$	−120631.	−1.06779
$106$	152344.	1.31693
$107$	83691.3	0.706677	0.353338	−	0.935496i	$-0.385046\pi$
$107$	83691.3	0.706677	0.353338	+	0.935496i	$0.385046\pi$
$108$	−3392.76	−0.0279894
$109$	62991.4	0.507826	0.253913	−	0.967227i	$-0.418282\pi$
$109$	62991.4	0.507826	0.253913	+	0.967227i	$0.418282\pi$
$110$	−19204.8	−0.151331
$111$	−88932.9	−0.685102
$112$	−262341.	−1.97616
$113$	201880.	1.48730	0.743649	−	0.668570i	$-0.233093\pi$
$113$	201880.	1.48730	0.743649	+	0.668570i	$0.233093\pi$
$114$	51462.2	0.370874
$115$	53880.2	0.379913
$116$	41851.6	0.288780
$117$	−115576.	−0.780554
$118$	199051.	1.31601
$119$	−282467.	−1.82853
$120$	−84443.1	−0.535317
$121$	14641.0	0.0909091
$122$	−270320.	−1.64429
$123$	−183796.	−1.09540
$124$	−3622.95	−0.0211597
$125$	15625.0	0.0894427
$126$	−356341.	−1.99958
$127$	250781.	1.37970	0.689851	−	0.723951i	$-0.257676\pi$
$127$	250781.	1.37970	0.689851	+	0.723951i	$0.257676\pi$
$128$	−223623.	−1.20640
$129$	−55400.0	−0.293114
$130$	70231.4	0.364480
$131$	−156745.	−0.798023	−0.399011	−	0.916946i	$-0.630647\pi$
$131$	−156745.	−0.798023	−0.399011	+	0.916946i	$0.630647\pi$
$132$	−22566.4	−0.112727
$133$	77576.4	0.380277
$134$	−22445.8	−0.107988
$135$	−10212.1	−0.0482257
$136$	−197730.	−0.916695
$137$	154367.	0.702672	0.351336	−	0.936249i	$-0.385727\pi$
$137$	154367.	0.702672	0.351336	+	0.936249i	$0.385727\pi$
$138$	307235.	1.37332
$139$	303213.	1.33110	0.665550	−	0.746353i	$-0.268197\pi$
$139$	303213.	1.33110	0.665550	+	0.746353i	$0.268197\pi$
$140$	44621.3	0.192407
$141$	−384645.	−1.62934
$142$	219329.	0.912799
$143$	−53541.8	−0.218954
$144$	−318863.	−1.28144
$145$	125971.	0.497568
$146$	−57318.8	−0.222544
$147$	−659525.	−2.51732
$148$	32896.1	0.123450
$149$	−186944.	−0.689837	−0.344918	−	0.938633i	$-0.612093\pi$
$149$	−186944.	−0.689837	−0.344918	+	0.938633i	$0.612093\pi$
$150$	89096.7	0.323321
$151$	−476803.	−1.70175	−0.850877	−	0.525365i	$-0.823929\pi$
$151$	−476803.	−1.70175	−0.850877	+	0.525365i	$0.823929\pi$
$152$	54304.2	0.190645
$153$	−343325.	−1.18571
$154$	−165079.	−0.560905
$155$	−10904.9	−0.0364581
$156$	82525.0	0.271502
$157$	371660.	1.20336	0.601681	−	0.798737i	$-0.294498\pi$
$157$	371660.	1.20336	0.601681	+	0.798737i	$0.294498\pi$
$158$	−19935.7	−0.0635315
$159$	538816.	1.69024
$160$	73419.8	0.226732
$161$	463139.	1.40814
$162$	344717.	1.03199
$163$	451810.	1.33195	0.665974	−	0.745975i	$-0.268016\pi$
$163$	451810.	1.33195	0.665974	+	0.745975i	$0.268016\pi$
$164$	67985.6	0.197382
$165$	−67924.0	−0.194229
$166$	271574.	0.764923
$167$	−350751.	−0.973211	−0.486606	−	0.873622i	$-0.661765\pi$
$167$	−350751.	−0.973211	−0.486606	+	0.873622i	$0.661765\pi$
$168$	−725849.	−1.98414
$169$	−175492.	−0.472650
$170$	208627.	0.553665
$171$	94290.2	0.246591
$172$	20492.3	0.0528166
$173$	704705.	1.79016	0.895080	−	0.445905i	$-0.147118\pi$
$173$	704705.	1.79016	0.895080	+	0.445905i	$0.147118\pi$
$174$	718313.	1.79862
$175$	134308.	0.331518
$176$	−147717.	−0.359458
$177$	704009.	1.68906
$178$	−528363.	−1.24992
$179$	−244688.	−0.570794	−0.285397	−	0.958409i	$-0.592125\pi$
$179$	−244688.	−0.570794	−0.285397	+	0.958409i	$0.592125\pi$
$180$	54234.9	0.124766
$181$	−824064.	−1.86967	−0.934834	−	0.355084i	$-0.884452\pi$
$181$	−824064.	−1.86967	−0.934834	+	0.355084i	$0.884452\pi$
$182$	603690.	1.35094
$183$	−956077.	−2.11040
$184$	324202.	0.705945
$185$	99015.8	0.212704
$186$	−62182.0	−0.131790
$187$	−159049.	−0.332604
$188$	142279.	0.293594
$189$	−87780.0	−0.178748
$190$	−57296.9	−0.115145
$191$	−161668.	−0.320657	−0.160329	−	0.987064i	$-0.551255\pi$
$191$	−161668.	−0.320657	−0.160329	+	0.987064i	$0.551255\pi$
$192$	−458533.	−0.897672
$193$	−532383.	−1.02880	−0.514400	−	0.857550i	$-0.671985\pi$
$193$	−532383.	−1.02880	−0.514400	+	0.857550i	$0.671985\pi$
$194$	270161.	0.515370
$195$	248397.	0.467799
$196$	243957.	0.453600
$197$	66466.1	0.122021	0.0610105	−	0.998137i	$-0.480568\pi$
$197$	66466.1	0.122021	0.0610105	+	0.998137i	$0.480568\pi$
$198$	−200645.	−0.363719
$199$	173073.	0.309810	0.154905	−	0.987929i	$-0.450493\pi$
$199$	173073.	0.309810	0.154905	+	0.987929i	$0.450493\pi$
$200$	94017.0	0.166200
$201$	−79387.1	−0.138599
$202$	−679567.	−1.17180
$203$	1.08282e6	1.84423
$204$	245145.	0.412428
$205$	204634.	0.340089
$206$	507150.	0.832662
$207$	562923.	0.913109
$208$	540197.	0.865752
$209$	43681.0	0.0691714
$210$	765850.	1.19838
$211$	−843188.	−1.30382	−0.651911	−	0.758295i	$-0.726032\pi$
$211$	−843188.	−1.30382	−0.651911	+	0.758295i	$0.726032\pi$
$212$	−199307.	−0.304567
$213$	775730.	1.17155
$214$	−531330.	−0.793103
$215$	61681.1	0.0910031
$216$	−61446.8	−0.0896118
$217$	−93735.8	−0.135131
$218$	−399913.	−0.569933
$219$	−202727.	−0.285628
$220$	25124.9	0.0349984
$221$	581640.	0.801075
$222$	564607.	0.768889
$223$	1.04352e6	1.40520	0.702599	−	0.711586i	$-0.252023\pi$
