LMFDB - Embedded newform 1045.6.a.g.1.9

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:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-6.68564 q^{2} -22.1881 q^{3} +12.6977 q^{4} -25.0000 q^{5} +148.342 q^{6} +35.5129 q^{7} +129.048 q^{8} +249.314 q^{9} +O(q^{10})$	\(q-6.68564 q^{2} -22.1881 q^{3} +12.6977 q^{4} -25.0000 q^{5} +148.342 q^{6} +35.5129 q^{7} +129.048 q^{8} +249.314 q^{9} +167.141 q^{10} -121.000 q^{11} -281.739 q^{12} -166.277 q^{13} -237.426 q^{14} +554.704 q^{15} -1269.09 q^{16} -1548.54 q^{17} -1666.82 q^{18} +361.000 q^{19} -317.443 q^{20} -787.966 q^{21} +808.962 q^{22} -984.692 q^{23} -2863.34 q^{24} +625.000 q^{25} +1111.67 q^{26} -140.093 q^{27} +450.933 q^{28} +1373.70 q^{29} -3708.55 q^{30} +8464.53 q^{31} +4355.17 q^{32} +2684.77 q^{33} +10353.0 q^{34} -887.823 q^{35} +3165.72 q^{36} +12295.3 q^{37} -2413.51 q^{38} +3689.39 q^{39} -3226.20 q^{40} +9628.61 q^{41} +5268.05 q^{42} -6575.14 q^{43} -1536.42 q^{44} -6232.85 q^{45} +6583.29 q^{46} +9268.12 q^{47} +28158.9 q^{48} -15545.8 q^{49} -4178.52 q^{50} +34359.2 q^{51} -2111.34 q^{52} +19134.7 q^{53} +936.612 q^{54} +3025.00 q^{55} +4582.87 q^{56} -8009.92 q^{57} -9184.06 q^{58} +18252.5 q^{59} +7043.47 q^{60} -37171.3 q^{61} -56590.8 q^{62} +8853.86 q^{63} +11494.0 q^{64} +4156.93 q^{65} -17949.4 q^{66} -28522.7 q^{67} -19662.9 q^{68} +21848.5 q^{69} +5935.66 q^{70} +1833.77 q^{71} +32173.5 q^{72} -33156.6 q^{73} -82201.6 q^{74} -13867.6 q^{75} +4583.88 q^{76} -4297.06 q^{77} -24665.9 q^{78} -53735.5 q^{79} +31727.4 q^{80} -57474.9 q^{81} -64373.4 q^{82} -38027.0 q^{83} -10005.4 q^{84} +38713.4 q^{85} +43959.0 q^{86} -30479.9 q^{87} -15614.8 q^{88} +110791. q^{89} +41670.5 q^{90} -5904.99 q^{91} -12503.3 q^{92} -187812. q^{93} -61963.3 q^{94} -9025.00 q^{95} -96633.2 q^{96} +41540.4 q^{97} +103934. q^{98} -30167.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) $ 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * 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 $

$2$	−6.68564	−1.18186	−0.590932	−	0.806721i	$-0.701240\pi$
$2$	−6.68564	−1.18186	−0.590932	+	0.806721i	$0.701240\pi$
$3$	−22.1881	−1.42337	−0.711685	−	0.702499i	$-0.752068\pi$
$3$	−22.1881	−1.42337	−0.711685	+	0.702499i	$0.752068\pi$
$4$	12.6977	0.396804
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	148.342	1.68223
$7$	35.5129	0.273931	0.136966	−	0.990576i	$-0.456265\pi$
$7$	35.5129	0.273931	0.136966	+	0.990576i	$0.456265\pi$
$8$	129.048	0.712896
$9$	249.314	1.02598
$10$	167.141	0.528546
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−281.739	−0.564799
$13$	−166.277	−0.272882	−0.136441	−	0.990648i	$-0.543566\pi$
$13$	−166.277	−0.272882	−0.136441	+	0.990648i	$0.543566\pi$
$14$	−237.426	−0.323749
$15$	554.704	0.636551
$16$	−1269.09	−1.23935
$17$	−1548.54	−1.29957	−0.649785	−	0.760118i	$-0.725141\pi$
$17$	−1548.54	−1.29957	−0.649785	+	0.760118i	$0.725141\pi$
$18$	−1666.82	−1.21257
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−317.443	−0.177456
$21$	−787.966	−0.389905
$22$	808.962	0.356346
$23$	−984.692	−0.388133	−0.194067	−	0.980988i	$-0.562168\pi$
$23$	−984.692	−0.388133	−0.194067	+	0.980988i	$0.562168\pi$
$24$	−2863.34	−1.01472
$25$	625.000	0.200000
$26$	1111.67	0.322509
$27$	−140.093	−0.0369835
$28$	450.933	0.108697
$29$	1373.70	0.303317	0.151659	−	0.988433i	$-0.451539\pi$
$29$	1373.70	0.303317	0.151659	+	0.988433i	$0.451539\pi$
$30$	−3708.55	−0.752317
$31$	8464.53	1.58197	0.790986	−	0.611835i	$-0.209568\pi$
$31$	8464.53	1.58197	0.790986	+	0.611835i	$0.209568\pi$
$32$	4355.17	0.751848
$33$	2684.77	0.429162
$34$	10353.0	1.53592
$35$	−887.823	−0.122506
$36$	3165.72	0.407114
$37$	12295.3	1.47650	0.738250	−	0.674528i	$-0.235653\pi$
$37$	12295.3	1.47650	0.738250	+	0.674528i	$0.235653\pi$
$38$	−2413.51	−0.271138
$39$	3689.39	0.388412
$40$	−3226.20	−0.318817
$41$	9628.61	0.894548	0.447274	−	0.894397i	$-0.352395\pi$
$41$	9628.61	0.894548	0.447274	+	0.894397i	$0.352395\pi$
$42$	5268.05	0.460815
$43$	−6575.14	−0.542293	−0.271147	−	0.962538i	$-0.587403\pi$
$43$	−6575.14	−0.542293	−0.271147	+	0.962538i	$0.587403\pi$
$44$	−1536.42	−0.119641
$45$	−6232.85	−0.458834
$46$	6583.29	0.458721
$47$	9268.12	0.611994	0.305997	−	0.952033i	$-0.401010\pi$
$47$	9268.12	0.611994	0.305997	+	0.952033i	$0.401010\pi$
$48$	28158.9	1.76405
$49$	−15545.8	−0.924962
$50$	−4178.52	−0.236373
$51$	34359.2	1.84977
$52$	−2111.34	−0.108281
$53$	19134.7	0.935691	0.467845	−	0.883810i	$-0.345030\pi$
$53$	19134.7	0.935691	0.467845	+	0.883810i	$0.345030\pi$
$54$	936.612	0.0437095
$55$	3025.00	0.134840
$56$	4582.87	0.195284
$57$	−8009.92	−0.326544
$58$	−9184.06	−0.358480
$59$	18252.5	0.682639	0.341320	−	0.939947i	$-0.389126\pi$
