LMFDB - Embedded newform 1045.6.a.c.1.20

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:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+0.814963 q^{2} -1.30743 q^{3} -31.3358 q^{4} -25.0000 q^{5} -1.06551 q^{6} +233.682 q^{7} -51.6164 q^{8} -241.291 q^{9} +O(q^{10})$	\(q+0.814963 q^{2} -1.30743 q^{3} -31.3358 q^{4} -25.0000 q^{5} -1.06551 q^{6} +233.682 q^{7} -51.6164 q^{8} -241.291 q^{9} -20.3741 q^{10} -121.000 q^{11} +40.9695 q^{12} -526.548 q^{13} +190.442 q^{14} +32.6858 q^{15} +960.681 q^{16} +824.339 q^{17} -196.643 q^{18} -361.000 q^{19} +783.396 q^{20} -305.524 q^{21} -98.6105 q^{22} +1295.48 q^{23} +67.4850 q^{24} +625.000 q^{25} -429.117 q^{26} +633.178 q^{27} -7322.62 q^{28} -3062.55 q^{29} +26.6377 q^{30} -3019.92 q^{31} +2434.64 q^{32} +158.199 q^{33} +671.806 q^{34} -5842.05 q^{35} +7561.04 q^{36} +9311.57 q^{37} -294.202 q^{38} +688.427 q^{39} +1290.41 q^{40} -9039.17 q^{41} -248.991 q^{42} +18247.0 q^{43} +3791.64 q^{44} +6032.27 q^{45} +1055.77 q^{46} -7488.62 q^{47} -1256.03 q^{48} +37800.3 q^{49} +509.352 q^{50} -1077.77 q^{51} +16499.8 q^{52} -11389.4 q^{53} +516.016 q^{54} +3025.00 q^{55} -12061.8 q^{56} +471.983 q^{57} -2495.86 q^{58} +33980.2 q^{59} -1024.24 q^{60} -26375.6 q^{61} -2461.13 q^{62} -56385.3 q^{63} -28757.7 q^{64} +13163.7 q^{65} +128.927 q^{66} -64484.0 q^{67} -25831.4 q^{68} -1693.76 q^{69} -4761.06 q^{70} -34637.0 q^{71} +12454.5 q^{72} +61969.7 q^{73} +7588.59 q^{74} -817.146 q^{75} +11312.2 q^{76} -28275.5 q^{77} +561.042 q^{78} +102631. q^{79} -24017.0 q^{80} +57805.8 q^{81} -7366.59 q^{82} +103414. q^{83} +9573.84 q^{84} -20608.5 q^{85} +14870.7 q^{86} +4004.08 q^{87} +6245.58 q^{88} -88465.5 q^{89} +4916.07 q^{90} -123045. q^{91} -40595.0 q^{92} +3948.35 q^{93} -6102.95 q^{94} +9025.00 q^{95} -3183.13 q^{96} -36291.8 q^{97} +30805.9 q^{98} +29196.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * 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 $

$2$	0.814963	0.144066	0.0720332	−	0.997402i	$-0.477051\pi$
$2$	0.814963	0.144066	0.0720332	+	0.997402i	$0.477051\pi$
$3$	−1.30743	−0.0838719	−0.0419359	−	0.999120i	$-0.513353\pi$
$3$	−1.30743	−0.0838719	−0.0419359	+	0.999120i	$0.513353\pi$
$4$	−31.3358	−0.979245
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−1.06551	−0.0120831
$7$	233.682	1.80252	0.901261	−	0.433277i	$-0.142643\pi$
$7$	233.682	1.80252	0.901261	+	0.433277i	$0.142643\pi$
$8$	−51.6164	−0.285143
$9$	−241.291	−0.992966
$10$	−20.3741	−0.0644285
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	40.9695	0.0821311
$13$	−526.548	−0.864131	−0.432066	−	0.901842i	$-0.642215\pi$
$13$	−526.548	−0.864131	−0.432066	+	0.901842i	$0.642215\pi$
$14$	190.442	0.259683
$15$	32.6858	0.0375087
$16$	960.681	0.938165
$17$	824.339	0.691805	0.345902	−	0.938270i	$-0.387573\pi$
$17$	824.339	0.691805	0.345902	+	0.938270i	$0.387573\pi$
$18$	−196.643	−0.143053
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	783.396	0.437932
$21$	−305.524	−0.151181
$22$	−98.6105	−0.0434377
$23$	1295.48	0.510636	0.255318	−	0.966857i	$-0.417820\pi$
$23$	1295.48	0.510636	0.255318	+	0.966857i	$0.417820\pi$
$24$	67.4850	0.0239155
$25$	625.000	0.200000
$26$	−429.117	−0.124492
$27$	633.178	0.167154
$28$	−7322.62	−1.76511
$29$	−3062.55	−0.676220	−0.338110	−	0.941107i	$-0.609788\pi$
$29$	−3062.55	−0.676220	−0.338110	+	0.941107i	$0.609788\pi$
$30$	26.6377	0.00540374
$31$	−3019.92	−0.564406	−0.282203	−	0.959355i	$-0.591065\pi$
$31$	−3019.92	−0.564406	−0.282203	+	0.959355i	$0.591065\pi$
$32$	2434.64	0.420301
$33$	158.199	0.0252883
$34$	671.806	0.0996659
$35$	−5842.05	−0.806112
$36$	7561.04	0.972356
$37$	9311.57	1.11820	0.559099	−	0.829101i	$-0.311147\pi$
$37$	9311.57	1.11820	0.559099	+	0.829101i	$0.311147\pi$
$38$	−294.202	−0.0330511
$39$	688.427	0.0724763
$40$	1290.41	0.127520
$41$	−9039.17	−0.839786	−0.419893	−	0.907574i	$-0.637932\pi$
$41$	−9039.17	−0.839786	−0.419893	+	0.907574i	$0.637932\pi$
$42$	−248.991	−0.0217801
$43$	18247.0	1.50495	0.752473	−	0.658623i	$-0.228861\pi$
$43$	18247.0	1.50495	0.752473	+	0.658623i	$0.228861\pi$
$44$	3791.64	0.295253
$45$	6032.27	0.444068
$46$	1055.77	0.0735655
$47$	−7488.62	−0.494489	−0.247245	−	0.968953i	$-0.579525\pi$
$47$	−7488.62	−0.494489	−0.247245	+	0.968953i	$0.579525\pi$
$48$	−1256.03	−0.0786857
$49$	37800.3	2.24908
$50$	509.352	0.0288133
$51$	−1077.77	−0.0580230
$52$	16499.8	0.846196
$53$	−11389.4	−0.556943	−0.278471	−	0.960445i	$-0.589828\pi$
$53$	−11389.4	−0.556943	−0.278471	+	0.960445i	$0.589828\pi$
$54$	516.016	0.0240813
$55$	3025.00	0.134840
$56$	−12061.8	−0.513976
$57$	471.983	0.0192415
$58$	−2495.86	−0.0974207
$59$	33980.2	1.27085	0.635427	−	0.772161i	$-0.280824\pi$
$59$	33980.2	1.27085	0.635427	+	0.772161i	$0.280824\pi$
$60$	−1024.24	−0.0367302
$61$	−26375.6	−0.907563	−0.453782	−	0.891113i	$-0.649925\pi$
$61$	−26375.6	−0.907563	−0.453782	+	0.891113i	$0.649925\pi$
$62$	−2461.13	−0.0813120
$63$	−56385.3	−1.78984
$64$	−28757.7	−0.877614
$65$	13163.7	0.386451
$66$	128.927	0.00364320
$67$	−64484.0	−1.75495	−0.877475	−	0.479622i	$-0.840774\pi$
$67$	−64484.0	−1.75495	−0.877475	+	0.479622i	$0.840774\pi$
$68$	−25831.4	−0.677446
$69$	−1693.76	−0.0428280
$70$	−4761.06	−0.116134
$71$	−34637.0	−0.815444	−0.407722	−	0.913106i	$-0.633677\pi$
$71$	−34637.0	−0.815444	−0.407722	+	0.913106i	$0.633677\pi$
$72$	12454.5	0.283137
$73$	61969.7	1.36104	0.680522	−	0.732727i	$-0.261753\pi$
$73$	61969.7	1.36104	0.680522	+	0.732727i	$0.261753\pi$
$74$	7588.59	0.161095
$75$	−817.146	−0.0167744
$76$	11312.2	0.224654
$77$	−28275.5	−0.543481
$78$	561.042	0.0104414
$79$	102631.	1.85017	0.925087	−	0.379756i	$-0.123992\pi$
$79$	102631.	1.85017	0.925087	+	0.379756i	$0.123992\pi$