$223$	1.04352e6	1.40520	0.702599	+	0.711586i	$0.252023\pi$
$224$	631096.	0.840380
$225$	163245.	0.214973
$226$	−1.28167e6	−1.66919
$227$	−962243.	−1.23942	−0.619712	−	0.784829i	$-0.712751\pi$
$227$	−962243.	−1.23942	−0.619712	+	0.784829i	$0.712751\pi$
$228$	−67326.3	−0.0857724
$229$	−529304.	−0.666986	−0.333493	−	0.942753i	$-0.608227\pi$
$229$	−529304.	−0.666986	−0.333493	+	0.942753i	$0.608227\pi$
$230$	−342068.	−0.426376
$231$	−583856.	−0.719906
$232$	757981.	0.924567
$233$	66677.7	0.0804620	0.0402310	−	0.999190i	$-0.487191\pi$
$233$	66677.7	0.0804620	0.0402310	+	0.999190i	$0.487191\pi$
$234$	733755.	0.876015
$235$	428255.	0.505863
$236$	−260411.	−0.304355
$237$	−70509.2	−0.0815408
$238$	1.79330e6	2.05215
$239$	−1.13029e6	−1.27996	−0.639980	−	0.768392i	$-0.721057\pi$
$239$	−1.13029e6	−1.27996	−0.639980	+	0.768392i	$0.721057\pi$
$240$	685302.	0.767987
$241$	−1.39564e6	−1.54786	−0.773931	−	0.633271i	$-0.781712\pi$
$241$	−1.39564e6	−1.54786	−0.773931	+	0.633271i	$0.781712\pi$
$242$	−92951.1	−0.102027
$243$	1.31847e6	1.43237
$244$	353651.	0.380277
$245$	734300.	0.781553
$246$	1.16686e6	1.22937
$247$	−159741.	−0.166599
$248$	−65616.0	−0.0677455
$249$	960511.	0.981757
$250$	−99198.2	−0.100381
$251$	−226197.	−0.226622	−0.113311	−	0.993560i	$-0.536146\pi$
$251$	−226197.	−0.226622	−0.113311	+	0.993560i	$0.536146\pi$
$252$	466188.	0.462445
$253$	260780.	0.256138
$254$	−1.59213e6	−1.54844
$255$	737877.	0.710614
$256$	766243.	0.730746
$257$	−172685.	−0.163088	−0.0815442	−	0.996670i	$-0.525985\pi$
$257$	−172685.	−0.163088	−0.0815442	+	0.996670i	$0.525985\pi$
$258$	351717.	0.328961
$259$	851113.	0.788384
$260$	−91881.4	−0.0842935
$261$	1.31611e6	1.19589
$262$	995124.	0.895620
$263$	717612.	0.639735	0.319867	−	0.947462i	$-0.396362\pi$
$263$	717612.	0.639735	0.319867	+	0.947462i	$0.396362\pi$
$264$	−408705.	−0.360911
$265$	−599905.	−0.524769
$266$	−492508.	−0.426785
$267$	−1.86873e6	−1.60424
$268$	29365.1	0.0249744
$269$	1.02921e6	0.867212	0.433606	−	0.901103i	$-0.357241\pi$
$269$	1.02921e6	0.867212	0.433606	+	0.901103i	$0.357241\pi$
$270$	64833.1	0.0541237
$271$	−690396.	−0.571051	−0.285525	−	0.958371i	$-0.592168\pi$
$271$	−690396.	−0.571051	−0.285525	+	0.958371i	$0.592168\pi$
$272$	1.60469e6	1.31513
$273$	2.13515e6	1.73389
$274$	−980026.	−0.788608
$275$	75625.0	0.0603023
$276$	−401945.	−0.317610
$277$	−1.51090e6	−1.18314	−0.591570	−	0.806254i	$-0.701492\pi$
$277$	−1.51090e6	−1.18314	−0.591570	+	0.806254i	$0.701492\pi$
$278$	−1.92500e6	−1.49389
$279$	−113931.	−0.0876259
$280$	808144.	0.616018
$281$	463522.	0.350191	0.175095	−	0.984551i	$-0.443977\pi$
$281$	463522.	0.350191	0.175095	+	0.984551i	$0.443977\pi$
$282$	2.44199e6	1.82861
$283$	−260470.	−0.193327	−0.0966633	−	0.995317i	$-0.530817\pi$
$283$	−260470.	−0.193327	−0.0966633	+	0.995317i	$0.530817\pi$
$284$	−286941.	−0.211104
$285$	−202649.	−0.147786
$286$	339920.	0.245732
$287$	1.75898e6	1.26054
$288$	767066.	0.544944
$289$	307937.	0.216879
$290$	−799753.	−0.558420
$291$	955515.	0.661462
$292$	74988.3	0.0514679
$293$	3216.72	0.00218899	0.00109450	−	0.999999i	$-0.499652\pi$
$293$	3216.72	0.00218899	0.00109450	+	0.999999i	$0.499652\pi$
$294$	4.18712e6	2.82518
$295$	−783827.	−0.524403
$296$	595787.	0.395241
$297$	−49426.4	−0.0325138
$298$	1.18685e6	0.774203
$299$	−953668.	−0.616906
$300$	−116562.	−0.0747746
$301$	530194.	0.337302
$302$	3.02707e6	1.90988
$303$	−2.40351e6	−1.50397
$304$	−440708.	−0.273506
$305$	1.06447e6	0.655217
$306$	2.17966e6	1.33072
$307$	1.38589e6	0.839234	0.419617	−	0.907701i	$-0.362164\pi$
$307$	1.38589e6	0.839234	0.419617	+	0.907701i	$0.362164\pi$
$308$	215967.	0.129721
$309$	1.79370e6	1.06870
$310$	69232.0	0.0409169
$311$	−1.45086e6	−0.850600	−0.425300	−	0.905052i	$-0.639831\pi$
$311$	−1.45086e6	−0.850600	−0.425300	+	0.905052i	$0.639831\pi$
$312$	1.49462e6	0.869252
$313$	−1.89622e6	−1.09403	−0.547014	−	0.837123i	$-0.684236\pi$
$313$	−1.89622e6	−1.09403	−0.547014	+	0.837123i	$0.684236\pi$
$314$	−2.35955e6	−1.35053
$315$	1.40321e6	0.796793
$316$	26081.2	0.0146930
$317$	−2.57214e6	−1.43763	−0.718814	−	0.695202i	$-0.755315\pi$
$317$	−2.57214e6	−1.43763	−0.718814	+	0.695202i	$0.755315\pi$
$318$	−3.42077e6	−1.89695
$319$	609702.	0.335460
$320$	510520.	0.278700
$321$	−1.87922e6	−1.01792
$322$	−2.94032e6	−1.58036
$323$	−474519.	−0.253074
$324$	−450982.	−0.238669
$325$	−276559.	−0.145238
$326$	−2.86840e6	−1.49484
$327$	−1.41442e6	−0.731493
$328$	1.23130e6	0.631945
$329$	3.68116e6	1.87497
$330$	431228.	0.217983
$331$	909532.	0.456298	0.228149	−	0.973626i	$-0.426733\pi$
$331$	909532.	0.456298	0.228149	+	0.973626i	$0.426733\pi$
$332$	−355291.	−0.176904
$333$	1.03449e6	0.511227
$334$	2.22680e6	1.09223
$335$	88387.8	0.0430309
$336$	5.89066e6	2.84653
$337$	−2.37849e6	−1.14084	−0.570422	−	0.821352i	$-0.693220\pi$