$59$	18252.5	0.682639	0.341320	+	0.939947i	$0.389126\pi$
$60$	7043.47	0.252586
$61$	−37171.3	−1.27904	−0.639518	−	0.768776i	$-0.720866\pi$
$61$	−37171.3	−1.27904	−0.639518	+	0.768776i	$0.720866\pi$
$62$	−56590.8	−1.86968
$63$	8853.86	0.281049
$64$	11494.0	0.350768
$65$	4156.93	0.122036
$66$	−17949.4	−0.507212
$67$	−28522.7	−0.776254	−0.388127	−	0.921606i	$-0.626878\pi$
$67$	−28522.7	−0.776254	−0.388127	+	0.921606i	$0.626878\pi$
$68$	−19662.9	−0.515674
$69$	21848.5	0.552457
$70$	5935.66	0.144785
$71$	1833.77	0.0431717	0.0215859	−	0.999767i	$-0.493128\pi$
$71$	1833.77	0.0431717	0.0215859	+	0.999767i	$0.493128\pi$
$72$	32173.5	0.731419
$73$	−33156.6	−0.728221	−0.364110	−	0.931356i	$-0.618627\pi$
$73$	−33156.6	−0.728221	−0.364110	+	0.931356i	$0.618627\pi$
$74$	−82201.6	−1.74502
$75$	−13867.6	−0.284674
$76$	4583.88	0.0910330
$77$	−4297.06	−0.0825933
$78$	−24665.9	−0.459050
$79$	−53735.5	−0.968709	−0.484355	−	0.874872i	$-0.660946\pi$
$79$	−53735.5	−0.968709	−0.484355	+	0.874872i	$0.660946\pi$
$80$	31727.4	0.554254
$81$	−57474.9	−0.973342
$82$	−64373.4	−1.05724
$83$	−38027.0	−0.605895	−0.302947	−	0.953007i	$-0.597971\pi$
$83$	−38027.0	−0.605895	−0.302947	+	0.953007i	$0.597971\pi$
$84$	−10005.4	−0.154716
$85$	38713.4	0.581185
$86$	43959.0	0.640917
$87$	−30479.9	−0.431733
$88$	−15614.8	−0.214946
$89$	110791.	1.48262	0.741309	−	0.671163i	$-0.234205\pi$
$89$	110791.	1.48262	0.741309	+	0.671163i	$0.234205\pi$
$90$	41670.5	0.542279
$91$	−5904.99	−0.0747508
$92$	−12503.3	−0.154013
$93$	−187812.	−2.25173
$94$	−61963.3	−0.723294
$95$	−9025.00	−0.102598
$96$	−96633.2	−1.07016
$97$	41540.4	0.448272	0.224136	−	0.974558i	$-0.428044\pi$
$97$	41540.4	0.448272	0.224136	+	0.974558i	$0.428044\pi$
$98$	103934.	1.09318
$99$	−30167.0	−0.309346
$100$	7936.08	0.0793608
$101$	67193.2	0.655423	0.327712	−	0.944778i	$-0.393723\pi$
$101$	67193.2	0.655423	0.327712	+	0.944778i	$0.393723\pi$
$102$	−229713.	−2.18618
$103$	116070.	1.07802	0.539011	−	0.842299i	$-0.318798\pi$
$103$	116070.	1.07802	0.539011	+	0.842299i	$0.318798\pi$
$104$	−21457.8	−0.194536
$105$	19699.1	0.174371
$106$	−127928.	−1.10586
$107$	−209668.	−1.77041	−0.885204	−	0.465203i	$-0.845981\pi$
$107$	−209668.	−1.77041	−0.885204	+	0.465203i	$0.845981\pi$
$108$	−1778.86	−0.0146752
$109$	−78024.4	−0.629020	−0.314510	−	0.949254i	$-0.601840\pi$
$109$	−78024.4	−0.629020	−0.314510	+	0.949254i	$0.601840\pi$
$110$	−20224.0	−0.159363
$111$	−272809.	−2.10161
$112$	−45069.3	−0.339497
$113$	66567.5	0.490418	0.245209	−	0.969470i	$-0.421143\pi$
$113$	66567.5	0.490418	0.245209	+	0.969470i	$0.421143\pi$
$114$	53551.4	0.385930
$115$	24617.3	0.173578
$116$	17442.9	0.120357
$117$	−41455.3	−0.279972
$118$	−122029.	−0.806787
$119$	−54993.1	−0.355992
$120$	71583.4	0.453794
$121$	14641.0	0.0909091
$122$	248514.	1.51165
$123$	−213641.	−1.27327
$124$	107480.	0.627732
$125$	−15625.0	−0.0894427
$126$	−59193.7	−0.332161
$127$	−340801.	−1.87496	−0.937480	−	0.348040i	$-0.886847\pi$
$127$	−340801.	−1.87496	−0.937480	+	0.348040i	$0.886847\pi$
$128$	−216210.	−1.16641
$129$	145890.	0.771884
$130$	−27791.7	−0.144231
$131$	−236452.	−1.20383	−0.601915	−	0.798560i	$-0.705595\pi$
$131$	−236452.	−1.20383	−0.601915	+	0.798560i	$0.705595\pi$
$132$	34090.4	0.170293
$133$	12820.2	0.0628441
$134$	190693.	0.917428
$135$	3502.33	0.0165395
$136$	−199836.	−0.926458
$137$	105071.	0.478279	0.239139	−	0.970985i	$-0.423135\pi$
$137$	105071.	0.478279	0.239139	+	0.970985i	$0.423135\pi$
$138$	−146071.	−0.652930
$139$	83682.8	0.367366	0.183683	−	0.982986i	$-0.441198\pi$
$139$	83682.8	0.367366	0.183683	+	0.982986i	$0.441198\pi$
$140$	−11273.3	−0.0486107
$141$	−205642.	−0.871094
$142$	−12259.9	−0.0510232
$143$	20119.6	0.0822770
$144$	−316403.	−1.27155
$145$	−34342.5	−0.135648
$146$	221673.	0.860658
$147$	344933.	1.31656
$148$	156122.	0.585881
$149$	470944.	1.73781	0.868907	−	0.494975i	$-0.164823\pi$
$149$	470944.	1.73781	0.868907	+	0.494975i	$0.164823\pi$
$150$	92713.7	0.336446
$151$	340151.	1.21403	0.607014	−	0.794691i	$-0.292367\pi$
$151$	340151.	1.21403	0.607014	+	0.794691i	$0.292367\pi$
$152$	46586.3	0.163550
$153$	−386072.	−1.33334
$154$	28728.6	0.0976141
$155$	−211613.	−0.707479
$156$	46846.8	0.154123
$157$	65119.7	0.210845	0.105423	−	0.994428i	$-0.466380\pi$
$157$	65119.7	0.210845	0.105423	+	0.994428i	$0.466380\pi$
$158$	359256.	1.14488
$159$	−424564.	−1.33183
$160$	−108879.	−0.336237
$161$	−34969.3	−0.106322
$162$	384256.	1.15036
$163$	239258.	0.705339	0.352669	−	0.935748i	$-0.385274\pi$
$163$	239258.	0.705339	0.352669	+	0.935748i	$0.385274\pi$
$164$	122261.	0.354960
$165$	−67119.1	−0.191927
$166$	254235.	0.716085
$167$	−699811.	−1.94173	−0.970867	−	0.239618i	$-0.922978\pi$
$167$	−699811.	−1.94173	−0.970867	+	0.239618i	$0.922978\pi$