$80$	−24017.0	−0.419560
$81$	57805.8	0.978946
$82$	−7366.59	−0.120985
$83$	103414.	1.64773	0.823863	−	0.566790i	$-0.191815\pi$
$83$	103414.	1.64773	0.823863	+	0.566790i	$0.191815\pi$
$84$	9573.84	0.148043
$85$	−20608.5	−0.309385
$86$	14870.7	0.216812
$87$	4004.08	0.0567159
$88$	6245.58	0.0859738
$89$	−88465.5	−1.18386	−0.591928	−	0.805991i	$-0.701633\pi$
$89$	−88465.5	−1.18386	−0.591928	+	0.805991i	$0.701633\pi$
$90$	4916.07	0.0639753
$91$	−123045.	−1.55762
$92$	−40595.0	−0.500038
$93$	3948.35	0.0473378
$94$	−6102.95	−0.0712393
$95$	9025.00	0.102598
$96$	−3183.13	−0.0352514
$97$	−36291.8	−0.391633	−0.195817	−	0.980641i	$-0.562736\pi$
$97$	−36291.8	−0.391633	−0.195817	+	0.980641i	$0.562736\pi$
$98$	30805.9	0.324017
$99$	29196.2	0.299390
$100$	−19584.9	−0.195849
$101$	12492.5	0.121856	0.0609279	−	0.998142i	$-0.480594\pi$
$101$	12492.5	0.121856	0.0609279	+	0.998142i	$0.480594\pi$
$102$	−878.341	−0.00835917
$103$	19556.2	0.181631	0.0908156	−	0.995868i	$-0.471053\pi$
$103$	19556.2	0.181631	0.0908156	+	0.995868i	$0.471053\pi$
$104$	27178.5	0.246401
$105$	7638.10	0.0676101
$106$	−9281.92	−0.0802368
$107$	173127.	1.46186	0.730930	−	0.682453i	$-0.239087\pi$
$107$	173127.	1.46186	0.730930	+	0.682453i	$0.239087\pi$
$108$	−19841.2	−0.163684
$109$	176009.	1.41896	0.709478	−	0.704727i	$-0.248931\pi$
$109$	176009.	1.41896	0.709478	+	0.704727i	$0.248931\pi$
$110$	2465.26	0.0194259
$111$	−12174.3	−0.0937854
$112$	224494.	1.69106
$113$	−56561.3	−0.416700	−0.208350	−	0.978054i	$-0.566809\pi$
$113$	−56561.3	−0.416700	−0.208350	+	0.978054i	$0.566809\pi$
$114$	384.649	0.00277206
$115$	−32387.0	−0.228363
$116$	95967.6	0.662185
$117$	127051.	0.858053
$118$	27692.6	0.183088
$119$	192633.	1.24699
$120$	−1687.12	−0.0106953
$121$	14641.0	0.0909091
$122$	−21495.1	−0.130749
$123$	11818.1	0.0704345
$124$	94631.8	0.552692
$125$	−15625.0	−0.0894427
$126$	−45951.9	−0.257856
$127$	−236485.	−1.30105	−0.650524	−	0.759485i	$-0.725451\pi$
$127$	−236485.	−1.30105	−0.650524	+	0.759485i	$0.725451\pi$
$128$	−101345.	−0.546736
$129$	−23856.8	−0.126223
$130$	10727.9	0.0556747
$131$	−310568.	−1.58117	−0.790585	−	0.612352i	$-0.790224\pi$
$131$	−310568.	−1.58117	−0.790585	+	0.612352i	$0.790224\pi$
$132$	−4957.31	−0.0247635
$133$	−84359.2	−0.413527
$134$	−52552.1	−0.252829
$135$	−15829.4	−0.0747535
$136$	−42549.4	−0.197263
$137$	98917.8	0.450270	0.225135	−	0.974328i	$-0.427718\pi$
$137$	98917.8	0.450270	0.225135	+	0.974328i	$0.427718\pi$
$138$	−1380.35	−0.00617008
$139$	−107645.	−0.472558	−0.236279	−	0.971685i	$-0.575928\pi$
$139$	−107645.	−0.472558	−0.236279	+	0.971685i	$0.575928\pi$
$140$	183066.	0.789381
$141$	9790.87	0.0414738
$142$	−28227.9	−0.117478
$143$	63712.3	0.260545
$144$	−231803.	−0.931566
$145$	76563.8	0.302415
$146$	50503.0	0.196081
$147$	−49421.4	−0.188635
$148$	−291786.	−1.09499
$149$	432252.	1.59504	0.797520	−	0.603293i	$-0.206145\pi$
$149$	432252.	1.59504	0.797520	+	0.603293i	$0.206145\pi$
$150$	−665.944	−0.00241663
$151$	−221540.	−0.790696	−0.395348	−	0.918531i	$-0.629376\pi$
$151$	−221540.	−0.790696	−0.395348	+	0.918531i	$0.629376\pi$
$152$	18633.5	0.0654162
$153$	−198905.	−0.686938
$154$	−23043.5	−0.0782973
$155$	75498.1	0.252410
$156$	−21572.4	−0.0709721
$157$	−326863.	−1.05832	−0.529159	−	0.848523i	$-0.677492\pi$
$157$	−326863.	−1.05832	−0.529159	+	0.848523i	$0.677492\pi$
$158$	83640.8	0.266548
$159$	14890.9	0.0467118
$160$	−60866.1	−0.187964
$161$	302731.	0.920432
$162$	47109.6	0.141033
$163$	156404.	0.461082	0.230541	−	0.973063i	$-0.425950\pi$
$163$	156404.	0.461082	0.230541	+	0.973063i	$0.425950\pi$
$164$	283250.	0.822356
$165$	−3954.99	−0.0113093
$166$	84278.7	0.237382
$167$	−416387.	−1.15533	−0.577665	−	0.816274i	$-0.696036\pi$
$167$	−416387.	−1.15533	−0.577665	+	0.816274i	$0.696036\pi$
$168$	15770.0	0.0431081
$169$	−94039.9	−0.253277
$170$	−16795.1	−0.0445719
$171$	87105.9	0.227802
$172$	−571786.	−1.47371
$173$	−512183.	−1.30110	−0.650549	−	0.759464i	$-0.725461\pi$
$173$	−512183.	−1.30110	−0.650549	+	0.759464i	$0.725461\pi$
$174$	3263.18	0.00817086
$175$	146051.	0.360504
$176$	−116242.	−0.282867
$177$	−44426.9	−0.106589
$178$	−72096.1	−0.170554
$179$	−327960.	−0.765046	−0.382523	−	0.923946i	$-0.624945\pi$
$179$	−327960.	−0.765046	−0.382523	+	0.923946i	$0.624945\pi$
$180$	−189026.	−0.434851
$181$	−263104.	−0.596942	−0.298471	−	0.954419i	$-0.596477\pi$
$181$	−263104.	−0.596942	−0.298471	+	0.954419i	$0.596477\pi$
$182$	−100277.	−0.224400
$183$	34484.3	0.0761191
$184$	−66868.0	−0.145604
$185$	−232789.	−0.500073
$186$	3217.76	0.00681979
$187$	−99745.0	−0.208587
$188$	234662.	0.484226
$189$	147962.	0.301298
$190$	7355.04	0.0147809
$191$	64400.9	0.127735	0.0638673	−	0.997958i	$-0.479657\pi$
$191$	64400.9	0.127735	0.0638673	+	0.997958i	$0.479657\pi$
$192$	37598.7	0.0736072
$193$	−572298.	−1.10593	−0.552967	−	0.833203i	$-0.686504\pi$
$193$	−572298.	−1.10593	−0.552967	+	0.833203i	$0.686504\pi$
$194$	−29576.5	−0.0564212
$195$	−17210.7	−0.0324124
$196$	−1.18450e6	−2.20240
$197$	−1.01224e6	−1.85830	−0.929152	−	0.369699i	$-0.879461\pi$
$197$	−1.01224e6	−1.85830	−0.929152	+	0.369699i	$0.879461\pi$
$198$	23793.8	0.0431321
$199$	509339.	0.911747	0.455873	−	0.890045i	$-0.349327\pi$
$199$	509339.	0.911747	0.455873	+	0.890045i	$0.349327\pi$
$200$	−32260.2	−0.0570286
$201$	84308.5	0.147191
$202$	10180.9	0.0175553
$203$	−715663.	−1.21890
$204$	33772.8	0.0568187
$205$	225979.	0.375564
$206$	15937.5	0.0261670
$207$	−312587.	−0.507044
$208$	−505845.	−0.810698
$209$	43681.0	0.0691714
$210$	6224.76	0.00974035
$211$	−701909.	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$211$	−701909.	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$212$	356896.	0.545383