$337$	−2.37849e6	−1.14084	−0.570422	+	0.821352i	$0.693220\pi$
$338$	1.11414e6	0.530454
$339$	−4.53307e6	−2.14236
$340$	−272939.	−0.128047
$341$	−52779.9	−0.0245800
$342$	−598619.	−0.276748
$343$	2.70013e6	1.23922
$344$	371141.	0.169100
$345$	−1.20984e6	−0.547242
$346$	−4.47395e6	−2.00910
$347$	434960.	0.193921	0.0969606	−	0.995288i	$-0.469088\pi$
$347$	434960.	0.193921	0.0969606	+	0.995288i	$0.469088\pi$
$348$	−939744.	−0.415969
$349$	2.16783e6	0.952712	0.476356	−	0.879252i	$-0.341957\pi$
$349$	2.16783e6	0.952712	0.476356	+	0.879252i	$0.341957\pi$
$350$	−852680.	−0.372062
$351$	180751.	0.0783093
$352$	355352.	0.152863
$353$	1.85492e6	0.792298	0.396149	−	0.918186i	$-0.370346\pi$
$353$	1.85492e6	0.792298	0.396149	+	0.918186i	$0.370346\pi$
$354$	−4.46953e6	−1.89563
$355$	−863679.	−0.363732
$356$	691239.	0.289070
$357$	6.34258e6	2.63388
$358$	1.55344e6	0.640601
$359$	2.92377e6	1.19731	0.598656	−	0.801006i	$-0.295702\pi$
$359$	2.92377e6	1.19731	0.598656	+	0.801006i	$0.295702\pi$
$360$	982259.	0.399457
$361$	130321.	0.0526316
$362$	5.23172e6	2.09833
$363$	−328752.	−0.130949
$364$	−789787.	−0.312433
$365$	225712.	0.0886792
$366$	6.06983e6	2.36850
$367$	−1.47511e6	−0.571687	−0.285843	−	0.958276i	$-0.592274\pi$
$367$	−1.47511e6	−0.571687	−0.285843	+	0.958276i	$0.592274\pi$
$368$	−2.63107e6	−1.01278
$369$	2.13795e6	0.817393
$370$	−628620.	−0.238717
$371$	−5.15662e6	−1.94505
$372$	81350.6	0.0304792
$373$	146573.	0.0545484	0.0272742	−	0.999628i	$-0.491317\pi$
$373$	146573.	0.0545484	0.0272742	+	0.999628i	$0.491317\pi$
$374$	1.00975e6	0.373281
$375$	−350847.	−0.128837
$376$	2.57685e6	0.939981
$377$	−2.22967e6	−0.807954
$378$	557287.	0.200609
$379$	972954.	0.347932	0.173966	−	0.984752i	$-0.444342\pi$
$379$	972954.	0.347932	0.173966	+	0.984752i	$0.444342\pi$
$380$	74959.5	0.0266298
$381$	−5.63109e6	−1.98738
$382$	1.02638e6	0.359873
$383$	−211037.	−0.0735126	−0.0367563	−	0.999324i	$-0.511703\pi$
$383$	−211037.	−0.0735126	−0.0367563	+	0.999324i	$0.511703\pi$
$384$	5.02127e6	1.73774
$385$	650051.	0.223509
$386$	3.37993e6	1.15462
$387$	644424.	0.218723
$388$	−353443.	−0.119190
$389$	4.80689e6	1.61061	0.805305	−	0.592861i	$-0.202001\pi$
$389$	4.80689e6	1.61061	0.805305	+	0.592861i	$0.202001\pi$
$390$	−1.57699e6	−0.525010
$391$	−2.83293e6	−0.937116
$392$	4.41835e6	1.45226
$393$	3.51958e6	1.14950
$394$	−421972.	−0.136944
$395$	78503.3	0.0253160
$396$	262497.	0.0841175
$397$	4.71304e6	1.50081	0.750403	−	0.660980i	$-0.229859\pi$
$397$	4.71304e6	1.50081	0.750403	+	0.660980i	$0.229859\pi$
$398$	−1.09878e6	−0.347700
$399$	−1.74192e6	−0.547766
$400$	−762999.	−0.238437
$401$	2.26556e6	0.703583	0.351791	−	0.936078i	$-0.385573\pi$
$401$	2.26556e6	0.703583	0.351791	+	0.936078i	$0.385573\pi$
$402$	504004.	0.155549
$403$	193015.	0.0592009
$404$	889054.	0.271003
$405$	−1.35744e6	−0.411227
$406$	−6.87445e6	−2.06977
$407$	479237.	0.143405
$408$	4.43987e6	1.32044
$409$	−373709.	−0.110465	−0.0552325	−	0.998474i	$-0.517590\pi$
$409$	−373709.	−0.110465	−0.0552325	+	0.998474i	$0.517590\pi$
$410$	−1.29916e6	−0.381682
$411$	−3.46619e6	−1.01216
$412$	−663487.	−0.192570
$413$	−6.73756e6	−1.94369
$414$	−3.57382e6	−1.02478
$415$	−1.06941e6	−0.304807
$416$	−1.29951e6	−0.368170
$417$	−6.80841e6	−1.91737
$418$	−277317.	−0.0776310
$419$	1.38493e6	0.385383	0.192692	−	0.981259i	$-0.438278\pi$
$419$	1.38493e6	0.385383	0.192692	+	0.981259i	$0.438278\pi$
$420$	−1.00194e6	−0.277151
$421$	2.63129e6	0.723542	0.361771	−	0.932267i	$-0.382172\pi$
$421$	2.63129e6	0.723542	0.361771	+	0.932267i	$0.382172\pi$
$422$	5.35313e6	1.46328
$423$	4.47427e6	1.21582
$424$	−3.60968e6	−0.975112
$425$	−821535.	−0.220624
$426$	−4.92486e6	−1.31483
$427$	9.14992e6	2.42855
$428$	695120.	0.183422
$429$	1.20224e6	0.315390
$430$	−391594.	−0.102133
$431$	4.19027e6	1.08655	0.543273	−	0.839556i	$-0.317185\pi$
$431$	4.19027e6	1.08655	0.543273	+	0.839556i	$0.317185\pi$
$432$	498675.	0.128561
$433$	6.50673e6	1.66780	0.833898	−	0.551918i	$-0.186104\pi$
$433$	6.50673e6	1.66780	0.833898	+	0.551918i	$0.186104\pi$
$434$	595099.	0.151658
$435$	−2.82859e6	−0.716716
$436$	523192.	0.131809
$437$	778030.	0.194891
$438$	1.28705e6	0.320561
$439$	−2.98302e6	−0.738744	−0.369372	−	0.929282i	$-0.620427\pi$
$439$	−2.98302e6	−0.738744	−0.369372	+	0.929282i	$0.620427\pi$
$440$	455042.	0.112052
$441$	7.67173e6	1.87844
$442$	−3.69264e6	−0.899046
$443$	4.41180e6	1.06809	0.534044	−	0.845457i	$-0.320672\pi$
$443$	4.41180e6	1.06809	0.534044	+	0.845457i	$0.320672\pi$
$444$	−738656.	−0.177822
$445$	2.08060e6	0.498068
$446$	−6.62496e6	−1.57705
$447$	4.19768e6	0.993667
$448$	4.38829e6	1.03300
$449$	−6.39547e6	−1.49712	−0.748560	−	0.663068i	$-0.769254\pi$
$449$	−6.39547e6	−1.49712	−0.748560	+	0.663068i	$0.769254\pi$
$450$	−1.03639e6	−0.241264
$451$	990428.	0.229288
$452$	1.67677e6	0.386036
$453$	1.07062e7	2.45127