$168$	−101685.	−0.277962
$169$	−343645.	−0.925535
$170$	−258824.	−0.686882
$171$	90002.3	0.235377
$172$	−83489.3	−0.215184
$173$	−329401.	−0.836776	−0.418388	−	0.908268i	$-0.637405\pi$
$173$	−329401.	−0.836776	−0.418388	+	0.908268i	$0.637405\pi$
$174$	203777.	0.510250
$175$	22195.6	0.0547862
$176$	153560.	0.373678
$177$	−404988.	−0.971648
$178$	−740708.	−1.75225
$179$	−166904.	−0.389344	−0.194672	−	0.980868i	$-0.562364\pi$
$179$	−166904.	−0.389344	−0.194672	+	0.980868i	$0.562364\pi$
$180$	−79143.0	−0.182067
$181$	−711939.	−1.61527	−0.807637	−	0.589680i	$-0.799254\pi$
$181$	−711939.	−1.61527	−0.807637	+	0.589680i	$0.799254\pi$
$182$	39478.6	0.0883453
$183$	824762.	1.82054
$184$	−127073.	−0.276699
$185$	−307381.	−0.660311
$186$	1.25564e6	2.66124
$187$	187373.	0.391835
$188$	117684.	0.242841
$189$	−4975.12	−0.0101309
$190$	60337.9	0.121257
$191$	782288.	1.55161	0.775806	−	0.630972i	$-0.217344\pi$
$191$	782288.	1.55161	0.775806	+	0.630972i	$0.217344\pi$
$192$	−255030.	−0.499272
$193$	−13156.6	−0.0254244	−0.0127122	−	0.999919i	$-0.504047\pi$
$193$	−13156.6	−0.0254244	−0.0127122	+	0.999919i	$0.504047\pi$
$194$	−277724.	−0.529796
$195$	−92234.7	−0.173703
$196$	−197397.	−0.367028
$197$	−24127.9	−0.0442950	−0.0221475	−	0.999755i	$-0.507050\pi$
$197$	−24127.9	−0.0442950	−0.0221475	+	0.999755i	$0.507050\pi$
$198$	201685.	0.365605
$199$	125864.	0.225303	0.112652	−	0.993635i	$-0.464066\pi$
$199$	125864.	0.225303	0.112652	+	0.993635i	$0.464066\pi$
$200$	80655.0	0.142579
$201$	632867.	1.10490
$202$	−449229.	−0.774622
$203$	48784.1	0.0830880
$204$	436283.	0.733995
$205$	−240715.	−0.400054
$206$	−776003.	−1.27408
$207$	−245497.	−0.398218
$208$	211022.	0.338196
$209$	−43681.0	−0.0691714
$210$	−131701.	−0.206083
$211$	865597.	1.33847	0.669236	−	0.743050i	$-0.266621\pi$
$211$	865597.	1.33847	0.669236	+	0.743050i	$0.266621\pi$
$212$	242967.	0.371286
$213$	−40688.0	−0.0614494
$214$	1.40177e6	2.09238
$215$	164379.	0.242521
$216$	−18078.8	−0.0263654
$217$	300600.	0.433351
$218$	521643.	0.743416
$219$	735684.	1.03653
$220$	38410.6	0.0535050
$221$	257487.	0.354629
$222$	1.82390e6	2.48381
$223$	−1.08884e6	−1.46624	−0.733118	−	0.680102i	$-0.761936\pi$
$223$	−1.08884e6	−1.46624	−0.733118	+	0.680102i	$0.761936\pi$
$224$	154665.	0.205955
$225$	155821.	0.205197
$226$	−445046.	−0.579607
$227$	−1.03724e6	−1.33602	−0.668011	−	0.744151i	$-0.732854\pi$
$227$	−1.03724e6	−1.33602	−0.668011	+	0.744151i	$0.732854\pi$
$228$	−101708.	−0.129574
$229$	341167.	0.429911	0.214955	−	0.976624i	$-0.431039\pi$
$229$	341167.	0.429911	0.214955	+	0.976624i	$0.431039\pi$
$230$	−164582.	−0.205146
$231$	95343.9	0.117561
$232$	177273.	0.216234
$233$	−1.46786e6	−1.77131	−0.885654	−	0.464345i	$-0.846290\pi$
$233$	−1.46786e6	−1.77131	−0.885654	+	0.464345i	$0.846290\pi$
$234$	277155.	0.330889
$235$	−231703.	−0.273692
$236$	231765.	0.270874
$237$	1.19229e6	1.37883
$238$	367664.	0.420735
$239$	−1.30351e6	−1.47611	−0.738055	−	0.674740i	$-0.764256\pi$
$239$	−1.30351e6	−1.47611	−0.738055	+	0.674740i	$0.764256\pi$
$240$	−703972.	−0.788909
$241$	−827953.	−0.918255	−0.459128	−	0.888370i	$-0.651838\pi$
$241$	−827953.	−0.918255	−0.459128	+	0.888370i	$0.651838\pi$
$242$	−97884.4	−0.107442
$243$	1.30930e6	1.42241
$244$	−471991.	−0.507527
$245$	388646.	0.413655
$246$	1.42833e6	1.50484
$247$	−60026.1	−0.0626034
$248$	1.09233e6	1.12778
$249$	843749.	0.862413
$250$	104463.	0.105709
$251$	−649074.	−0.650295	−0.325147	−	0.945663i	$-0.605414\pi$
$251$	−649074.	−0.650295	−0.325147	+	0.945663i	$0.605414\pi$
$252$	112424.	0.111521
$253$	119148.	0.117027
$254$	2.27847e6	2.21595
$255$	−858980.	−0.827242
$256$	1.07769e6	1.02777
$257$	−1.15585e6	−1.09161	−0.545807	−	0.837911i	$-0.683777\pi$
$257$	−1.15585e6	−1.09161	−0.545807	+	0.837911i	$0.683777\pi$
$258$	−975369.	−0.912262
$259$	436640.	0.404459
$260$	52783.6	0.0484245
$261$	342483.	0.311198
$262$	1.58083e6	1.42276
$263$	−1.76645e6	−1.57475	−0.787377	−	0.616471i	$-0.788562\pi$
$263$	−1.76645e6	−1.57475	−0.787377	+	0.616471i	$0.788562\pi$
$264$	346464.	0.305948
$265$	−478368.	−0.418454
$266$	−85710.9	−0.0742732
$267$	−2.45825e6	−2.11032
$268$	−362174.	−0.308021
$269$	−775536.	−0.653463	−0.326732	−	0.945117i	$-0.605947\pi$
$269$	−775536.	−0.653463	−0.326732	+	0.945117i	$0.605947\pi$
$270$	−23415.3	−0.0195475
$271$	523310.	0.432848	0.216424	−	0.976299i	$-0.430561\pi$
$271$	523310.	0.432848	0.216424	+	0.976299i	$0.430561\pi$
$272$	1.96524e6	1.61062
$273$	131021.	0.106398
$274$	−702466.	−0.565261
$275$	−75625.0	−0.0603023
$276$	277426.	0.219217
$277$	1.66224e6	1.30165	0.650827	−	0.759226i	$-0.274423\pi$
$277$	1.66224e6	1.30165	0.650827	+	0.759226i	$0.274423\pi$
$278$	−559473.	−0.434177
$279$	2.11032e6	1.62308
$280$	−114572.	−0.0873338