$213$	45285.5	0.0683928
$214$	141092.	0.210605
$215$	−456176.	−0.673033
$216$	−32682.3	−0.0476627
$217$	−705702.	−1.01735
$218$	143441.	0.204424
$219$	−81021.3	−0.114153
$220$	−94790.9	−0.132041
$221$	−434054.	−0.597810
$222$	−9921.57	−0.0135113
$223$	−49228.2	−0.0662906	−0.0331453	−	0.999451i	$-0.510552\pi$
$223$	−49228.2	−0.0662906	−0.0331453	+	0.999451i	$0.510552\pi$
$224$	568933.	0.757601
$225$	−150807.	−0.198593
$226$	−46095.4	−0.0600325
$227$	−385541.	−0.496600	−0.248300	−	0.968683i	$-0.579872\pi$
$227$	−385541.	−0.496600	−0.248300	+	0.968683i	$0.579872\pi$
$228$	−14790.0	−0.0188422
$229$	−123074.	−0.155088	−0.0775441	−	0.996989i	$-0.524708\pi$
$229$	−123074.	−0.155088	−0.0775441	+	0.996989i	$0.524708\pi$
$230$	−26394.2	−0.0328995
$231$	36968.4	0.0455827
$232$	158078.	0.192819
$233$	−1.29520e6	−1.56296	−0.781478	−	0.623932i	$-0.785534\pi$
$233$	−1.29520e6	−1.56296	−0.781478	+	0.623932i	$0.785534\pi$
$234$	103542.	0.123617
$235$	187215.	0.221142
$236$	−1.06480e6	−1.24448
$237$	−134184.	−0.155178
$238$	156989.	0.179650
$239$	1.21039e6	1.37067	0.685333	−	0.728230i	$-0.259657\pi$
$239$	1.21039e6	1.37067	0.685333	+	0.728230i	$0.259657\pi$
$240$	31400.7	0.0351893
$241$	−873457.	−0.968722	−0.484361	−	0.874868i	$-0.660948\pi$
$241$	−873457.	−0.968722	−0.484361	+	0.874868i	$0.660948\pi$
$242$	11931.9	0.0130969
$243$	−229439.	−0.249260
$244$	826500.	0.888727
$245$	−945008.	−1.00582
$246$	9631.32	0.0101472
$247$	190084.	0.198245
$248$	155877.	0.160936
$249$	−135207.	−0.138198
$250$	−12733.8	−0.0128857
$251$	−657220.	−0.658456	−0.329228	−	0.944251i	$-0.606788\pi$
$251$	−657220.	−0.658456	−0.329228	+	0.944251i	$0.606788\pi$
$252$	1.76688e6	1.75269
$253$	−156753.	−0.153963
$254$	−192726.	−0.187437
$255$	26944.2	0.0259487
$256$	837653.	0.798848
$257$	−1.17245e6	−1.10729	−0.553646	−	0.832752i	$-0.686764\pi$
$257$	−1.17245e6	−1.10729	−0.553646	+	0.832752i	$0.686764\pi$
$258$	−19442.4	−0.0181845
$259$	2.17595e6	2.01558
$260$	−412496.	−0.378430
$261$	738965.	0.671463
$262$	−253102.	−0.227794
$263$	−630350.	−0.561943	−0.280972	−	0.959716i	$-0.590657\pi$
$263$	−630350.	−0.561943	−0.280972	+	0.959716i	$0.590657\pi$
$264$	−8165.68	−0.00721078
$265$	284735.	0.249072
$266$	−68749.7	−0.0595753
$267$	115663.	0.0992922
$268$	2.02066e6	1.71853
$269$	−922891.	−0.777624	−0.388812	−	0.921317i	$-0.627114\pi$
$269$	−922891.	−0.777624	−0.388812	+	0.921317i	$0.627114\pi$
$270$	−12900.4	−0.0107695
$271$	1.25562e6	1.03857	0.519286	−	0.854600i	$-0.326198\pi$
$271$	1.25562e6	1.03857	0.519286	+	0.854600i	$0.326198\pi$
$272$	791927.	0.649027
$273$	160873.	0.130640
$274$	80614.3	0.0648688
$275$	−75625.0	−0.0603023
$276$	53075.2	0.0419391
$277$	−80012.5	−0.0626554	−0.0313277	−	0.999509i	$-0.509974\pi$
$277$	−80012.5	−0.0626554	−0.0313277	+	0.999509i	$0.509974\pi$
$278$	−87726.4	−0.0680798
$279$	728679.	0.560436
$280$	301545.	0.229857
$281$	83572.6	0.0631390	0.0315695	−	0.999502i	$-0.489949\pi$
$281$	83572.6	0.0631390	0.0315695	+	0.999502i	$0.489949\pi$
$282$	7979.20	0.00597498
$283$	−2.21290e6	−1.64247	−0.821233	−	0.570593i	$-0.806713\pi$
$283$	−2.21290e6	−1.64247	−0.821233	+	0.570593i	$0.806713\pi$
$284$	1.08538e6	0.798519
$285$	−11799.6	−0.00860508
$286$	51923.2	0.0375359
$287$	−2.11229e6	−1.51373
$288$	−587457.	−0.417344
$289$	−740322.	−0.521406
$290$	62396.6	0.0435678
$291$	47449.2	0.0328470
$292$	−1.94187e6	−1.33280
$293$	−636918.	−0.433425	−0.216713	−	0.976235i	$-0.569533\pi$
$293$	−636918.	−0.433425	−0.216713	+	0.976235i	$0.569533\pi$
$294$	−40276.6	−0.0271759
$295$	−849505.	−0.568344
$296$	−480630.	−0.318846
$297$	−76614.5	−0.0503988
$298$	352269.	0.229792
$299$	−682133.	−0.441257
$300$	25606.0	0.0164262
$301$	4.26401e6	2.71270
$302$	−180547.	−0.113913
$303$	−16333.1	−0.0102203
$304$	−346806.	−0.215230
$305$	659389.	0.405875
$306$	−162100.	−0.0989648
$307$	410610.	0.248647	0.124324	−	0.992242i	$-0.460324\pi$
$307$	410610.	0.248647	0.124324	+	0.992242i	$0.460324\pi$
$308$	886038.	0.532201
$309$	−25568.4	−0.0152338
$310$	61528.2	0.0363638
$311$	−1.26966e6	−0.744365	−0.372183	−	0.928159i	$-0.621391\pi$
$311$	−1.26966e6	−0.744365	−0.372183	+	0.928159i	$0.621391\pi$
$312$	−35534.1	−0.0206661
$313$	259461.	0.149697	0.0748483	−	0.997195i	$-0.476153\pi$
$313$	259461.	0.149697	0.0748483	+	0.997195i	$0.476153\pi$
$314$	−266381.	−0.152468
$315$	1.40963e6	0.800441
$316$	−3.21604e6	−1.81177
$317$	1.68376e6	0.941094	0.470547	−	0.882375i	$-0.344057\pi$
$317$	1.68376e6	0.941094	0.470547	+	0.882375i	$0.344057\pi$
$318$	12135.5	0.00672961
$319$	370569.	0.203888
$320$	718941.	0.392481
$321$	−226352.	−0.122609
$322$	246714.	0.132603
$323$	−297586.	−0.158711
$324$	−1.81139e6	−0.958628
$325$	−329093.	−0.172826
$326$	127463.	0.0664265
$327$	−230120.	−0.119011
$328$	466569.	0.239459
$329$	−1.74996e6	−0.891328
$330$	−3223.17	−0.00162929
$331$	2.90614e6	1.45796	0.728980	−	0.684535i	$-0.239995\pi$
$331$	2.90614e6	1.45796	0.728980	+	0.684535i	$0.239995\pi$
$332$	−3.24057e6	−1.61353
$333$	−2.24680e6	−1.11033
$334$	−339340.	−0.166444
$335$	1.61210e6	0.784838
$336$	−293511.	−0.141833
$337$	−914141.	−0.438468	−0.219234	−	0.975672i	$-0.570356\pi$
$337$	−914141.	−0.438468	−0.219234	+	0.975672i	$0.570356\pi$
$338$	−76639.1	−0.0364887
$339$	73950.2	0.0349494
$340$	645784.	0.302963
$341$	365411.	0.170175
$342$	70988.1	0.0328186
$343$	4.90577e6	2.25150
$344$	−941845.	−0.429125
$345$	42343.9	0.0191533
$346$	−417410.	−0.187445
$347$	−2.16764e6	−0.966414	−0.483207	−	0.875506i	$-0.660528\pi$
$347$	−2.16764e6	−0.966414	−0.483207	+	0.875506i	$0.660528\pi$
$348$	−125471.	−0.0555387
$349$	1.16608e6	0.512467	0.256234	−	0.966615i	$-0.417518\pi$
$349$	1.16608e6	0.512467	0.256234	+	0.966615i	$0.417518\pi$