$454$	6.10897e6	1.39100
$455$	−2.37722e6	−0.538322
$456$	−1.21936e6	−0.274612
$457$	−1.32493e6	−0.296758	−0.148379	−	0.988931i	$-0.547406\pi$
$457$	−1.32493e6	−0.296758	−0.148379	+	0.988931i	$0.547406\pi$
$458$	3.36038e6	0.748557
$459$	536932.	0.118956
$460$	447516.	0.0986084
$461$	−3.88934e6	−0.852361	−0.426181	−	0.904638i	$-0.640141\pi$
$461$	−3.88934e6	−0.852361	−0.426181	+	0.904638i	$0.640141\pi$
$462$	3.70671e6	0.807949
$463$	6.41968e6	1.39175	0.695875	−	0.718163i	$-0.255017\pi$
$463$	6.41968e6	1.39175	0.695875	+	0.718163i	$0.255017\pi$
$464$	−6.15143e6	−1.32642
$465$	244862.	0.0525157
$466$	−423316.	−0.0903025
$467$	5.96749e6	1.26619	0.633096	−	0.774073i	$-0.281784\pi$
$467$	5.96749e6	1.26619	0.633096	+	0.774073i	$0.281784\pi$
$468$	−959946.	−0.202597
$469$	759756.	0.159493
$470$	−2.71885e6	−0.567729
$471$	−8.34532e6	−1.73337
$472$	−4.71636e6	−0.974432
$473$	298537.	0.0613543
$474$	447641.	0.0915132
$475$	225625.	0.0458831
$476$	−2.34611e6	−0.474603
$477$	−6.26761e6	−1.26126
$478$	7.17587e6	1.43650
$479$	−3.09227e6	−0.615799	−0.307900	−	0.951419i	$-0.599626\pi$
$479$	−3.09227e6	−0.615799	−0.307900	+	0.951419i	$0.599626\pi$
$480$	−1.64858e6	−0.326594
$481$	−1.75256e6	−0.345390
$482$	8.86050e6	1.73716
$483$	−1.03994e7	−2.02834
$484$	121605.	0.0235959
$485$	−1.06385e6	−0.205364
$486$	−8.37053e6	−1.60754
$487$	−864592.	−0.165192	−0.0825960	−	0.996583i	$-0.526321\pi$
$487$	−864592.	−0.165192	−0.0825960	+	0.996583i	$0.526321\pi$
$488$	6.40503e6	1.21751
$489$	−1.01450e7	−1.91859
$490$	−4.66184e6	−0.877136
$491$	3.38763e6	0.634150	0.317075	−	0.948400i	$-0.397299\pi$
$491$	3.38763e6	0.634150	0.317075	+	0.948400i	$0.397299\pi$
$492$	−1.52656e6	−0.284317
$493$	−6.62336e6	−1.22733
$494$	1.01414e6	0.186974
$495$	790105.	0.144935
$496$	532509.	0.0971903
$497$	−7.42395e6	−1.34817
$498$	−6.09798e6	−1.10182
$499$	6.51412e6	1.17113	0.585564	−	0.810626i	$-0.300873\pi$
$499$	6.51412e6	1.17113	0.585564	+	0.810626i	$0.300873\pi$
$500$	129778.	0.0232153
$501$	7.87583e6	1.40185
$502$	1.43605e6	0.254338
$503$	2.21176e6	0.389779	0.194889	−	0.980825i	$-0.437565\pi$
$503$	2.21176e6	0.389779	0.194889	+	0.980825i	$0.437565\pi$
$504$	8.44322e6	1.48058
$505$	2.67602e6	0.466939
$506$	−1.65561e6	−0.287463
$507$	3.94053e6	0.680823
$508$	2.08293e6	0.358109
$509$	−4.25125e6	−0.727314	−0.363657	−	0.931533i	$-0.618472\pi$
$509$	−4.25125e6	−0.727314	−0.363657	+	0.931533i	$0.618472\pi$
$510$	−4.68455e6	−0.797521
$511$	1.94015e6	0.328688
$512$	2.29129e6	0.386282
$513$	−147462.	−0.0247393
$514$	1.09632e6	0.183034
$515$	−1.99707e6	−0.331799
$516$	−460140.	−0.0760791
$517$	2.07275e6	0.341053
$518$	−5.40344e6	−0.884802
$519$	−1.58236e7	−2.57862
$520$	−1.66408e6	−0.269877
$521$	4.84292e6	0.781651	0.390826	−	0.920465i	$-0.372190\pi$
$521$	4.84292e6	0.781651	0.390826	+	0.920465i	$0.372190\pi$
$522$	−8.35555e6	−1.34214
$523$	1.44653e6	0.231245	0.115623	−	0.993293i	$-0.463114\pi$
$523$	1.44653e6	0.231245	0.115623	+	0.993293i	$0.463114\pi$
$524$	−1.30189e6	−0.207131
$525$	−3.01578e6	−0.477531
$526$	−4.55589e6	−0.717974
$527$	573363.	0.0899296
$528$	3.31686e6	0.517777
$529$	−1.79142e6	−0.278329
$530$	3.80861e6	0.588947
$531$	−8.18917e6	−1.26039
$532$	644331.	0.0987029
$533$	−3.62198e6	−0.552239
$534$	1.18640e7	1.80043
$535$	2.09228e6	0.316036
$536$	531837.	0.0799588
$537$	5.49427e6	0.822193
$538$	−6.53416e6	−0.973271
$539$	3.55401e6	0.526923
$540$	−84818.9	−0.0125172
$541$	−1.37576e6	−0.202093	−0.101046	−	0.994882i	$-0.532219\pi$
$541$	−1.37576e6	−0.202093	−0.101046	+	0.994882i	$0.532219\pi$
$542$	4.38310e6	0.640890
$543$	1.85037e7	2.69314
$544$	−3.86028e6	−0.559271
$545$	1.57479e6	0.227107
$546$	−1.35554e7	−1.94594
$547$	173572.	0.0248034	0.0124017	−	0.999923i	$-0.496052\pi$
$547$	173572.	0.0248034	0.0124017	+	0.999923i	$0.496052\pi$
$548$	1.28213e6	0.182382
$549$	1.11213e7	1.57479
$550$	−480119.	−0.0676772
$551$	1.81903e6	0.255247
$552$	−7.27970e6	−1.01687
$553$	674793.	0.0938334
$554$	9.59222e6	1.32784
$555$	−2.22332e6	−0.306387
$556$	2.51842e6	0.345494
$557$	3.70243e6	0.505649	0.252824	−	0.967512i	$-0.418641\pi$
$557$	3.70243e6	0.505649	0.252824	+	0.967512i	$0.418641\pi$
$558$	723313.	0.0983424
$559$	−1.09174e6	−0.147771
$560$	−6.55853e6	−0.883764
$561$	3.57132e6	0.479096
$562$	−2.94276e6	−0.393019
$563$	−1.15351e6	−0.153373	−0.0766866	−	0.997055i	$-0.524434\pi$
$563$	−1.15351e6	−0.153373	−0.0766866	+	0.997055i	$0.524434\pi$
$564$	−3.19477e6	−0.422904
$565$	5.04701e6	0.665140
$566$	1.65364e6	0.216970
$567$	−1.16681e7	−1.52421
$568$	−5.19683e6	−0.675878
$569$	−9.98168e6	−1.29248	−0.646238	−	0.763136i	$-0.723659\pi$
$569$	−9.98168e6	−1.29248	−0.646238	+	0.763136i	$0.723659\pi$
$570$	1.28656e6	0.165860
$571$	8.84063e6	1.13473	0.567365	−	0.823466i	$-0.307963\pi$
$571$	8.84063e6	1.13473	0.567365	+	0.823466i	$0.307963\pi$