$281$	1.94659e6	1.47065	0.735325	−	0.677715i	$-0.237030\pi$
$281$	1.94659e6	1.47065	0.735325	+	0.677715i	$0.237030\pi$
$282$	1.37485e6	1.02951
$283$	432373.	0.320917	0.160458	−	0.987043i	$-0.448703\pi$
$283$	432373.	0.320917	0.160458	+	0.987043i	$0.448703\pi$
$284$	23284.7	0.0171307
$285$	200248.	0.146035
$286$	−134512.	−0.0972403
$287$	341940.	0.245045
$288$	1.08580e6	0.771384
$289$	978112.	0.688881
$290$	229602.	0.160317
$291$	−921705.	−0.638057
$292$	−421014.	−0.288961
$293$	731725.	0.497942	0.248971	−	0.968511i	$-0.419908\pi$
$293$	731725.	0.497942	0.248971	+	0.968511i	$0.419908\pi$
$294$	−2.30610e6	−1.55600
$295$	−456311.	−0.305286
$296$	1.58668e6	1.05259
$297$	16951.3	0.0111509
$298$	−3.14856e6	−2.05386
$299$	163732.	0.105915
$300$	−176087.	−0.112960
$301$	−233502.	−0.148551
$302$	−2.27412e6	−1.43482
$303$	−1.49089e6	−0.932910
$304$	−458143.	−0.284327
$305$	929282.	0.572003
$306$	2.58114e6	1.57582
$307$	2.42838e6	1.47052	0.735260	−	0.677786i	$-0.237060\pi$
$307$	2.42838e6	1.47052	0.735260	+	0.677786i	$0.237060\pi$
$308$	−54562.9	−0.0327733
$309$	−2.57538e6	−1.53443
$310$	1.41477e6	0.836144
$311$	2.24370e6	1.31542	0.657710	−	0.753271i	$-0.271525\pi$
$311$	2.24370e6	1.31542	0.657710	+	0.753271i	$0.271525\pi$
$312$	476108.	0.276897
$313$	−2.03791e6	−1.17577	−0.587887	−	0.808943i	$-0.700040\pi$
$313$	−2.03791e6	−1.17577	−0.587887	+	0.808943i	$0.700040\pi$
$314$	−435367.	−0.249190
$315$	−221347.	−0.125689
$316$	−682318.	−0.384388
$317$	939301.	0.524997	0.262498	−	0.964932i	$-0.415454\pi$
$317$	939301.	0.524997	0.262498	+	0.964932i	$0.415454\pi$
$318$	2.83848e6	1.57405
$319$	−166218.	−0.0914536
$320$	−287349.	−0.156868
$321$	4.65215e6	2.51995
$322$	233792.	0.125658
$323$	−559022.	−0.298142
$324$	−729800.	−0.386226
$325$	−103923.	−0.0545764
$326$	−1.59959e6	−0.833615
$327$	1.73122e6	0.895328
$328$	1.24255e6	0.637720
$329$	329138.	0.167644
$330$	448734.	0.226832
$331$	1.54738e6	0.776295	0.388147	−	0.921597i	$-0.373115\pi$
$331$	1.54738e6	0.776295	0.388147	+	0.921597i	$0.373115\pi$
$332$	−482857.	−0.240421
$333$	3.06538e6	1.51486
$334$	4.67868e6	2.29487
$335$	713068.	0.347152
$336$	1.00000e6	0.483229
$337$	−1.59567e6	−0.765363	−0.382681	−	0.923880i	$-0.624999\pi$
$337$	−1.59567e6	−0.765363	−0.382681	+	0.923880i	$0.624999\pi$
$338$	2.29748e6	1.09386
$339$	−1.47701e6	−0.698046
$340$	491573.	0.230616
$341$	−1.02421e6	−0.476982
$342$	−601723.	−0.278183
$343$	−1.14894e6	−0.527307
$344$	−848509.	−0.386599
$345$	−546212.	−0.247066
$346$	2.20225e6	0.988956
$347$	2.08613e6	0.930074	0.465037	−	0.885291i	$-0.346041\pi$
$347$	2.08613e6	0.930074	0.465037	+	0.885291i	$0.346041\pi$
$348$	−387025.	−0.171313
$349$	−601849.	−0.264499	−0.132249	−	0.991216i	$-0.542220\pi$
$349$	−601849.	−0.264499	−0.132249	+	0.991216i	$0.542220\pi$
$350$	−148392.	−0.0647499
$351$	23294.3	0.0100921
$352$	−526976.	−0.226691
$353$	−2.24122e6	−0.957300	−0.478650	−	0.878006i	$-0.658874\pi$
$353$	−2.24122e6	−0.957300	−0.478650	+	0.878006i	$0.658874\pi$
$354$	2.70760e6	1.14836
$355$	−45844.3	−0.0193070
$356$	1.40679e6	0.588309
$357$	1.22019e6	0.506709
$358$	1.11586e6	0.460151
$359$	487671.	0.199706	0.0998530	−	0.995002i	$-0.468163\pi$
$359$	487671.	0.199706	0.0998530	+	0.995002i	$0.468163\pi$
$360$	−804336.	−0.327101
$361$	130321.	0.0526316
$362$	4.75976e6	1.90904
$363$	−324857.	−0.129397
$364$	−74980.0	−0.0296614
$365$	828916.	0.325670
$366$	−5.51406e6	−2.15164
$367$	914684.	0.354492	0.177246	−	0.984167i	$-0.443281\pi$
$367$	914684.	0.354492	0.177246	+	0.984167i	$0.443281\pi$
$368$	1.24967e6	0.481033
$369$	2.40055e6	0.917791
$370$	2.05504e6	0.780398
$371$	679530.	0.256315
$372$	−2.38479e6	−0.893495
$373$	−4.84404e6	−1.80275	−0.901376	−	0.433038i	$-0.857442\pi$
$373$	−4.84404e6	−1.80275	−0.901376	+	0.433038i	$0.857442\pi$
$374$	−1.25271e6	−0.463096
$375$	346690.	0.127310
$376$	1.19603e6	0.436288
$377$	−228415.	−0.0827698
$378$	33261.8	0.0119734
$379$	−4.29573e6	−1.53617	−0.768085	−	0.640348i	$-0.778790\pi$
$379$	−4.29573e6	−1.53617	−0.768085	+	0.640348i	$0.778790\pi$
$380$	−114597.	−0.0407112
$381$	7.56175e6	2.66876
$382$	−5.23009e6	−1.83379
$383$	999930.	0.348315	0.174158	−	0.984718i	$-0.444280\pi$
$383$	999930.	0.348315	0.174158	+	0.984718i	$0.444280\pi$
$384$	4.79730e6	1.66023
$385$	107427.	0.0369369
$386$	87960.2	0.0300482
$387$	−1.63927e6	−0.556383
$388$	527468.	0.177876
$389$	5.48333e6	1.83726	0.918629	−	0.395122i	$-0.129298\pi$
$389$	5.48333e6	1.83726	0.918629	+	0.395122i	$0.129298\pi$
$390$	616647.	0.205294
$391$	1.52483e6	0.504406
$392$	−2.00616e6	−0.659402
$393$	5.24643e6	1.71349
$394$	161310.	0.0523506
$395$	1.34339e6	0.433220
$396$	−383052.	−0.122749
$397$	−4.09761e6	−1.30483	−0.652415	−	0.757862i	$-0.726244\pi$