$350$	119026.	0.0519366
$351$	−333399.	−0.144443
$352$	−294592.	−0.126725
$353$	−199707.	−0.0853015	−0.0426508	−	0.999090i	$-0.513580\pi$
$353$	−199707.	−0.0853015	−0.0426508	+	0.999090i	$0.513580\pi$
$354$	−36206.2	−0.0153559
$355$	865924.	0.364678
$356$	2.77214e6	1.15928
$357$	−251855.	−0.104588
$358$	−267275.	−0.110218
$359$	1.86741e6	0.764720	0.382360	−	0.924013i	$-0.375111\pi$
$359$	1.86741e6	0.764720	0.382360	+	0.924013i	$0.375111\pi$
$360$	−311364.	−0.126623
$361$	130321.	0.0526316
$362$	−214420.	−0.0859992
$363$	−19142.1	−0.00762472
$364$	3.85572e6	1.52529
$365$	−1.54924e6	−0.608678
$366$	28103.4	0.0109662
$367$	2.47863e6	0.960607	0.480304	−	0.877102i	$-0.340526\pi$
$367$	2.47863e6	0.960607	0.480304	+	0.877102i	$0.340526\pi$
$368$	1.24454e6	0.479061
$369$	2.18107e6	0.833879
$370$	−189715.	−0.0720438
$371$	−2.66150e6	−1.00390
$372$	−123725.	−0.0463553
$373$	−2.95092e6	−1.09821	−0.549106	−	0.835753i	$-0.685032\pi$
$373$	−2.95092e6	−1.09821	−0.549106	+	0.835753i	$0.685032\pi$
$374$	−81288.5	−0.0300504
$375$	20428.6	0.00750173
$376$	386535.	0.141000
$377$	1.61258e6	0.584343
$378$	120584.	0.0434070
$379$	−1.03046e6	−0.368498	−0.184249	−	0.982880i	$-0.558985\pi$
$379$	−1.03046e6	−0.368498	−0.184249	+	0.982880i	$0.558985\pi$
$380$	−282806.	−0.100468
$381$	309188.	0.109121
$382$	52484.3	0.0184023
$383$	−4.26937e6	−1.48719	−0.743596	−	0.668630i	$-0.766881\pi$
$383$	−4.26937e6	−1.48719	−0.743596	+	0.668630i	$0.766881\pi$
$384$	132502.	0.0458558
$385$	706888.	0.243052
$386$	−466402.	−0.159328
$387$	−4.40284e6	−1.49436
$388$	1.13724e6	0.383505
$389$	1.55480e6	0.520954	0.260477	−	0.965480i	$-0.416120\pi$
$389$	1.55480e6	0.520954	0.260477	+	0.965480i	$0.416120\pi$
$390$	−14026.1	−0.00466954
$391$	1.06792e6	0.353261
$392$	−1.95112e6	−0.641310
$393$	406047.	0.132616
$394$	−824935.	−0.267719
$395$	−2.56578e6	−0.827423
$396$	−914886.	−0.293176
$397$	−2.28163e6	−0.726556	−0.363278	−	0.931681i	$-0.618343\pi$
$397$	−2.28163e6	−0.726556	−0.363278	+	0.931681i	$0.618343\pi$
$398$	415092.	0.131352
$399$	110294.	0.0346833
$400$	600426.	0.187633
$401$	−2.01816e6	−0.626750	−0.313375	−	0.949629i	$-0.601460\pi$
$401$	−2.01816e6	−0.626750	−0.313375	+	0.949629i	$0.601460\pi$
$402$	68708.3	0.0212053
$403$	1.59014e6	0.487721
$404$	−391463.	−0.119327
$405$	−1.44514e6	−0.437798
$406$	−583239.	−0.175603
$407$	−1.12670e6	−0.337149
$408$	55630.5	0.0165448
$409$	−5.12778e6	−1.51573	−0.757863	−	0.652413i	$-0.773757\pi$
$409$	−5.12778e6	−1.51573	−0.757863	+	0.652413i	$0.773757\pi$
$410$	184165.	0.0541062
$411$	−129328.	−0.0377650
$412$	−612808.	−0.177861
$413$	7.94057e6	2.29074
$414$	−254747.	−0.0730480
$415$	−2.58535e6	−0.736885
$416$	−1.28196e6	−0.363195
$417$	140738.	0.0396344
$418$	35598.4	0.00996528
$419$	1.03188e6	0.287142	0.143571	−	0.989640i	$-0.454142\pi$
$419$	1.03188e6	0.287142	0.143571	+	0.989640i	$0.454142\pi$
$420$	−239346.	−0.0662069
$421$	−1.45616e6	−0.400409	−0.200204	−	0.979754i	$-0.564161\pi$
$421$	−1.45616e6	−0.400409	−0.200204	+	0.979754i	$0.564161\pi$
$422$	−572030.	−0.156364
$423$	1.80693e6	0.491011
$424$	587878.	0.158808
$425$	515212.	0.138361
$426$	36906.0	0.00985311
$427$	−6.16349e6	−1.63590
$428$	−5.42508e6	−1.43152
$429$	−83299.6	−0.0218524
$430$	−371766.	−0.0969614
$431$	3.76123e6	0.975297	0.487649	−	0.873040i	$-0.337855\pi$
$431$	3.76123e6	0.975297	0.487649	+	0.873040i	$0.337855\pi$
$432$	608282.	0.156818
$433$	−3.84419e6	−0.985337	−0.492668	−	0.870217i	$-0.663978\pi$
$433$	−3.84419e6	−0.985337	−0.492668	+	0.870217i	$0.663978\pi$
$434$	−575121.	−0.146567
$435$	−100102.	−0.0253641
$436$	−5.51540e6	−1.38951
$437$	−467669.	−0.117148
$438$	−66029.3	−0.0164457
$439$	−1.22775e6	−0.304052	−0.152026	−	0.988376i	$-0.548580\pi$
$439$	−1.22775e6	−0.304052	−0.152026	+	0.988376i	$0.548580\pi$
$440$	−156139.	−0.0384486
$441$	−9.12086e6	−2.23326
$442$	−353738.	−0.0861244
$443$	4.89598e6	1.18530	0.592652	−	0.805458i	$-0.298081\pi$
$443$	4.89598e6	1.18530	0.592652	+	0.805458i	$0.298081\pi$
$444$	381491.	0.0918389
$445$	2.21164e6	0.529436
$446$	−40119.2	−0.00955025
$447$	−565141.	−0.133779
$448$	−6.72015e6	−1.58192
$449$	2.77820e6	0.650350	0.325175	−	0.945654i	$-0.394577\pi$
$449$	2.77820e6	0.650350	0.325175	+	0.945654i	$0.394577\pi$
$450$	−122902.	−0.0286106
$451$	1.09374e6	0.253205
$452$	1.77240e6	0.408051
$453$	289649.	0.0663172
$454$	−314202.	−0.0715433
$455$	3.07612e6	0.696587
$456$	−24362.1	−0.00548658
$457$	5.72398e6	1.28206	0.641029	−	0.767517i	$-0.278508\pi$
$457$	5.72398e6	1.28206	0.641029	+	0.767517i	$0.278508\pi$
$458$	−100301.	−0.0223430
$459$	521953.	0.115638
$460$	1.01487e6	0.223624
$461$	−6.31106e6	−1.38309	−0.691544	−	0.722334i	$-0.743069\pi$
$461$	−6.31106e6	−1.38309	−0.691544	+	0.722334i	$0.743069\pi$
$462$	30127.9	0.00656694
$463$	1.97905e6	0.429047	0.214524	−	0.976719i	$-0.431180\pi$
$463$	1.97905e6	0.429047	0.214524	+	0.976719i	$0.431180\pi$
$464$	−2.94213e6	−0.634406
$465$	−98708.8	−0.0211701
$466$	−1.05554e6	−0.225170
$467$	−299017.	−0.0634460	−0.0317230	−	0.999497i	$-0.510099\pi$
$467$	−299017.	−0.0634460	−0.0317230	+	0.999497i	$0.510099\pi$
$468$	−3.98125e6	−0.840244
$469$	−1.50688e7	−3.16334
$470$	152574.	0.0318592
$471$	427351.	0.0887631
$472$	−1.75393e6	−0.362375
$473$	−2.20789e6	−0.453758
$474$	−109355.	−0.0223559
$475$	−225625.	−0.0458831
$476$	−6.03633e6	−1.22111
$477$	2.74815e6	0.553025
$478$	986425.	0.197467
$479$	6.09112e6	1.21299	0.606496	−	0.795086i	$-0.292574\pi$
$479$	6.09112e6	1.21299	0.606496	+	0.795086i	$0.292574\pi$
$480$	79578.3	0.0157649
$481$	−4.90299e6	−0.966270
$482$	−711835.	−0.139560
$483$	−395800.	−0.0771984
$484$	−458788.	−0.0890223
$485$	907296.	0.175144
$486$	−186985.	−0.0359100