$572$	−444706.	−0.0568307
$573$	3.63013e6	0.461887
$574$	−1.11672e7	−1.41470
$575$	1.34700e6	0.169902
$576$	5.33374e6	0.669847
$577$	−1.06489e7	−1.33158	−0.665788	−	0.746141i	$-0.731904\pi$
$577$	−1.06489e7	−1.33158	−0.665788	+	0.746141i	$0.731904\pi$
$578$	−1.95500e6	−0.243403
$579$	1.19542e7	1.48192
$580$	1.04629e6	0.129146
$581$	−9.19236e6	−1.12976
$582$	−6.06626e6	−0.742358
$583$	−2.90354e6	−0.353799
$584$	1.35813e6	0.164781
$585$	−2.88940e6	−0.349074
$586$	−20421.9	−0.00245670
$587$	7.69130e6	0.921307	0.460653	−	0.887580i	$-0.347615\pi$
$587$	7.69130e6	0.921307	0.460653	+	0.887580i	$0.347615\pi$
$588$	−5.47786e6	−0.653383
$589$	−157467.	−0.0187026
$590$	4.97627e6	0.588537
$591$	−1.49244e6	−0.175764
$592$	−4.83514e6	−0.567028
$593$	4.06429e6	0.474622	0.237311	−	0.971434i	$-0.423734\pi$
$593$	4.06429e6	0.474622	0.237311	+	0.971434i	$0.423734\pi$
$594$	313792.	0.0364902
$595$	−7.06169e6	−0.817741
$596$	−1.55271e6	−0.179051
$597$	−3.88621e6	−0.446263
$598$	6.05453e6	0.692353
$599$	−5.33011e6	−0.606972	−0.303486	−	0.952836i	$-0.598151\pi$
$599$	−5.33011e6	−0.606972	−0.303486	+	0.952836i	$0.598151\pi$
$600$	−2.11108e6	−0.239401
$601$	2.81513e6	0.317916	0.158958	−	0.987285i	$-0.449187\pi$
$601$	2.81513e6	0.317916	0.158958	+	0.987285i	$0.449187\pi$
$602$	−3.36603e6	−0.378553
$603$	923446.	0.103423
$604$	−3.96021e6	−0.441699
$605$	366025.	0.0406558
$606$	1.52591e7	1.68791
$607$	7.34287e6	0.808899	0.404449	−	0.914560i	$-0.367463\pi$
$607$	7.34287e6	0.808899	0.404449	+	0.914560i	$0.367463\pi$
$608$	1.06018e6	0.116311
$609$	−2.43138e7	−2.65650
$610$	−6.75800e6	−0.735350
$611$	−7.58002e6	−0.821424
$612$	−2.85158e6	−0.307756
$613$	7.56546e6	0.813176	0.406588	−	0.913612i	$-0.366719\pi$
$613$	7.56546e6	0.813176	0.406588	+	0.913612i	$0.366719\pi$
$614$	−8.79858e6	−0.941871
$615$	−4.59489e6	−0.489878
$616$	3.91142e6	0.415319
$617$	4.37973e6	0.463163	0.231582	−	0.972815i	$-0.425610\pi$
$617$	4.37973e6	0.463163	0.231582	+	0.972815i	$0.425610\pi$
$618$	−1.13877e7	−1.19940
$619$	1.23890e7	1.29960	0.649802	−	0.760104i	$-0.274852\pi$
$619$	1.23890e7	1.29960	0.649802	+	0.760104i	$0.274852\pi$
$620$	−90573.8	−0.00946288
$621$	−880364.	−0.0916080
$622$	9.21107e6	0.954628
$623$	1.78843e7	1.84608
$624$	−1.21297e7	−1.24706
$625$	390625.	0.0400000
$626$	1.20385e7	1.22783
$627$	−980823.	−0.0996372
$628$	3.08692e6	0.312339
$629$	−5.20608e6	−0.524667
$630$	−8.90852e6	−0.894240
$631$	−8.71435e6	−0.871287	−0.435644	−	0.900119i	$-0.643479\pi$
$631$	−8.71435e6	−0.871287	−0.435644	+	0.900119i	$0.643479\pi$
$632$	472361.	0.0470415
$633$	1.89331e7	1.87808
$634$	1.63297e7	1.61345
$635$	6.26953e6	0.617022
$636$	4.47528e6	0.438710
$637$	−1.29970e7	−1.26909
$638$	−3.87080e6	−0.376487
$639$	−9.02344e6	−0.874218
$640$	−5.59056e6	−0.539518
$641$	−1.03994e7	−0.999689	−0.499844	−	0.866115i	$-0.666610\pi$
$641$	−1.03994e7	−0.999689	−0.499844	+	0.866115i	$0.666610\pi$
$642$	1.19306e7	1.14242
$643$	−8.89559e6	−0.848491	−0.424245	−	0.905547i	$-0.639461\pi$
$643$	−8.89559e6	−0.848491	−0.424245	+	0.905547i	$0.639461\pi$
$644$	3.84672e6	0.365491
$645$	−1.38500e6	−0.131084
$646$	3.01257e6	0.284024
$647$	7.13614e6	0.670197	0.335099	−	0.942183i	$-0.391230\pi$
$647$	7.13614e6	0.670197	0.335099	+	0.942183i	$0.391230\pi$
$648$	−8.16781e6	−0.764132
$649$	−3.79372e6	−0.353553
$650$	1.75579e6	0.163000
$651$	2.10476e6	0.194648
$652$	3.75263e6	0.345714
$653$	8.51933e6	0.781849	0.390924	−	0.920423i	$-0.372155\pi$
$653$	8.51933e6	0.781849	0.390924	+	0.920423i	$0.372155\pi$
$654$	8.97972e6	0.820953
$655$	−3.91862e6	−0.356887
$656$	−9.99267e6	−0.906613
$657$	2.35816e6	0.213138
$658$	−2.33705e7	−2.10428
$659$	−7.43040e6	−0.666498	−0.333249	−	0.942839i	$-0.608145\pi$
$659$	−7.43040e6	−0.666498	−0.333249	+	0.942839i	$0.608145\pi$
$660$	−564161.	−0.0504130
$661$	−1.74159e7	−1.55039	−0.775195	−	0.631722i	$-0.782349\pi$
$661$	−1.74159e7	−1.55039	−0.775195	+	0.631722i	$0.782349\pi$
$662$	−5.77433e6	−0.512102
$663$	−1.30603e7	−1.15390
$664$	−6.43474e6	−0.566383
$665$	1.93941e6	0.170065
$666$	−6.56762e6	−0.573749
$667$	1.08598e7	0.945163
$668$	−2.91325e6	−0.252602
$669$	−2.34314e7	−2.02410
$670$	−561146.	−0.0482935
$671$	5.15205e6	0.441747
$672$	−1.41708e7	−1.21052
$673$	1.83440e7	1.56120	0.780598	−	0.625034i	$-0.214915\pi$
$673$	1.83440e7	1.56120	0.780598	+	0.625034i	$0.214915\pi$
$674$	1.51003e7	1.28037
$675$	−255301.	−0.0215672
$676$	−1.45759e6	−0.122679
$677$	7.17551e6	0.601701	0.300851	−	0.953671i	$-0.402729\pi$
$677$	7.17551e6	0.601701	0.300851	+	0.953671i	$0.402729\pi$
$678$	2.87790e7	2.40437
$679$	−9.14454e6	−0.761180
$680$	−4.94325e6	−0.409959
$681$	2.16064e7	1.78531
$682$	335083.	0.0275862
$683$	4.40234e6	0.361104	0.180552	−	0.983565i	$-0.442212\pi$
$683$	4.40234e6	0.361104	0.180552	+	0.983565i	$0.442212\pi$
$684$	783152.	0.0640038