$397$	−4.09761e6	−1.30483	−0.652415	+	0.757862i	$0.726244\pi$
$398$	−841478.	−0.266278
$399$	−284456.	−0.0894504
$400$	−793184.	−0.247870
$401$	4.70932e6	1.46251	0.731253	−	0.682107i	$-0.238936\pi$
$401$	4.70932e6	1.46251	0.731253	+	0.682107i	$0.238936\pi$
$402$	−4.23112e6	−1.30584
$403$	−1.40746e6	−0.431691
$404$	853201.	0.260074
$405$	1.43687e6	0.435292
$406$	−326153.	−0.0981988
$407$	−1.48773e6	−0.445181
$408$	4.43398e6	1.31869
$409$	−1.78524e6	−0.527702	−0.263851	−	0.964563i	$-0.584993\pi$
$409$	−1.78524e6	−0.527702	−0.263851	+	0.964563i	$0.584993\pi$
$410$	1.60933e6	0.472810
$411$	−2.33133e6	−0.680768
$412$	1.47383e6	0.427763
$413$	648198.	0.186996
$414$	1.64131e6	0.470640
$415$	950676.	0.270964
$416$	−724166.	−0.205166
$417$	−1.85677e6	−0.522898
$418$	292035.	0.0817513
$419$	−2.84105e6	−0.790576	−0.395288	−	0.918557i	$-0.629355\pi$
$419$	−2.84105e6	−0.790576	−0.395288	+	0.918557i	$0.629355\pi$
$420$	250134.	0.0691911
$421$	592616.	0.162955	0.0814775	−	0.996675i	$-0.474036\pi$
$421$	592616.	0.162955	0.0814775	+	0.996675i	$0.474036\pi$
$422$	−5.78706e6	−1.58189
$423$	2.31067e6	0.627895
$424$	2.46930e6	0.667050
$425$	−967836.	−0.259914
$426$	272025.	0.0726248
$427$	−1.32006e6	−0.350368
$428$	−2.66231e6	−0.702505
$429$	−446416.	−0.117111
$430$	−1.09898e6	−0.286627
$431$	4.45493e6	1.15517	0.577587	−	0.816329i	$-0.303994\pi$
$431$	4.45493e6	1.15517	0.577587	+	0.816329i	$0.303994\pi$
$432$	177792.	0.0458355
$433$	−4.22344e6	−1.08255	−0.541273	−	0.840847i	$-0.682057\pi$
$433$	−4.22344e6	−1.08255	−0.541273	+	0.840847i	$0.682057\pi$
$434$	−2.00970e6	−0.512162
$435$	761997.	0.193077
$436$	−990732.	−0.249597
$437$	−355474.	−0.0890439
$438$	−4.91852e6	−1.22504
$439$	6.78138e6	1.67941	0.839706	−	0.543042i	$-0.182727\pi$
$439$	6.78138e6	1.67941	0.839706	+	0.543042i	$0.182727\pi$
$440$	390370.	0.0961269
$441$	−3.87579e6	−0.948995
$442$	−1.72146e6	−0.419123
$443$	−1.39693e6	−0.338193	−0.169097	−	0.985599i	$-0.554085\pi$
$443$	−1.39693e6	−0.338193	−0.169097	+	0.985599i	$0.554085\pi$
$444$	−3.46405e6	−0.833925
$445$	−2.76978e6	−0.663047
$446$	7.27962e6	1.73289
$447$	−1.04494e7	−2.47355
$448$	408184.	0.0960862
$449$	7.19058e6	1.68325	0.841624	−	0.540063i	$-0.181600\pi$
$449$	7.19058e6	1.68325	0.841624	+	0.540063i	$0.181600\pi$
$450$	−1.04176e6	−0.242515
$451$	−1.16506e6	−0.269716
$452$	845256.	0.194600
$453$	−7.54731e6	−1.72801
$454$	6.93459e6	1.57900
$455$	147625.	0.0334296
$456$	−1.03366e6	−0.232792
$457$	153622.	0.0344084	0.0172042	−	0.999852i	$-0.494523\pi$
$457$	153622.	0.0344084	0.0172042	+	0.999852i	$0.494523\pi$
$458$	−2.28092e6	−0.508096
$459$	216940.	0.0480626
$460$	312584.	0.0688766
$461$	3.41474e6	0.748351	0.374175	−	0.927358i	$-0.377926\pi$
$461$	3.41474e6	0.748351	0.374175	+	0.927358i	$0.377926\pi$
$462$	−637434.	−0.138941
$463$	−681818.	−0.147814	−0.0739071	−	0.997265i	$-0.523547\pi$
$463$	−681818.	−0.147814	−0.0739071	+	0.997265i	$0.523547\pi$
$464$	−1.74336e6	−0.375916
$465$	4.69531e6	1.00700
$466$	9.81356e6	2.09345
$467$	7.23419e6	1.53496	0.767481	−	0.641072i	$-0.221510\pi$
$467$	7.23419e6	1.53496	0.767481	+	0.641072i	$0.221510\pi$
$468$	−526387.	−0.111094
$469$	−1.01293e6	−0.212640
$470$	1.54908e6	0.323467
$471$	−1.44489e6	−0.300111
$472$	2.35544e6	0.486651
$473$	795592.	0.163507
$474$	−7.97122e6	−1.62959
$475$	225625.	0.0458831
$476$	−698287.	−0.141259
$477$	4.77055e6	0.960003
$478$	8.71478e6	1.74456
$479$	−1.06971e6	−0.213024	−0.106512	−	0.994311i	$-0.533968\pi$
$479$	−1.06971e6	−0.213024	−0.106512	+	0.994311i	$0.533968\pi$
$480$	2.41583e6	0.478589
$481$	−2.04442e6	−0.402910
$482$	5.53539e6	1.08525
$483$	775904.	0.151335
$484$	185907.	0.0360731
$485$	−1.03851e6	−0.200473
$486$	−8.75353e6	−1.68110
$487$	7.90364e6	1.51010	0.755048	−	0.655669i	$-0.227613\pi$
$487$	7.90364e6	1.51010	0.755048	+	0.655669i	$0.227613\pi$
$488$	−4.79688e6	−0.911821
$489$	−5.30869e6	−1.00396
$490$	−2.59834e6	−0.488885
$491$	−5.77178e6	−1.08045	−0.540227	−	0.841519i	$-0.681662\pi$
$491$	−5.77178e6	−1.08045	−0.540227	+	0.841519i	$0.681662\pi$
$492$	−2.71275e6	−0.505240
$493$	−2.12723e6	−0.394182
$494$	401313.	0.0739887
$495$	754174.	0.138344
$496$	−1.07423e7	−1.96062
$497$	65122.6	0.0118261
$498$	−5.64100e6	−1.01925
$499$	−9.97587e6	−1.79349	−0.896746	−	0.442545i	$-0.854076\pi$
$499$	−9.97587e6	−1.79349	−0.896746	+	0.442545i	$0.854076\pi$
$500$	−198402.	−0.0354912
$501$	1.55275e7	2.76381
$502$	4.33948e6	0.768560
$503$	585791.	0.103234	0.0516170	−	0.998667i	$-0.483563\pi$
$503$	585791.	0.103234	0.0516170	+	0.998667i	$0.483563\pi$
$504$	1.14257e6	0.200358
$505$	−1.67983e6	−0.293114
$506$	−796578.	−0.138310
$507$	7.62484e6	1.31738
$508$	−4.32740e6	−0.743991
$509$	9.78958e6	1.67483	0.837413	−	0.546571i	$-0.184067\pi$