$487$	7.72556e6	1.47607	0.738036	−	0.674761i	$-0.235753\pi$
$487$	7.72556e6	1.47607	0.738036	+	0.674761i	$0.235753\pi$
$488$	1.36141e6	0.258785
$489$	−204488.	−0.0386718
$490$	−770147.	−0.144905
$491$	−1.01093e6	−0.189242	−0.0946211	−	0.995513i	$-0.530164\pi$
$491$	−1.01093e6	−0.189242	−0.0946211	+	0.995513i	$0.530164\pi$
$492$	−370330.	−0.0689726
$493$	−2.52458e6	−0.467813
$494$	154911.	0.0285605
$495$	−729904.	−0.133891
$496$	−2.90118e6	−0.529506
$497$	−8.09404e6	−1.46986
$498$	−110189.	−0.0199097
$499$	2.57115e6	0.462248	0.231124	−	0.972924i	$-0.425760\pi$
$499$	2.57115e6	0.462248	0.231124	+	0.972924i	$0.425760\pi$
$500$	489622.	0.0875863
$501$	544398.	0.0968997
$502$	−535610.	−0.0948613
$503$	−462533.	−0.0815122	−0.0407561	−	0.999169i	$-0.512977\pi$
$503$	−462533.	−0.0815122	−0.0407561	+	0.999169i	$0.512977\pi$
$504$	2.91040e6	0.510360
$505$	−312313.	−0.0544956
$506$	−127748.	−0.0221808
$507$	122951.	0.0212428
$508$	7.41044e6	1.27405
$509$	−8.36609e6	−1.43129	−0.715646	−	0.698464i	$-0.753867\pi$
$509$	−8.36609e6	−1.43129	−0.715646	+	0.698464i	$0.753867\pi$
$510$	21958.5	0.00373833
$511$	1.44812e7	2.45331
$512$	3.92570e6	0.661823
$513$	−228577.	−0.0383477
$514$	−955504.	−0.159523
$515$	−488904.	−0.0812279
$516$	747572.	0.123603
$517$	906123.	0.149094
$518$	1.77332e6	0.290377
$519$	669646.	0.109126
$520$	−679463.	−0.110194
$521$	2.95413e6	0.476799	0.238400	−	0.971167i	$-0.423377\pi$
$521$	2.95413e6	0.476799	0.238400	+	0.971167i	$0.423377\pi$
$522$	602229.	0.0967354
$523$	8.12566e6	1.29899	0.649493	−	0.760368i	$-0.274981\pi$
$523$	8.12566e6	1.29899	0.649493	+	0.760368i	$0.274981\pi$
$524$	9.73191e6	1.54835
$525$	−190952.	−0.0302362
$526$	−513712.	−0.0809572
$527$	−2.48944e6	−0.390459
$528$	151979.	0.0237246
$529$	−4.75807e6	−0.739251
$530$	232048.	0.0358830
$531$	−8.19910e6	−1.26192
$532$	2.64347e6	0.404944
$533$	4.75956e6	0.725686
$534$	94260.8	0.0143047
$535$	−4.32818e6	−0.653764
$536$	3.32843e6	0.500411
$537$	428785.	0.0641659
$538$	−752122.	−0.112030
$539$	−4.57384e6	−0.678124
$540$	496029.	0.0732019
$541$	7.12913e6	1.04723	0.523617	−	0.851954i	$-0.324582\pi$
$541$	7.12913e6	1.04723	0.523617	+	0.851954i	$0.324582\pi$
$542$	1.02329e6	0.149623
$543$	343992.	0.0500666
$544$	2.00697e6	0.290766
$545$	−4.40023e6	−0.634577
$546$	131106.	0.0188209
$547$	1.32861e7	1.89859	0.949294	−	0.314390i	$-0.101800\pi$
$547$	1.32861e7	1.89859	0.949294	+	0.314390i	$0.101800\pi$
$548$	−3.09967e6	−0.440925
$549$	6.36417e6	0.901179
$550$	−61631.6	−0.00868753
$551$	1.10558e6	0.155136
$552$	87425.5	0.0122121
$553$	2.39831e7	3.33498
$554$	−65207.2	−0.00902654
$555$	304357.	0.0419421
$556$	3.37313e6	0.462750
$557$	−1.06428e7	−1.45352	−0.726758	−	0.686894i	$-0.758974\pi$
$557$	−1.06428e7	−1.45352	−0.726758	+	0.686894i	$0.758974\pi$
$558$	593847.	0.0807400
$559$	−9.60794e6	−1.30047
$560$	−5.61235e6	−0.756266
$561$	130410.	0.0174946
$562$	68108.5	0.00909621
$563$	−1.09240e7	−1.45248	−0.726239	−	0.687442i	$-0.758733\pi$
$563$	−1.09240e7	−1.45248	−0.726239	+	0.687442i	$0.758733\pi$
$564$	−306805.	−0.0406130
$565$	1.41403e6	0.186354
$566$	−1.80343e6	−0.236624
$567$	1.35082e7	1.76457
$568$	1.78783e6	0.232518
$569$	−9.81653e6	−1.27109	−0.635546	−	0.772063i	$-0.719225\pi$
$569$	−9.81653e6	−1.27109	−0.635546	+	0.772063i	$0.719225\pi$
$570$	−9616.23	−0.00123970
$571$	731692.	0.0939157	0.0469578	−	0.998897i	$-0.485047\pi$
$571$	731692.	0.0939157	0.0469578	+	0.998897i	$0.485047\pi$
$572$	−1.99648e6	−0.255138
$573$	−84199.9	−0.0107133
$574$	−1.72144e6	−0.218078
$575$	809676.	0.102127
$576$	6.93895e6	0.871441
$577$	−1.45867e7	−1.82397	−0.911986	−	0.410220i	$-0.865452\pi$
$577$	−1.45867e7	−1.82397	−0.911986	+	0.410220i	$0.865452\pi$
$578$	−603335.	−0.0751171
$579$	748242.	0.0927568
$580$	−2.39919e6	−0.296138
$581$	2.41660e7	2.97006
$582$	38669.3	0.00473216
$583$	1.37812e6	0.167925
$584$	−3.19865e6	−0.388092
$585$	−3.17628e6	−0.383733
$586$	−519064.	−0.0624420
$587$	1.26167e6	0.151130	0.0755648	−	0.997141i	$-0.475924\pi$
$587$	1.26167e6	0.151130	0.0755648	+	0.997141i	$0.475924\pi$
$588$	1.54866e6	0.184720
$589$	1.09019e6	0.129484
$590$	−692315.	−0.0818792
$591$	1.32343e6	0.155859
$592$	8.94546e6	1.04905
$593$	9.47697e6	1.10671	0.553354	−	0.832946i	$-0.313348\pi$
$593$	9.47697e6	1.10671	0.553354	+	0.832946i	$0.313348\pi$
$594$	−62438.0	−0.00726077
$595$	−4.81583e6	−0.557672
$596$	−1.35450e7	−1.56193
$597$	−665927.	−0.0764699
$598$	−555913.	−0.0635703
$599$	−2.70493e6	−0.308028	−0.154014	−	0.988069i	$-0.549220\pi$
$599$	−2.70493e6	−0.308028	−0.154014	+	0.988069i	$0.549220\pi$
$600$	42178.1	0.00478309
$601$	−3.38751e6	−0.382555	−0.191278	−	0.981536i	$-0.561263\pi$
$601$	−3.38751e6	−0.382555	−0.191278	+	0.981536i	$0.561263\pi$
$602$	3.47501e6	0.390809
$603$	1.55594e7	1.74261
$604$	6.94214e6	0.774285
$605$	−366025.	−0.0406558
$606$	−13310.9	−0.00147240
$607$	−5.38371e6	−0.593076	−0.296538	−	0.955021i	$-0.595832\pi$
$607$	−5.38371e6	−0.593076	−0.296538	+	0.955021i	$0.595832\pi$
$608$	−878906.	−0.0964236
$609$	935682.	0.102232
$610$	537377.	0.0584729
$611$	3.94312e6	0.427304
$612$	6.23286e6	0.672681
$613$	6.10707e6	0.656420	0.328210	−	0.944605i	$-0.393555\pi$
$613$	6.10707e6	0.656420	0.328210	+	0.944605i	$0.393555\pi$
$614$	334632.	0.0358217
$615$	−295453.	−0.0314993
$616$	1.45948e6	0.154970
$617$	1.29314e7	1.36751	0.683757	−	0.729709i	$-0.260345\pi$
$617$	1.29314e7	1.36751	0.683757	+	0.729709i	$0.260345\pi$
$618$	−20837.3	−0.00219467
$619$	6.43505e6	0.675034	0.337517	−	0.941319i	$-0.390413\pi$
$619$	6.43505e6	0.675034	0.337517	+	0.941319i	$0.390413\pi$
$620$	−2.36580e6	−0.247171
$621$	820270.	0.0853548
$622$	−1.03473e6	−0.107238
$623$	−2.06728e7	−2.13392
$624$	661359.	0.0679948
$625$	390625.	0.0400000