$685$	3.85917e6	0.314245
$686$	−1.71423e7	−1.39078
$687$	1.18851e7	0.960752
$688$	−3.01201e6	−0.242597
$689$	1.06182e7	0.852123
$690$	7.68087e6	0.614169
$691$	8.79245e6	0.700511	0.350256	−	0.936654i	$-0.386095\pi$
$691$	8.79245e6	0.700511	0.350256	+	0.936654i	$0.386095\pi$
$692$	5.85311e6	0.464645
$693$	6.79152e6	0.537198
$694$	−2.76142e6	−0.217638
$695$	7.58032e6	0.595286
$696$	−1.70199e7	−1.33178
$697$	−1.07593e7	−0.838883
$698$	−1.37629e7	−1.06923
$699$	−1.49720e6	−0.115901
$700$	1.11553e6	0.0860472
$701$	−1.56298e6	−0.120132	−0.0600660	−	0.998194i	$-0.519131\pi$
$701$	−1.56298e6	−0.120132	−0.0600660	+	0.998194i	$0.519131\pi$
$702$	−1.14753e6	−0.0878865
$703$	1.42979e6	0.109115
$704$	2.47092e6	0.187900
$705$	−9.61613e6	−0.728664
$706$	−1.17763e7	−0.889196
$707$	2.30023e7	1.73070
$708$	5.84733e6	0.438404
$709$	−2.47555e7	−1.84950	−0.924752	−	0.380570i	$-0.875728\pi$
$709$	−2.47555e7	−1.84950	−0.924752	+	0.380570i	$0.875728\pi$
$710$	5.48323e6	0.408216
$711$	820177.	0.0608462
$712$	1.25192e7	0.925497
$713$	−940097.	−0.0692546
$714$	−4.02670e7	−2.95600
$715$	−1.33855e6	−0.0979193
$716$	−2.03232e6	−0.148152
$717$	2.53798e7	1.84370
$718$	−1.85621e7	−1.34374
$719$	2.11341e7	1.52462	0.762311	−	0.647211i	$-0.224065\pi$
$719$	2.11341e7	1.52462	0.762311	+	0.647211i	$0.224065\pi$
$720$	−7.97156e6	−0.573076
$721$	−1.71662e7	−1.22981
$722$	−827367.	−0.0590684
$723$	3.13381e7	2.22960
$724$	−6.84448e6	−0.485282
$725$	3.14929e6	0.222519
$726$	2.08714e6	0.146964
$727$	1.83094e7	1.28481	0.642405	−	0.766366i	$-0.277937\pi$
$727$	1.83094e7	1.28481	0.642405	+	0.766366i	$0.277937\pi$
$728$	−1.43040e7	−1.00029
$729$	−1.64109e7	−1.14370
$730$	−1.43297e6	−0.0995246
$731$	−3.24308e6	−0.224473
$732$	−7.94095e6	−0.547765
$733$	2.29199e6	0.157563	0.0787813	−	0.996892i	$-0.474897\pi$
$733$	2.29199e6	0.157563	0.0787813	+	0.996892i	$0.474897\pi$
$734$	9.36498e6	0.641603
$735$	−1.64881e7	−1.12578
$736$	6.32940e6	0.430693
$737$	427797.	0.0290114
$738$	−1.35732e7	−0.917360
$739$	−1.99162e7	−1.34151	−0.670756	−	0.741678i	$-0.734030\pi$
$739$	−1.99162e7	−1.34151	−0.670756	+	0.741678i	$0.734030\pi$
$740$	822402.	0.0552084
$741$	3.58685e6	0.239976
$742$	3.27377e7	2.18292
$743$	−2.76901e7	−1.84015	−0.920074	−	0.391745i	$-0.871872\pi$
$743$	−2.76901e7	−1.84015	−0.920074	+	0.391745i	$0.871872\pi$
$744$	1.47336e6	0.0975832
$745$	−4.67360e6	−0.308504
$746$	−930545.	−0.0612196
$747$	−1.11729e7	−0.732593
$748$	−1.32102e6	−0.0863290
$749$	1.79847e7	1.17138
$750$	2.22742e6	0.144593
$751$	−8.97875e6	−0.580920	−0.290460	−	0.956887i	$-0.593808\pi$
$751$	−8.97875e6	−0.580920	−0.290460	+	0.956887i	$0.593808\pi$
$752$	−2.09125e7	−1.34853
$753$	5.07907e6	0.326435
$754$	1.41555e7	0.906766
$755$	−1.19201e7	−0.761048
$756$	−729080.	−0.0463949
$757$	3.20582e6	0.203329	0.101664	−	0.994819i	$-0.467583\pi$
$757$	3.20582e6	0.203329	0.101664	+	0.994819i	$0.467583\pi$
$758$	−6.17697e6	−0.390484
$759$	−5.85561e6	−0.368950
$760$	1.35761e6	0.0852589
$761$	2.39816e7	1.50113	0.750563	−	0.660798i	$-0.229782\pi$
$761$	2.39816e7	1.50113	0.750563	+	0.660798i	$0.229782\pi$
$762$	3.57500e7	2.23043
$763$	1.35364e7	0.841768
$764$	−1.34278e6	−0.0832282
$765$	−8.58313e6	−0.530264
$766$	1.33981e6	0.0825031
$767$	1.38736e7	0.851530
$768$	−1.72054e7	−1.05259
$769$	1.43654e7	0.875993	0.437996	−	0.898977i	$-0.355688\pi$
$769$	1.43654e7	0.875993	0.437996	+	0.898977i	$0.355688\pi$
$770$	−4.12697e6	−0.250844
$771$	3.87752e6	0.234919
$772$	−4.42185e6	−0.267030
$773$	−6.44514e6	−0.387957	−0.193978	−	0.981006i	$-0.562139\pi$
$773$	−6.44514e6	−0.387957	−0.193978	+	0.981006i	$0.562139\pi$
$774$	−4.09124e6	−0.245473
$775$	−272623.	−0.0163046
$776$	−6.40127e6	−0.381603
$777$	−1.91111e7	−1.13562
$778$	−3.05174e7	−1.80759
$779$	2.95491e6	0.174462
$780$	2.06312e6	0.121420
$781$	−4.18021e6	−0.245228
$782$	1.79853e7	1.05172
$783$	−2.05828e6	−0.119978
$784$	−3.58573e7	−2.08347
$785$	9.29149e6	0.538160
$786$	−2.23447e7	−1.29009
$787$	−2.51823e7	−1.44930	−0.724651	−	0.689116i	$-0.757999\pi$
$787$	−2.51823e7	−1.44930	−0.724651	+	0.689116i	$0.757999\pi$
$788$	552052.	0.0316712
$789$	−1.61134e7	−0.921499
$790$	−498393.	−0.0284121
$791$	4.33827e7	2.46533
$792$	4.75413e6	0.269314
$793$	−1.88409e7	−1.06395
$794$	−2.99216e7	−1.68435
$795$	1.34704e7	0.755897
$796$	1.43750e6	0.0804128
$797$	−9.18132e6	−0.511988	−0.255994	−	0.966678i	$-0.582403\pi$
$797$	−9.18132e6	−0.511988	−0.255994	+	0.966678i	$0.582403\pi$
$798$	1.10589e7	0.614757
$799$	−2.25169e7	−1.24779
$800$	1.83550e6	0.101398
$801$	2.17374e7	1.19709
$802$	−1.43833e7	−0.789630
$803$	1.09244e6	0.0597875
$804$	−659370.	−0.0359741
$805$	1.15785e7	0.629741
$806$	−1.22539e6	−0.0664412
$807$	−2.31102e7	−1.24917
$808$	1.61018e7	0.867654
$809$	−3.43308e6	−0.184422	−0.0922110	−	0.995739i	$-0.529393\pi$
$809$	−3.43308e6	−0.184422	−0.0922110	+	0.995739i	$0.529393\pi$