$509$	9.78958e6	1.67483	0.837413	+	0.546571i	$0.184067\pi$
$510$	5.74282e6	0.977688
$511$	−1.17749e6	−0.199482
$512$	−286351.	−0.0482752
$513$	−50573.7	−0.00848459
$514$	7.72760e6	1.29014
$515$	−2.90176e6	−0.482106
$516$	1.85247e6	0.306286
$517$	−1.12144e6	−0.184523
$518$	−2.91922e6	−0.478016
$519$	7.30879e6	1.19104
$520$	536444.	0.0869994
$521$	−7.41031e6	−1.19603	−0.598015	−	0.801485i	$-0.704044\pi$
$521$	−7.41031e6	−1.19603	−0.598015	+	0.801485i	$0.704044\pi$
$522$	−2.28971e6	−0.367794
$523$	−1.32264e6	−0.211440	−0.105720	−	0.994396i	$-0.533715\pi$
$523$	−1.32264e6	−0.211440	−0.105720	+	0.994396i	$0.533715\pi$
$524$	−3.00240e6	−0.477684
$525$	−492479.	−0.0779811
$526$	1.18099e7	1.86115
$527$	−1.31076e7	−2.05588
$528$	−3.40722e6	−0.531883
$529$	−5.46672e6	−0.849353
$530$	3.19819e6	0.494556
$531$	4.55059e6	0.700376
$532$	162787.	0.0249368
$533$	−1.60102e6	−0.244106
$534$	1.64349e7	2.49411
$535$	5.24171e6	0.791751
$536$	−3.68080e6	−0.553389
$537$	3.70328e6	0.554180
$538$	5.18495e6	0.772305
$539$	1.88105e6	0.278886
$540$	44471.6	0.00656294
$541$	1.01205e7	1.48665	0.743325	−	0.668930i	$-0.233248\pi$
$541$	1.01205e7	1.48665	0.743325	+	0.668930i	$0.233248\pi$
$542$	−3.49866e6	−0.511568
$543$	1.57966e7	2.29913
$544$	−6.74415e6	−0.977079
$545$	1.95061e6	0.281306
$546$	−875958.	−0.125748
$547$	6.76198e6	0.966286	0.483143	−	0.875541i	$-0.339495\pi$
$547$	6.76198e6	0.966286	0.483143	+	0.875541i	$0.339495\pi$
$548$	1.33416e6	0.189783
$549$	−9.26732e6	−1.31227
$550$	505601.	0.0712691
$551$	495906.	0.0695857
$552$	2.81950e6	0.393845
$553$	−1.90830e6	−0.265360
$554$	−1.11132e7	−1.53838
$555$	6.82022e6	0.939866
$556$	1.06258e6	0.145772
$557$	−3.96344e6	−0.541295	−0.270648	−	0.962678i	$-0.587238\pi$
$557$	−3.96344e6	−0.541295	−0.270648	+	0.962678i	$0.587238\pi$
$558$	−1.41089e7	−1.91826
$559$	1.09330e6	0.147982
$560$	1.12673e6	0.151827
$561$	−4.15746e6	−0.557726
$562$	−1.30142e7	−1.73811
$563$	9.71037e6	1.29112	0.645558	−	0.763712i	$-0.276625\pi$
$563$	9.71037e6	1.29112	0.645558	+	0.763712i	$0.276625\pi$
$564$	−2.61119e6	−0.345653
$565$	−1.66419e6	−0.219321
$566$	−2.89069e6	−0.379280
$567$	−2.04110e6	−0.266629
$568$	236645.	0.0307770
$569$	1.02415e7	1.32612	0.663062	−	0.748565i	$-0.269257\pi$
$569$	1.02415e7	1.32612	0.663062	+	0.748565i	$0.269257\pi$
$570$	−1.33879e6	−0.172593
$571$	−5.36956e6	−0.689205	−0.344602	−	0.938749i	$-0.611986\pi$
$571$	−5.36956e6	−0.689205	−0.344602	+	0.938749i	$0.611986\pi$
$572$	255473.	0.0326478
$573$	−1.73575e7	−2.20852
$574$	−2.28609e6	−0.289609
$575$	−615433.	−0.0776267
$576$	2.86560e6	0.359882
$577$	1.28865e6	0.161138	0.0805688	−	0.996749i	$-0.474326\pi$
$577$	1.28865e6	0.161138	0.0805688	+	0.996749i	$0.474326\pi$
$578$	−6.53930e6	−0.814164
$579$	291920.	0.0361883
$580$	−436072.	−0.0538255
$581$	−1.35045e6	−0.165973
$582$	6.16218e6	0.754097
$583$	−2.31530e6	−0.282121
$584$	−4.27880e6	−0.519146
$585$	1.03638e6	0.125207
$586$	−4.89205e6	−0.588500
$587$	−484314.	−0.0580139	−0.0290069	−	0.999579i	$-0.509234\pi$
$587$	−484314.	−0.0580139	−0.0290069	+	0.999579i	$0.509234\pi$
$588$	4.37987e6	0.522417
$589$	3.05570e6	0.362929
$590$	3.05073e6	0.360806
$591$	535354.	0.0630481
$592$	−1.56038e7	−1.82990
$593$	6.79273e6	0.793246	0.396623	−	0.917982i	$-0.370182\pi$
$593$	6.79273e6	0.793246	0.396623	+	0.917982i	$0.370182\pi$
$594$	−113330.	−0.0131789
$595$	1.37483e6	0.159205
$596$	5.97991e6	0.689571
$597$	−2.79268e6	−0.320690
$598$	−1.09465e6	−0.125177
$599$	1.08899e7	1.24010	0.620048	−	0.784564i	$-0.287113\pi$
$599$	1.08899e7	1.24010	0.620048	+	0.784564i	$0.287113\pi$
$600$	−1.78959e6	−0.202943
$601$	−6.18380e6	−0.698344	−0.349172	−	0.937059i	$-0.613537\pi$
$601$	−6.18380e6	−0.698344	−0.349172	+	0.937059i	$0.613537\pi$
$602$	1.56111e6	0.175567
$603$	−7.11111e6	−0.796424
$604$	4.31914e6	0.481731
$605$	−366025.	−0.0406558
$606$	9.96757e6	1.10257
$607$	−8.29052e6	−0.913293	−0.456646	−	0.889648i	$-0.650949\pi$
$607$	−8.29052e6	−0.913293	−0.456646	+	0.889648i	$0.650949\pi$
$608$	1.57222e6	0.172486
$609$	−1.08243e6	−0.118265
$610$	−6.21284e6	−0.676030
$611$	−1.54108e6	−0.167002
$612$	−4.90223e6	−0.529073
$613$	−1.38843e7	−1.49236	−0.746178	−	0.665746i	$-0.768113\pi$
$613$	−1.38843e7	−1.49236	−0.746178	+	0.665746i	$0.768113\pi$
$614$	−1.62353e7	−1.73795
$615$	5.34102e6	0.569425
$616$	−554527.	−0.0588805
$617$	−1.15606e7	−1.22255	−0.611276	−	0.791417i	$-0.709344\pi$
$617$	−1.15606e7	−1.22255	−0.611276	+	0.791417i	$0.709344\pi$
$618$	1.72181e7	1.81348
$619$	3.35792e6	0.352244	0.176122	−	0.984368i	$-0.443645\pi$
$619$	3.35792e6	0.352244	0.176122	+	0.984368i	$0.443645\pi$
$620$	−2.68701e6	−0.280730
$621$	137949.	0.0143545
$622$	−1.50006e7	−1.55465
$623$	3.93451e6	0.406135
$624$	−4.68218e6	−0.481379