$626$	211451.	0.0215663
$627$	−57110.0	−0.00580154
$628$	1.02425e7	1.03635
$629$	7.67589e6	0.773575
$630$	1.14880e6	0.115317
$631$	1.21805e7	1.21784	0.608921	−	0.793231i	$-0.291602\pi$
$631$	1.21805e7	1.21784	0.608921	+	0.793231i	$0.291602\pi$
$632$	−5.29746e6	−0.527564
$633$	917699.	0.0910314
$634$	1.37221e6	0.135580
$635$	5.91211e6	0.581847
$636$	−466618.	−0.0457423
$637$	−1.99037e7	−1.94350
$638$	302000.	0.0293734
$639$	8.35758e6	0.809708
$640$	2.53362e6	0.244508
$641$	−9.28308e6	−0.892375	−0.446187	−	0.894940i	$-0.647218\pi$
$641$	−9.28308e6	−0.892375	−0.446187	+	0.894940i	$0.647218\pi$
$642$	−184469.	−0.0176638
$643$	−8.28126e6	−0.789894	−0.394947	−	0.918704i	$-0.629237\pi$
$643$	−8.28126e6	−0.789894	−0.394947	+	0.918704i	$0.629237\pi$
$644$	−9.48632e6	−0.901329
$645$	596420.	0.0564485
$646$	−242522.	−0.0228649
$647$	4.84699e6	0.455209	0.227605	−	0.973754i	$-0.426911\pi$
$647$	4.84699e6	0.455209	0.227605	+	0.973754i	$0.426911\pi$
$648$	−2.98372e6	−0.279139
$649$	−4.11160e6	−0.383177
$650$	−268198.	−0.0248985
$651$	922659.	0.0853274
$652$	−4.90104e6	−0.451512
$653$	−1.28917e7	−1.18311	−0.591556	−	0.806264i	$-0.701486\pi$
$653$	−1.28917e7	−1.18311	−0.591556	+	0.806264i	$0.701486\pi$
$654$	−187540.	−0.0171454
$655$	7.76421e6	0.707121
$656$	−8.68376e6	−0.787858
$657$	−1.49527e7	−1.35147
$658$	−1.42615e6	−0.128410
$659$	1.17197e7	1.05124	0.525621	−	0.850719i	$-0.323833\pi$
$659$	1.17197e7	1.05124	0.525621	+	0.850719i	$0.323833\pi$
$660$	123933.	0.0110746
$661$	1.98017e6	0.176278	0.0881391	−	0.996108i	$-0.471908\pi$
$661$	1.98017e6	0.176278	0.0881391	+	0.996108i	$0.471908\pi$
$662$	2.36839e6	0.210043
$663$	567497.	0.0501395
$664$	−5.33786e6	−0.469837
$665$	2.10898e6	0.184935
$666$	−1.83105e6	−0.159962
$667$	−3.96748e6	−0.345303
$668$	1.30478e7	1.13135
$669$	64362.6	0.00555992
$670$	1.31380e6	0.113069
$671$	3.19144e6	0.273641
$672$	−743841.	−0.0635415
$673$	−1.05466e7	−0.897587	−0.448793	−	0.893636i	$-0.648146\pi$
$673$	−1.05466e7	−0.897587	−0.448793	+	0.893636i	$0.648146\pi$
$674$	−744991.	−0.0631686
$675$	395736.	0.0334308
$676$	2.94682e6	0.248020
$677$	−1.16282e7	−0.975082	−0.487541	−	0.873100i	$-0.662106\pi$
$677$	−1.16282e7	−0.975082	−0.487541	+	0.873100i	$0.662106\pi$
$678$	60266.6	0.00503504
$679$	−8.48076e6	−0.705928
$680$	1.06373e6	0.0882188
$681$	504070.	0.0416507
$682$	297796.	0.0245165
$683$	6.00025e6	0.492173	0.246086	−	0.969248i	$-0.420855\pi$
$683$	6.00025e6	0.492173	0.246086	+	0.969248i	$0.420855\pi$
$684$	−2.72954e6	−0.223074
$685$	−2.47295e6	−0.201367
$686$	3.99802e6	0.324365
$687$	160912.	0.0130075
$688$	1.75296e7	1.41189
$689$	5.99706e6	0.481272
$690$	34508.7	0.00275934
$691$	−1.35056e6	−0.107602	−0.0538009	−	0.998552i	$-0.517134\pi$
$691$	−1.35056e6	−0.107602	−0.0538009	+	0.998552i	$0.517134\pi$
$692$	1.60497e7	1.27409
$693$	6.82262e6	0.539657
$694$	−1.76654e6	−0.139228
$695$	2.69112e6	0.211334
$696$	−206676.	−0.0161721
$697$	−7.45134e6	−0.580968
$698$	950315.	0.0738293
$699$	1.69339e6	0.131088
$700$	−4.57664e6	−0.353022
$701$	974772.	0.0749218	0.0374609	−	0.999298i	$-0.488073\pi$
$701$	974772.	0.0749218	0.0374609	+	0.999298i	$0.488073\pi$
$702$	−271708.	−0.0208094
$703$	−3.36148e6	−0.256532
$704$	3.47968e6	0.264611
$705$	−244772.	−0.0185476
$706$	−162754.	−0.0122891
$707$	2.91928e6	0.219648
$708$	1.39215e6	0.104377
$709$	−2.37059e7	−1.77109	−0.885544	−	0.464555i	$-0.846214\pi$
$709$	−2.37059e7	−1.77109	−0.885544	+	0.464555i	$0.846214\pi$
$710$	705696.	0.0525378
$711$	−2.47640e7	−1.83716
$712$	4.56626e6	0.337568
$713$	−3.91226e6	−0.288206
$714$	−205253.	−0.0150676
$715$	−1.59281e6	−0.116519
$716$	1.02769e7	0.749168
$717$	−1.58251e6	−0.114960
$718$	1.52187e6	0.110171
$719$	1.45696e6	0.105106	0.0525528	−	0.998618i	$-0.483264\pi$
$719$	1.45696e6	0.105106	0.0525528	+	0.998618i	$0.483264\pi$
$720$	5.79508e6	0.416609
$721$	4.56992e6	0.327394
$722$	106207.	0.00758244
$723$	1.14199e6	0.0812485
$724$	8.24460e6	0.584552
$725$	−1.91409e6	−0.135244
$726$	−15600.1	−0.00109847
$727$	2.63923e7	1.85200	0.926001	−	0.377522i	$-0.123224\pi$
$727$	2.63923e7	1.85200	0.926001	+	0.377522i	$0.123224\pi$
$728$	6.35113e6	0.444143
$729$	−1.37468e7	−0.958040
$730$	−1.26258e6	−0.0876900
$731$	1.50417e7	1.04113
$732$	−1.08059e6	−0.0745392
$733$	−2.45625e7	−1.68855	−0.844273	−	0.535913i	$-0.819968\pi$
$733$	−2.45625e7	−1.68855	−0.844273	+	0.535913i	$0.819968\pi$
$734$	2.01999e6	0.138391
$735$	1.23554e6	0.0843601
$736$	3.15403e6	0.214621
$737$	7.80256e6	0.529137
$738$	1.77749e6	0.120134
$739$	−1.55376e7	−1.04658	−0.523292	−	0.852154i	$-0.675296\pi$
$739$	−1.55376e7	−1.04658	−0.523292	+	0.852154i	$0.675296\pi$
$740$	7.29465e6	0.489694
$741$	−248522.	−0.0166272
$742$	−2.16902e6	−0.144628
$743$	−2.13899e7	−1.42146	−0.710732	−	0.703462i	$-0.751636\pi$
$743$	−2.13899e7	−1.42146	−0.710732	+	0.703462i	$0.751636\pi$
$744$	−203799.	−0.0134980
$745$	−1.08063e7	−0.713323
$746$	−2.40489e6	−0.158215
$747$	−2.49529e7	−1.63613
$748$	3.12559e6	0.204258
$749$	4.04567e7	2.63503
$750$	16648.6	0.00108075
$751$	−9.35628e6	−0.605346	−0.302673	−	0.953094i	$-0.597879\pi$
$751$	−9.35628e6	−0.605346	−0.302673	+	0.953094i	$0.597879\pi$
$752$	−7.19418e6	−0.463913
$753$	859271.	0.0552259
$754$	1.31419e6	0.0841843
$755$	5.53850e6	0.353610
$756$	−4.63652e6	−0.295045
$757$	−1.60910e7	−1.02057	−0.510287	−	0.860004i	$-0.670461\pi$
$757$	−1.60910e7	−1.02057	−0.510287	+	0.860004i	$0.670461\pi$
$758$	−839790.	−0.0530882
$759$	204944.	0.0129131
$760$	−465838.	−0.0292550
$761$	1.71793e7	1.07533	0.537666	−	0.843158i	$-0.319306\pi$
$761$	1.71793e7	1.07533	0.537666	+	0.843158i	$0.319306\pi$
$762$	251977.	0.0157207
$763$	4.11302e7	2.55770
$764$	−2.01806e6	−0.125083
$765$	4.97263e6	0.307208