$810$	8.61793e6	0.461520
$811$	2.88260e7	1.53898	0.769490	−	0.638659i	$-0.220511\pi$
$811$	2.88260e7	1.53898	0.769490	+	0.638659i	$0.220511\pi$
$812$	8.99361e6	0.478679
$813$	1.55023e7	0.822564
$814$	−3.04252e6	−0.160943
$815$	1.12953e7	0.595665
$816$	−3.60320e7	−1.89436
$817$	890675.	0.0466836
$818$	2.37256e6	0.123975
$819$	−2.48365e7	−1.29384
$820$	1.69964e6	0.0882719
$821$	2.39942e7	1.24236	0.621181	−	0.783667i	$-0.286653\pi$
$821$	2.39942e7	1.24236	0.621181	+	0.783667i	$0.286653\pi$
$822$	2.20057e7	1.13594
$823$	−1.59498e6	−0.0820835	−0.0410417	−	0.999157i	$-0.513068\pi$
$823$	−1.59498e6	−0.0820835	−0.0410417	+	0.999157i	$0.513068\pi$
$824$	−1.20165e7	−0.616540
$825$	−1.69810e6	−0.0868617
$826$	4.27746e7	2.18140
$827$	3.38957e7	1.72338	0.861690	−	0.507435i	$-0.169406\pi$
$827$	3.38957e7	1.72338	0.861690	+	0.507435i	$0.169406\pi$
$828$	4.67550e6	0.237002
$829$	−1.65958e7	−0.838710	−0.419355	−	0.907822i	$-0.637744\pi$
$829$	−1.65958e7	−0.838710	−0.419355	+	0.907822i	$0.637744\pi$
$830$	6.78935e6	0.342084
$831$	3.39261e7	1.70424
$832$	−9.03609e6	−0.452556
$833$	−3.86082e7	−1.92782
$834$	4.32244e7	2.15186
$835$	−8.76876e6	−0.435233
$836$	362804.	0.0179538
$837$	178179.	0.00879109
$838$	−8.79249e6	−0.432515
$839$	1.90010e7	0.931906	0.465953	−	0.884809i	$-0.345712\pi$
$839$	1.90010e7	0.931906	0.465953	+	0.884809i	$0.345712\pi$
$840$	−1.81462e7	−0.887336
$841$	4.87895e6	0.237868
$842$	−1.67052e7	−0.812030
$843$	−1.04080e7	−0.504429
$844$	−7.00332e6	−0.338414
$845$	−4.38729e6	−0.211375
$846$	−2.84057e7	−1.36452
$847$	3.14625e6	0.150690
$848$	2.92945e7	1.39893
$849$	5.84865e6	0.278475
$850$	5.21566e6	0.247607
$851$	8.53599e6	0.404045
$852$	6.44303e6	0.304082
$853$	176459.	0.00830372	0.00415186	−	0.999991i	$-0.498678\pi$
$853$	176459.	0.00830372	0.00415186	+	0.999991i	$0.498678\pi$
$854$	−5.80899e7	−2.72556
$855$	2.35726e6	0.110279
$856$	1.25894e7	0.587249
$857$	1.16255e7	0.540703	0.270351	−	0.962762i	$-0.412860\pi$
$857$	1.16255e7	0.540703	0.270351	+	0.962762i	$0.412860\pi$
$858$	−7.63264e6	−0.353962
$859$	−2.09751e7	−0.969888	−0.484944	−	0.874545i	$-0.661160\pi$
$859$	−2.09751e7	−0.969888	−0.484944	+	0.874545i	$0.661160\pi$
$860$	512309.	0.0236203
$861$	−3.94964e7	−1.81572
$862$	−2.66027e7	−1.21943
$863$	2.75794e7	1.26054	0.630272	−	0.776375i	$-0.282944\pi$
$863$	2.75794e7	1.26054	0.630272	+	0.776375i	$0.282944\pi$
$864$	−1.19963e6	−0.0546717
$865$	1.76176e7	0.800584
$866$	−4.13092e7	−1.87177
$867$	−6.91449e6	−0.312401
$868$	−778547.	−0.0350740
$869$	379956.	0.0170681
$870$	1.79578e7	0.804369
$871$	−1.56444e6	−0.0698738
$872$	9.47562e6	0.422004
$873$	−1.11147e7	−0.493587
$874$	−4.93947e6	−0.218726
$875$	3.35770e6	0.148259
$876$	−1.68380e6	−0.0741363
$877$	−2.64105e7	−1.15952	−0.579760	−	0.814787i	$-0.696854\pi$
$877$	−2.64105e7	−1.15952	−0.579760	+	0.814787i	$0.696854\pi$
$878$	1.89382e7	0.829092
$879$	−72228.9	−0.00315311
$880$	−3.69292e6	−0.160754
$881$	9.19881e6	0.399293	0.199647	−	0.979868i	$-0.436021\pi$
$881$	9.19881e6	0.399293	0.199647	+	0.979868i	$0.436021\pi$
$882$	−4.87054e7	−2.10817
$883$	−1.84109e7	−0.794645	−0.397323	−	0.917679i	$-0.630061\pi$
$883$	−1.84109e7	−0.794645	−0.397323	+	0.917679i	$0.630061\pi$
$884$	4.83096e6	0.207923
$885$	1.76002e7	0.755371
$886$	−2.80091e7	−1.19871
$887$	1.18035e7	0.503734	0.251867	−	0.967762i	$-0.418956\pi$
$887$	1.18035e7	0.503734	0.251867	+	0.967762i	$0.418956\pi$
$888$	−1.33779e7	−0.569320
$889$	5.38911e7	2.28698
$890$	−1.32091e7	−0.558981
$891$	−6.56999e6	−0.277249
$892$	8.66720e6	0.364726
$893$	6.18400e6	0.259502
$894$	−2.66498e7	−1.11519
$895$	−6.11719e6	−0.255267
$896$	−4.80549e7	−1.99971
$897$	2.14139e7	0.888615
$898$	4.06028e7	1.68022
$899$	−2.19794e6	−0.0907019
$900$	1.35587e6	0.0557972
$901$	3.15420e7	1.29442
$902$	−6.28791e6	−0.257330
$903$	−1.19051e7	−0.485862
$904$	3.03683e7	1.23595
$905$	−2.06016e7	−0.836141
$906$	−6.79705e7	−2.75106
$907$	−3.85017e7	−1.55404	−0.777019	−	0.629478i	$-0.783269\pi$
$907$	−3.85017e7	−1.55404	−0.777019	+	0.629478i	$0.783269\pi$
$908$	−7.99216e6	−0.321699
$909$	2.79581e7	1.12227
$910$	1.50922e7	0.604158
$911$	−2.75916e7	−1.10149	−0.550746	−	0.834673i	$-0.685657\pi$
$911$	−2.75916e7	−1.10149	−0.550746	+	0.834673i	$0.685657\pi$
$912$	9.89576e6	0.393969
$913$	−5.17595e6	−0.205501
$914$	8.41156e6	0.333051
$915$	−2.39019e7	−0.943800
$916$	−4.39627e6	−0.173120
$917$	−3.36834e7	−1.32279
$918$	−3.40881e6	−0.133505
$919$	−4.44736e7	−1.73705	−0.868527	−	0.495641i	$-0.834933\pi$
$919$	−4.44736e7	−1.73705	−0.868527	+	0.495641i	$0.834933\pi$
$920$	8.10505e6	0.315708
$921$	−3.11191e7	−1.20886
$922$	2.46922e7	0.956604
$923$	1.52869e7	0.590631
$924$	−4.84937e6	−0.186855
$925$	2.47540e6	0.0951241
$926$	−4.07565e7	−1.56196
$927$	−2.08647e7	−0.797468
$928$	1.47981e7	0.564073