$625$	390625.	0.0400000
$626$	1.36247e7	1.38961
$627$	969200.	0.0984566
$628$	826872.	0.0836641
$629$	−1.90397e7	−1.91881
$630$	1.47984e6	0.148547
$631$	−1.16435e7	−1.16415	−0.582075	−	0.813135i	$-0.697759\pi$
$631$	−1.16435e7	−1.16415	−0.582075	+	0.813135i	$0.697759\pi$
$632$	−6.93446e6	−0.690589
$633$	−1.92060e7	−1.90514
$634$	−6.27982e6	−0.620475
$635$	8.52003e6	0.838507
$636$	−5.39099e6	−0.528477
$637$	2.58492e6	0.252405
$638$	1.11127e6	0.108086
$639$	457185.	0.0442935
$640$	5.40525e6	0.521634
$641$	−2.81925e6	−0.271012	−0.135506	−	0.990777i	$-0.543266\pi$
$641$	−2.81925e6	−0.271012	−0.135506	+	0.990777i	$0.543266\pi$
$642$	−3.11026e7	−2.97824
$643$	−2.92860e6	−0.279340	−0.139670	−	0.990198i	$-0.544604\pi$
$643$	−2.92860e6	−0.279340	−0.139670	+	0.990198i	$0.544604\pi$
$644$	−444030.	−0.0421889
$645$	−3.64726e6	−0.345197
$646$	3.73742e6	0.352363
$647$	1.87685e7	1.76266	0.881331	−	0.472499i	$-0.156648\pi$
$647$	1.87685e7	1.76266	0.881331	+	0.472499i	$0.156648\pi$
$648$	−7.41702e6	−0.693892
$649$	−2.20855e6	−0.205823
$650$	694794.	0.0645019
$651$	−6.66976e6	−0.616819
$652$	3.03803e6	0.279881
$653$	1.96320e7	1.80170	0.900848	−	0.434134i	$-0.142946\pi$
$653$	1.96320e7	1.80170	0.900848	+	0.434134i	$0.142946\pi$
$654$	−1.15743e7	−1.05816
$655$	5.91130e6	0.538369
$656$	−1.22196e7	−1.10866
$657$	−8.26641e6	−0.747142
$658$	−2.20050e6	−0.198133
$659$	1.46783e7	1.31662	0.658312	−	0.752745i	$-0.271271\pi$
$659$	1.46783e7	1.31662	0.658312	+	0.752745i	$0.271271\pi$
$660$	−852260.	−0.0761574
$661$	−5.47753e6	−0.487620	−0.243810	−	0.969823i	$-0.578397\pi$
$661$	−5.47753e6	−0.487620	−0.243810	+	0.969823i	$0.578397\pi$
$662$	−1.03452e7	−0.917476
$663$	−5.71315e6	−0.504768
$664$	−4.90731e6	−0.431940
$665$	−320504.	−0.0281047
$666$	−2.04940e7	−1.79036
$667$	−1.35267e6	−0.117728
$668$	−8.88601e6	−0.770488
$669$	2.41594e7	2.08700
$670$	−4.76731e6	−0.410286
$671$	4.49773e6	0.385644
$672$	−3.43173e6	−0.293150
$673$	−360211.	−0.0306563	−0.0153281	−	0.999883i	$-0.504879\pi$
$673$	−360211.	−0.0306563	−0.0153281	+	0.999883i	$0.504879\pi$
$674$	1.06680e7	0.904555
$675$	−87558.3	−0.00739670
$676$	−4.36351e6	−0.367256
$677$	−5.33166e6	−0.447086	−0.223543	−	0.974694i	$-0.571762\pi$
$677$	−5.33166e6	−0.447086	−0.223543	+	0.974694i	$0.571762\pi$
$678$	9.87475e6	0.824996
$679$	1.47522e6	0.122796
$680$	4.99589e6	0.414325
$681$	2.30144e7	1.90165
$682$	6.84748e6	0.563728
$683$	−1.48855e7	−1.22099	−0.610495	−	0.792020i	$-0.709029\pi$
$683$	−1.48855e7	−1.22099	−0.610495	+	0.792020i	$0.709029\pi$
$684$	1.14282e6	0.0933983
$685$	−2.62677e6	−0.213893
$686$	7.68142e6	0.623205
$687$	−7.56986e6	−0.611922
$688$	8.34448e6	0.672091
$689$	−3.18167e6	−0.255333
$690$	3.65178e6	0.291999
$691$	−1.99316e7	−1.58799	−0.793994	−	0.607926i	$-0.792002\pi$
$691$	−1.99316e7	−1.58799	−0.793994	+	0.607926i	$0.792002\pi$
$692$	−4.18264e6	−0.332036
$693$	−1.07132e6	−0.0847393
$694$	−1.39471e7	−1.09922
$695$	−2.09207e6	−0.164291
$696$	−3.93337e6	−0.307781
$697$	−1.49103e7	−1.16253
$698$	4.02374e6	0.312602
$699$	3.25690e7	2.52123
$700$	281833.	0.0217394
$701$	−1.23871e7	−0.952086	−0.476043	−	0.879422i	$-0.657929\pi$
$701$	−1.23871e7	−0.952086	−0.476043	+	0.879422i	$0.657929\pi$
$702$	−155737.	−0.0119275
$703$	4.43859e6	0.338732
$704$	−1.39077e6	−0.105760
$705$	5.14106e6	0.389565
$706$	1.49840e7	1.13140
$707$	2.38623e6	0.179541
$708$	−5.14243e6	−0.385554
$709$	1.90821e7	1.42564	0.712820	−	0.701347i	$-0.247418\pi$
$709$	1.90821e7	1.42564	0.712820	+	0.701347i	$0.247418\pi$
$710$	306498.	0.0228182
$711$	−1.33970e7	−0.993879
$712$	1.42974e7	1.05695
$713$	−8.33496e6	−0.614016
$714$	−8.15778e6	−0.598861
$715$	−502989.	−0.0367954
$716$	−2.11929e6	−0.154493
$717$	2.89224e7	2.10105
$718$	−3.26039e6	−0.236025
$719$	2.25581e7	1.62735	0.813673	−	0.581323i	$-0.197465\pi$
$719$	2.25581e7	1.62735	0.813673	+	0.581323i	$0.197465\pi$
$720$	7.91007e6	0.568656
$721$	4.12199e6	0.295304
$722$	−871279.	−0.0622034
$723$	1.83708e7	1.30702
$724$	−9.04000e6	−0.640947
$725$	858563.	0.0606634
$726$	2.17187e6	0.152930
$727$	2.67127e7	1.87448	0.937242	−	0.348678i	$-0.113369\pi$
$727$	2.67127e7	1.87448	0.937242	+	0.348678i	$0.113369\pi$
$728$	−762028.	−0.0532896
$729$	−1.50846e7	−1.05127
$730$	−5.54183e6	−0.384898
$731$	1.01819e7	0.704747
$732$	1.04726e7	0.722398
$733$	−1.84847e7	−1.27073	−0.635363	−	0.772214i	$-0.719150\pi$
$733$	−1.84847e7	−1.27073	−0.635363	+	0.772214i	$0.719150\pi$
$734$	−6.11524e6	−0.418961
$735$	−8.62333e6	−0.588785
$736$	−4.28850e6	−0.291817
$737$	3.45125e6	0.234050
$738$	−1.60492e7	−1.08471
$739$	−1.07891e7	−0.726730	−0.363365	−	0.931647i	$-0.618372\pi$
$739$	−1.07891e7	−0.726730	−0.363365	+	0.931647i	$0.618372\pi$
$740$	−3.90304e6	−0.262014
$741$	1.33187e6	0.0891078