$766$	−3.47938e6	−0.214254
$767$	−1.78922e7	−1.09819
$768$	−1.09518e6	−0.0670009
$769$	−1.69031e7	−1.03074	−0.515371	−	0.856967i	$-0.672346\pi$
$769$	−1.69031e7	−1.03074	−0.515371	+	0.856967i	$0.672346\pi$
$770$	576088.	0.0350156
$771$	1.53290e6	0.0928706
$772$	1.79334e7	1.08298
$773$	−2.25420e6	−0.135689	−0.0678443	−	0.997696i	$-0.521612\pi$
$773$	−2.25420e6	−0.135689	−0.0678443	+	0.997696i	$0.521612\pi$
$774$	−3.58815e6	−0.215287
$775$	−1.88745e6	−0.112881
$776$	1.87325e6	0.111671
$777$	−2.84491e6	−0.169050
$778$	1.26710e6	0.0750520
$779$	3.26314e6	0.192660
$780$	539311.	0.0317397
$781$	4.19107e6	0.245866
$782$	870312.	0.0508930
$783$	−1.93914e6	−0.113033
$784$	3.63141e7	2.11001
$785$	8.17156e6	0.473294
$786$	330913.	0.0191055
$787$	1.87774e7	1.08068	0.540342	−	0.841445i	$-0.318295\pi$
$787$	1.87774e7	1.08068	0.540342	+	0.841445i	$0.318295\pi$
$788$	3.17193e7	1.81973
$789$	824141.	0.0471313
$790$	−2.09102e6	−0.119204
$791$	−1.32174e7	−0.751110
$792$	−1.50700e6	−0.0853690
$793$	1.38880e7	0.784254
$794$	−1.85945e6	−0.104672
$795$	−372272.	−0.0208902
$796$	−1.59606e7	−0.892823
$797$	−2.08047e7	−1.16015	−0.580077	−	0.814561i	$-0.696978\pi$
$797$	−2.08047e7	−1.16015	−0.580077	+	0.814561i	$0.696978\pi$
$798$	89885.6	0.00499670
$799$	−6.17316e6	−0.342090
$800$	1.52165e6	0.0840602
$801$	2.13459e7	1.17553
$802$	−1.64472e6	−0.0902936
$803$	−7.49834e6	−0.410370
$804$	−2.64188e6	−0.144136
$805$	−7.56827e6	−0.411630
$806$	1.29590e6	0.0702643
$807$	1.20662e6	0.0652208
$808$	−644818.	−0.0347463
$809$	1.82932e7	0.982692	0.491346	−	0.870964i	$-0.336505\pi$
$809$	1.82932e7	0.982692	0.491346	+	0.870964i	$0.336505\pi$
$810$	−1.17774e6	−0.0630720
$811$	−2.42693e7	−1.29570	−0.647852	−	0.761766i	$-0.724333\pi$
$811$	−2.42693e7	−1.29570	−0.647852	+	0.761766i	$0.724333\pi$
$812$	2.24259e7	1.19360
$813$	−1.64165e6	−0.0871070
$814$	−918219.	−0.0485719
$815$	−3.91009e6	−0.206202
$816$	−1.03539e6	−0.0544352
$817$	−6.58718e6	−0.345258
$818$	−4.17895e6	−0.218365
$819$	2.96896e7	1.54666
$820$	−7.08125e6	−0.367769
$821$	−1.10785e7	−0.573616	−0.286808	−	0.957988i	$-0.592594\pi$
$821$	−1.10785e7	−0.573616	−0.286808	+	0.957988i	$0.592594\pi$
$822$	−105398.	−0.00544067
$823$	−1.21754e7	−0.626590	−0.313295	−	0.949656i	$-0.601433\pi$
$823$	−1.21754e7	−0.626590	−0.313295	+	0.949656i	$0.601433\pi$
$824$	−1.00942e6	−0.0517908
$825$	98874.7	0.00505767
$826$	6.47127e6	0.330019
$827$	2.74742e7	1.39688	0.698442	−	0.715666i	$-0.253877\pi$
$827$	2.74742e7	1.39688	0.698442	+	0.715666i	$0.253877\pi$
$828$	9.79519e6	0.496520
$829$	3.53674e6	0.178738	0.0893689	−	0.995999i	$-0.471515\pi$
$829$	3.53674e6	0.178738	0.0893689	+	0.995999i	$0.471515\pi$
$830$	−2.10697e6	−0.106160
$831$	104611.	0.00525502
$832$	1.51423e7	0.758374
$833$	3.11603e7	1.55593
$834$	114696.	0.00570998
$835$	1.04097e7	0.516679
$836$	−1.36878e6	−0.0677358
$837$	−1.91215e6	−0.0943426
$838$	840948.	0.0413675
$839$	2.65815e7	1.30369	0.651844	−	0.758353i	$-0.273996\pi$
$839$	2.65815e7	1.30369	0.651844	+	0.758353i	$0.273996\pi$
$840$	−394251.	−0.0192785
$841$	−1.11319e7	−0.542726
$842$	−1.18672e6	−0.0576854
$843$	−109266.	−0.00529559
$844$	2.19949e7	1.06284
$845$	2.35100e6	0.113269
$846$	1.47258e6	0.0707382
$847$	3.42134e6	0.163866
$848$	−1.09416e7	−0.522504
$849$	2.89322e6	0.137757
$850$	419879.	0.0199332
$851$	1.20630e7	0.570992
$852$	−1.41906e6	−0.0669733
$853$	−2.36697e7	−1.11383	−0.556917	−	0.830568i	$-0.688016\pi$
$853$	−2.36697e7	−1.11383	−0.556917	+	0.830568i	$0.688016\pi$
$854$	−5.02302e6	−0.235679
$855$	−2.17765e6	−0.101876
$856$	−8.93619e6	−0.416839
$857$	6.07084e6	0.282356	0.141178	−	0.989984i	$-0.454911\pi$
$857$	6.07084e6	0.282356	0.141178	+	0.989984i	$0.454911\pi$
$858$	−67886.1	−0.00314820
$859$	3.09752e7	1.43229	0.716145	−	0.697952i	$-0.245905\pi$
$859$	3.09752e7	1.43229	0.716145	+	0.697952i	$0.245905\pi$
$860$	1.42947e7	0.659064
$861$	2.76168e6	0.126960
$862$	3.06526e6	0.140508
$863$	3.46424e7	1.58336	0.791682	−	0.610933i	$-0.209206\pi$
$863$	3.46424e7	1.58336	0.791682	+	0.610933i	$0.209206\pi$
$864$	1.54156e6	0.0702549
$865$	1.28046e7	0.581869
$866$	−3.13287e6	−0.141954
$867$	967922.	0.0437313
$868$	2.21138e7	0.996239
$869$	−1.24184e7	−0.557848
$870$	−81579.4	−0.00365412
$871$	3.39539e7	1.51651
$872$	−9.08495e6	−0.404605
$873$	8.75688e6	0.388878
$874$	−381133.	−0.0168771
$875$	−3.65128e6	−0.161222
$876$	2.53887e6	0.111784
$877$	7.11972e6	0.312582	0.156291	−	0.987711i	$-0.450046\pi$
$877$	7.11972e6	0.312582	0.156291	+	0.987711i	$0.450046\pi$
$878$	−1.00057e6	−0.0438037
$879$	832727.	0.0363522
$880$	2.90606e6	0.126502
$881$	−5.88541e6	−0.255468	−0.127734	−	0.991808i	$-0.540770\pi$
$881$	−5.88541e6	−0.255468	−0.127734	+	0.991808i	$0.540770\pi$
$882$	−7.43317e6	−0.321738
$883$	−2.96047e7	−1.27779	−0.638893	−	0.769296i	$-0.720607\pi$
$883$	−2.96047e7	−1.27779	−0.638893	+	0.769296i	$0.720607\pi$
$884$	1.36015e7	0.585403
$885$	1.11067e6	0.0476681
$886$	3.99004e6	0.170763
$887$	8.36076e6	0.356810	0.178405	−	0.983957i	$-0.442906\pi$
$887$	8.36076e6	0.356810	0.178405	+	0.983957i	$0.442906\pi$
$888$	628391.	0.0267422
$889$	−5.52622e7	−2.34517
$890$	1.80240e6	0.0762740
$891$	−6.99450e6	−0.295163
$892$	1.54261e6	0.0649147
$893$	2.70339e6	0.113444
$894$	−460569.	−0.0192731
$895$	8.19899e6	0.342139
$896$	−2.36825e7	−0.985503
$897$	891844.	0.0370090
$898$	2.26413e6	0.0936937
$899$	9.24867e6	0.381663
$900$	4.72565e6	0.194471
$901$	−9.38871e6	−0.385296
$902$	891357.	0.0364784
$903$	−5.57490e6	−0.227519
$904$	2.91949e6	0.118819
$905$	6.57761e6	0.266960
$906$	236053.	0.00955408
$907$	3.12101e7	1.25973	0.629863	−	0.776706i	$-0.283111\pi$
$907$	3.12101e7	1.25973	0.629863	+	0.776706i	$0.283111\pi$
$908$	1.20813e7	0.486293