$929$	2.31988e7	0.881914	0.440957	−	0.897528i	$-0.354639\pi$
$929$	2.31988e7	0.881914	0.440957	+	0.897528i	$0.354639\pi$
$930$	−1.55455e6	−0.0589383
$931$	1.06033e7	0.400928
$932$	553809.	0.0208843
$933$	3.25780e7	1.22524
$934$	−3.78857e7	−1.42105
$935$	−3.97623e6	−0.148745
$936$	−1.73858e7	−0.648641
$937$	−3.03590e7	−1.12964	−0.564818	−	0.825215i	$-0.691054\pi$
$937$	−3.03590e7	−1.12964	−0.564818	+	0.825215i	$0.691054\pi$
$938$	−4.82345e6	−0.178999
$939$	4.25782e7	1.57588
$940$	3.55698e6	0.131299
$941$	−3.40477e6	−0.125347	−0.0626734	−	0.998034i	$-0.519963\pi$
$941$	−3.40477e6	−0.125347	−0.0626734	+	0.998034i	$0.519963\pi$
$942$	5.29818e7	1.94536
$943$	1.76411e7	0.646022
$944$	3.82758e7	1.39796
$945$	−2.19450e6	−0.0799385
$946$	−1.89531e6	−0.0688578
$947$	1.89364e7	0.686155	0.343077	−	0.939307i	$-0.388531\pi$
$947$	1.89364e7	0.686155	0.343077	+	0.939307i	$0.388531\pi$
$948$	−585633.	−0.0211643
$949$	−3.99505e6	−0.143998
$950$	−1.43242e6	−0.0514946
$951$	5.77554e7	2.07082
$952$	−4.24908e7	−1.51951
$953$	−2.70929e6	−0.0966325	−0.0483162	−	0.998832i	$-0.515386\pi$
$953$	−2.70929e6	−0.0966325	−0.0483162	+	0.998832i	$0.515386\pi$
$954$	3.97911e7	1.41552
$955$	−4.04170e6	−0.143402
$956$	−9.38794e6	−0.332220
$957$	−1.36904e7	−0.483210
$958$	1.96319e7	0.691111
$959$	3.31724e7	1.16474
$960$	−1.14633e7	−0.401451
$961$	−2.84389e7	−0.993354
$962$	1.11264e7	0.387631
$963$	2.18595e7	0.759581
$964$	−1.15919e7	−0.401755
$965$	−1.33096e7	−0.460094
$966$	6.60226e7	2.27641
$967$	−9.62962e6	−0.331164	−0.165582	−	0.986196i	$-0.552950\pi$
$967$	−9.62962e6	−0.331164	−0.165582	+	0.986196i	$0.552950\pi$
$968$	2.20240e6	0.0755455
$969$	1.06549e7	0.364537
$970$	6.75403e6	0.230480
$971$	1.14895e7	0.391068	0.195534	−	0.980697i	$-0.437356\pi$
$971$	1.14895e7	0.391068	0.195534	+	0.980697i	$0.437356\pi$
$972$	1.09509e7	0.371778
$973$	6.51584e7	2.20642
$974$	5.48902e6	0.185395
$975$	6.20992e6	0.209206
$976$	−5.19803e7	−1.74668
$977$	−6.23802e6	−0.209079	−0.104540	−	0.994521i	$-0.533337\pi$
$977$	−6.23802e6	−0.209079	−0.104540	+	0.994521i	$0.533337\pi$
$978$	6.44077e7	2.15323
$979$	1.00701e7	0.335797
$980$	6.09892e6	0.202856
$981$	1.64528e7	0.545844
$982$	−2.15070e7	−0.711706
$983$	3.14604e7	1.03844	0.519218	−	0.854642i	$-0.326223\pi$
$983$	3.14604e7	1.03844	0.519218	+	0.854642i	$0.326223\pi$
$984$	−2.76479e7	−0.910278
$985$	1.66165e6	0.0545694
$986$	4.20496e7	1.37743
$987$	−8.26575e7	−2.70078
$988$	−1.32677e6	−0.0432416
$989$	5.31743e6	0.172866
$990$	−5.01613e6	−0.162660
$991$	9.19142e6	0.297302	0.148651	−	0.988890i	$-0.452507\pi$
$991$	9.19142e6	0.297302	0.148651	+	0.988890i	$0.452507\pi$
$992$	−1.28102e6	−0.0413311
$993$	−2.04228e7	−0.657269
$994$	4.71323e7	1.51305
$995$	4.32682e6	0.138551
$996$	7.97778e6	0.254820
$997$	−4.36817e7	−1.39175	−0.695876	−	0.718162i	$-0.744984\pi$
$997$	−4.36817e7	−1.39175	−0.695876	+	0.718162i	$0.744984\pi$
$998$	−4.13561e7	−1.31436
$999$	−1.61785e6	−0.0512890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.10	✓	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-6.34868 q^{2} -22.4542 q^{3} +8.30576 q^{4} +25.0000 q^{5} +142.555 q^{6} +214.893 q^{7} +150.427 q^{8} +261.192 q^{9} +O(q^{10})\)	\(q-6.34868 q^{2} -22.4542 q^{3} +8.30576 q^{4} +25.0000 q^{5} +142.555 q^{6} +214.893 q^{7} +150.427 q^{8} +261.192 q^{9} -158.717 q^{10} +121.000 q^{11} -186.499 q^{12} -442.495 q^{13} -1364.29 q^{14} -561.355 q^{15} -1220.80 q^{16} -1314.46 q^{17} -1658.22 q^{18} +361.000 q^{19} +207.644 q^{20} -4825.25 q^{21} -768.191 q^{22} +2155.21 q^{23} -3377.72 q^{24} +625.000 q^{25} +2809.26 q^{26} -408.482 q^{27} +1784.85 q^{28} +5038.86 q^{29} +3563.87 q^{30} -436.198 q^{31} +2936.79 q^{32} -2716.96 q^{33} +8345.06 q^{34} +5372.33 q^{35} +2169.40 q^{36} +3960.63 q^{37} -2291.87 q^{38} +9935.87 q^{39} +3760.68 q^{40} +8185.36 q^{41} +30634.0 q^{42} +2467.24 q^{43} +1005.00 q^{44} +6529.79 q^{45} -13682.7 q^{46} +17130.2 q^{47} +27412.1 q^{48} +29372.0 q^{49} -3967.93 q^{50} +29515.1 q^{51} -3675.25 q^{52} -23996.2 q^{53} +2593.32 q^{54} +3025.00 q^{55} +32325.8 q^{56} -8105.97 q^{57} -31990.1 q^{58} -31353.1 q^{59} -4662.48 q^{60} +42578.9 q^{61} +2769.28 q^{62} +56128.3 q^{63} +20420.8 q^{64} -11062.4 q^{65} +17249.1 q^{66} +3535.51 q^{67} -10917.6 q^{68} -48393.5 q^{69} -34107.2 q^{70} -34547.2 q^{71} +39290.3 q^{72} +9028.46 q^{73} -25144.8 q^{74} -14033.9 q^{75} +2998.38 q^{76} +26002.1 q^{77} -63079.7 q^{78} +3140.13 q^{79} -30520.0 q^{80} -54297.5 q^{81} -51966.2 q^{82} -42776.4 q^{83} -40077.4 q^{84} -32861.4 q^{85} -15663.8 q^{86} -113144. q^{87} +18201.7 q^{88} +83224.0 q^{89} -41455.6 q^{90} -95089.0 q^{91} +17900.6 q^{92} +9794.47 q^{93} -108754. q^{94} +9025.00 q^{95} -65943.4 q^{96} -42553.9 q^{97} -186474. q^{98} +31604.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more