$909$	−3.01432e6	−0.120999
$910$	2.50693e6	0.100355
$911$	−1.32118e7	−0.527431	−0.263716	−	0.964600i	$-0.584948\pi$
$911$	−1.32118e7	−0.527431	−0.263716	+	0.964600i	$0.584948\pi$
$912$	453426.	0.0180517
$913$	−1.25131e7	−0.496808
$914$	4.66483e6	0.184702
$915$	−862107.	−0.0340415
$916$	3.85664e6	0.151869
$917$	−7.25742e7	−2.85009
$918$	425372.	0.0166595
$919$	−930586.	−0.0363469	−0.0181735	−	0.999835i	$-0.505785\pi$
$919$	−930586.	−0.0363469	−0.0181735	+	0.999835i	$0.505785\pi$
$920$	1.67170e6	0.0651162
$921$	−536845.	−0.0208545
$922$	−5.14328e6	−0.199257
$923$	1.82380e7	0.704651
$924$	−1.15844e6	−0.0446367
$925$	5.81973e6	0.223640
$926$	1.61285e6	0.0618113
$927$	−4.71872e6	−0.180354
$928$	−7.45622e6	−0.284216
$929$	−3.97347e7	−1.51054	−0.755268	−	0.655416i	$-0.772493\pi$
$929$	−3.97347e7	−1.51054	−0.755268	+	0.655416i	$0.772493\pi$
$930$	−80444.0	−0.00304990
$931$	−1.36459e7	−0.515975
$932$	4.05862e7	1.53052
$933$	1.65999e6	0.0624313
$934$	−243688.	−0.00914043
$935$	2.49363e6	0.0932829
$936$	−6.55792e6	−0.244668
$937$	4.63571e7	1.72491	0.862456	−	0.506132i	$-0.168925\pi$
$937$	4.63571e7	1.72491	0.862456	+	0.506132i	$0.168925\pi$
$938$	−1.22805e7	−0.455730
$939$	−339229.	−0.0125553
$940$	−5.86655e6	−0.216553
$941$	−1.15865e7	−0.426556	−0.213278	−	0.976992i	$-0.568414\pi$
$941$	−1.15865e7	−0.426556	−0.213278	+	0.976992i	$0.568414\pi$
$942$	348275.	0.0127878
$943$	−1.17101e7	−0.428825
$944$	3.26441e7	1.19227
$945$	−3.69906e6	−0.134745
$946$	−1.79935e6	−0.0653714
$947$	−2.65031e7	−0.960333	−0.480166	−	0.877177i	$-0.659424\pi$
$947$	−2.65031e7	−0.960333	−0.480166	+	0.877177i	$0.659424\pi$
$948$	4.20476e6	0.151957
$949$	−3.26300e7	−1.17612
$950$	−183876.	−0.00661022
$951$	−2.20141e6	−0.0789314
$952$	−9.94303e6	−0.355571
$953$	1.59153e7	0.567651	0.283825	−	0.958876i	$-0.408396\pi$
$953$	1.59153e7	0.567651	0.283825	+	0.958876i	$0.408396\pi$
$954$	2.23964e6	0.0796723
$955$	−1.61002e6	−0.0571246
$956$	−3.79287e7	−1.34222
$957$	−484494.	−0.0171005
$958$	4.96404e6	0.174752
$959$	2.31153e7	0.811621
$960$	−939968.	−0.0329181
$961$	−1.95092e7	−0.681446
$962$	−3.99576e6	−0.139207
$963$	−4.17740e7	−1.45158
$964$	2.73705e7	0.948616
$965$	1.43075e7	0.494589
$966$	−322563.	−0.0111217
$967$	−3.46028e6	−0.118999	−0.0594997	−	0.998228i	$-0.518951\pi$
$967$	−3.46028e6	−0.118999	−0.0594997	+	0.998228i	$0.518951\pi$
$968$	−755715.	−0.0259221
$969$	389074.	0.0133114
$970$	739413.	0.0252323
$971$	3.23863e7	1.10233	0.551166	−	0.834395i	$-0.314183\pi$
$971$	3.23863e7	1.10233	0.551166	+	0.834395i	$0.314183\pi$
$972$	7.18968e6	0.244086
$973$	−2.51546e7	−0.851796
$974$	6.29605e6	0.212653
$975$	430267.	0.0144953
$976$	−2.53385e7	−0.851444
$977$	1.09230e7	0.366106	0.183053	−	0.983103i	$-0.441402\pi$
$977$	1.09230e7	0.366106	0.183053	+	0.983103i	$0.441402\pi$
$978$	−166650.	−0.00557131
$979$	1.07043e7	0.356946
$980$	2.96126e7	0.984944
$981$	−4.24694e7	−1.40897
$982$	−823872.	−0.0272634
$983$	3.59940e7	1.18808	0.594041	−	0.804435i	$-0.297532\pi$
$983$	3.59940e7	1.18808	0.594041	+	0.804435i	$0.297532\pi$
$984$	−610008.	−0.0200839
$985$	2.53059e7	0.831058
$986$	−2.05744e6	−0.0673961
$987$	2.28795e6	0.0747574
$988$	−5.95644e6	−0.194131
$989$	2.36387e7	0.768480
$990$	−594845.	−0.0192893
$991$	4.49268e7	1.45318	0.726592	−	0.687069i	$-0.241103\pi$
$991$	4.49268e7	1.45318	0.726592	+	0.687069i	$0.241103\pi$
$992$	−7.35244e6	−0.237220
$993$	−3.79958e6	−0.122282
$994$	−6.59634e6	−0.211757
$995$	−1.27335e7	−0.407746
$996$	4.23683e6	0.135330
$997$	5.69216e7	1.81359	0.906794	−	0.421573i	$-0.138522\pi$
$997$	5.69216e7	1.81359	0.906794	+	0.421573i	$0.138522\pi$
$998$	2.09539e6	0.0665945
$999$	5.89588e6	0.186911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.c.1.20	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.c.1.20	✓	37	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)

\(f(q)\)	\(=\)	\(q+0.814963 q^{2} -1.30743 q^{3} -31.3358 q^{4} -25.0000 q^{5} -1.06551 q^{6} +233.682 q^{7} -51.6164 q^{8} -241.291 q^{9} +O(q^{10})\)	\(q+0.814963 q^{2} -1.30743 q^{3} -31.3358 q^{4} -25.0000 q^{5} -1.06551 q^{6} +233.682 q^{7} -51.6164 q^{8} -241.291 q^{9} -20.3741 q^{10} -121.000 q^{11} +40.9695 q^{12} -526.548 q^{13} +190.442 q^{14} +32.6858 q^{15} +960.681 q^{16} +824.339 q^{17} -196.643 q^{18} -361.000 q^{19} +783.396 q^{20} -305.524 q^{21} -98.6105 q^{22} +1295.48 q^{23} +67.4850 q^{24} +625.000 q^{25} -429.117 q^{26} +633.178 q^{27} -7322.62 q^{28} -3062.55 q^{29} +26.6377 q^{30} -3019.92 q^{31} +2434.64 q^{32} +158.199 q^{33} +671.806 q^{34} -5842.05 q^{35} +7561.04 q^{36} +9311.57 q^{37} -294.202 q^{38} +688.427 q^{39} +1290.41 q^{40} -9039.17 q^{41} -248.991 q^{42} +18247.0 q^{43} +3791.64 q^{44} +6032.27 q^{45} +1055.77 q^{46} -7488.62 q^{47} -1256.03 q^{48} +37800.3 q^{49} +509.352 q^{50} -1077.77 q^{51} +16499.8 q^{52} -11389.4 q^{53} +516.016 q^{54} +3025.00 q^{55} -12061.8 q^{56} +471.983 q^{57} -2495.86 q^{58} +33980.2 q^{59} -1024.24 q^{60} -26375.6 q^{61} -2461.13 q^{62} -56385.3 q^{63} -28757.7 q^{64} +13163.7 q^{65} +128.927 q^{66} -64484.0 q^{67} -25831.4 q^{68} -1693.76 q^{69} -4761.06 q^{70} -34637.0 q^{71} +12454.5 q^{72} +61969.7 q^{73} +7588.59 q^{74} -817.146 q^{75} +11312.2 q^{76} -28275.5 q^{77} +561.042 q^{78} +102631. q^{79} -24017.0 q^{80} +57805.8 q^{81} -7366.59 q^{82} +103414. q^{83} +9573.84 q^{84} -20608.5 q^{85} +14870.7 q^{86} +4004.08 q^{87} +6245.58 q^{88} -88465.5 q^{89} +4916.07 q^{90} -123045. q^{91} -40595.0 q^{92} +3948.35 q^{93} -6102.95 q^{94} +9025.00 q^{95} -3183.13 q^{96} -36291.8 q^{97} +30805.9 q^{98} +29196.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

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