$742$	−4.54309e6	−0.302929
$743$	1.14952e7	0.763915	0.381957	−	0.924180i	$-0.375250\pi$
$743$	1.14952e7	0.763915	0.381957	+	0.924180i	$0.375250\pi$
$744$	−2.42368e7	−1.60525
$745$	−1.17736e7	−0.777174
$746$	3.23855e7	2.13061
$747$	−9.48067e6	−0.621638
$748$	2.37921e6	0.155482
$749$	−7.44593e6	−0.484970
$750$	−2.31784e6	−0.150463
$751$	8.53498e6	0.552208	0.276104	−	0.961128i	$-0.410957\pi$
$751$	8.53498e6	0.552208	0.276104	+	0.961128i	$0.410957\pi$
$752$	−1.17621e7	−0.758475
$753$	1.44018e7	0.925610
$754$	1.52710e6	0.0978227
$755$	−8.50377e6	−0.542930
$756$	−63172.7	−0.00401999
$757$	2.92300e6	0.185391	0.0926957	−	0.995694i	$-0.470452\pi$
$757$	2.92300e6	0.185391	0.0926957	+	0.995694i	$0.470452\pi$
$758$	2.87197e7	1.81554
$759$	−2.64367e6	−0.166572
$760$	−1.16466e6	−0.0731416
$761$	1.98450e7	1.24220	0.621098	−	0.783733i	$-0.286687\pi$
$761$	1.98450e7	1.24220	0.621098	+	0.783733i	$0.286687\pi$
$762$	−5.05551e7	−3.15411
$763$	−2.77087e6	−0.172308
$764$	9.93327e6	0.615685
$765$	9.65180e6	0.596286
$766$	−6.68517e6	−0.411662
$767$	−3.03497e6	−0.186280
$768$	−2.39120e7	−1.46290
$769$	−1.85370e7	−1.13038	−0.565188	−	0.824962i	$-0.691196\pi$
$769$	−1.85370e7	−1.13038	−0.565188	+	0.824962i	$0.691196\pi$
$770$	−718215.	−0.0436544
$771$	2.56462e7	1.55377
$772$	−167059.	−0.0100885
$773$	−1.34448e7	−0.809296	−0.404648	−	0.914473i	$-0.632606\pi$
$773$	−1.34448e7	−0.809296	−0.404648	+	0.914473i	$0.632606\pi$
$774$	1.09596e7	0.657570
$775$	5.29033e6	0.316394
$776$	5.36071e6	0.319571
$777$	−9.68824e6	−0.575695
$778$	−3.66595e7	−2.17139
$779$	3.47593e6	0.205223
$780$	−1.17117e6	−0.0689261
$781$	−221886.	−0.0130168
$782$	−1.01945e7	−0.596140
$783$	−192446.	−0.0112177
$784$	1.97291e7	1.14635
$785$	−1.62799e6	−0.0942928
$786$	−3.50757e7	−2.02512
$787$	2.92785e7	1.68505	0.842524	−	0.538659i	$-0.181069\pi$
$787$	2.92785e7	1.68505	0.842524	+	0.538659i	$0.181069\pi$
$788$	−306370.	−0.0175764
$789$	3.91943e7	2.24146
$790$	−8.98140e6	−0.512007
$791$	2.36401e6	0.134341
$792$	−3.89299e6	−0.220531
$793$	6.18074e6	0.349026
$794$	2.73951e7	1.54213
$795$	1.06141e7	0.595615
$796$	1.59818e6	0.0894011
$797$	−1.96433e7	−1.09539	−0.547696	−	0.836677i	$-0.684495\pi$
$797$	−1.96433e7	−1.09539	−0.547696	+	0.836677i	$0.684495\pi$
$798$	1.90177e6	0.105718
$799$	−1.43520e7	−0.795328
$800$	2.72198e6	0.150370
$801$	2.76217e7	1.52114
$802$	−3.14848e7	−1.72848
$803$	4.01195e6	0.219567
$804$	8.03596e6	0.438428
$805$	874232.	0.0475485
$806$	9.40976e6	0.510201
$807$	1.72077e7	0.930120
$808$	8.67115e6	0.467249
$809$	−3.06800e6	−0.164810	−0.0824050	−	0.996599i	$-0.526260\pi$
$809$	−3.06800e6	−0.164810	−0.0824050	+	0.996599i	$0.526260\pi$
$810$	−9.60640e6	−0.514456
$811$	971492.	0.0518665	0.0259333	−	0.999664i	$-0.491744\pi$
$811$	971492.	0.0518665	0.0259333	+	0.999664i	$0.491744\pi$
$812$	619447.	0.0329696
$813$	−1.16113e7	−0.616104
$814$	9.94639e6	0.526144
$815$	−5.98145e6	−0.315437
$816$	−4.36051e7	−2.29251
$817$	−2.37363e6	−0.124411
$818$	1.19355e7	0.623672
$819$	−1.47220e6	−0.0766931
$820$	−3.05653e6	−0.158743
$821$	−1.18286e7	−0.612455	−0.306228	−	0.951958i	$-0.599067\pi$
$821$	−1.18286e7	−0.612455	−0.306228	+	0.951958i	$0.599067\pi$
$822$	1.55864e7	0.804576
$823$	−1.76285e7	−0.907226	−0.453613	−	0.891199i	$-0.649865\pi$
$823$	−1.76285e7	−0.907226	−0.453613	+	0.891199i	$0.649865\pi$
$824$	1.49786e7	0.768518
$825$	1.67798e6	0.0858325
$826$	−4.33361e6	−0.221004
$827$	5.27202e6	0.268049	0.134024	−	0.990978i	$-0.457210\pi$
$827$	5.27202e6	0.268049	0.134024	+	0.990978i	$0.457210\pi$
$828$	−3.11726e6	−0.158014
$829$	2.49222e7	1.25950	0.629752	−	0.776796i	$-0.283157\pi$
$829$	2.49222e7	1.25950	0.629752	+	0.776796i	$0.283157\pi$
$830$	−6.35587e6	−0.320243
$831$	−3.68821e7	−1.85273
$832$	−1.91118e6	−0.0957182
$833$	2.40733e7	1.20205
$834$	1.24137e7	0.617995
$835$	1.74953e7	0.868370
$836$	−554649.	−0.0274475
$837$	−1.18582e6	−0.0585068
$838$	1.89942e7	0.934353
$839$	−1.81703e7	−0.891161	−0.445580	−	0.895242i	$-0.647003\pi$
$839$	−1.81703e7	−0.891161	−0.445580	+	0.895242i	$0.647003\pi$
$840$	2.54214e6	0.124308
$841$	−1.86241e7	−0.907999
$842$	−3.96201e6	−0.192591
$843$	−4.31913e7	−2.09328
$844$	1.09911e7	0.531111
$845$	8.59112e6	0.413912
$846$	−1.54483e7	−0.742087
$847$	519945.	0.0249028
$848$	−2.42838e7	−1.15965
$849$	−9.59356e6	−0.456784
$850$	6.47060e6	0.307183
$851$	−1.21070e7	−0.573079
$852$	−516645.	−0.0243833
$853$	1.25538e7	0.590747	0.295374	−	0.955382i	$-0.404556\pi$
$853$	1.25538e7	0.590747	0.295374	+	0.955382i	$0.404556\pi$
$854$	8.82545e6	0.414087
$855$	−2.25006e6	−0.105264
$856$	−2.70573e7	−1.26212
$857$	−6.05850e6	−0.281782	−0.140891	−	0.990025i	$-0.544997\pi$
$857$	−6.05850e6	−0.281782	−0.140891	+	0.990025i	$0.544997\pi$
$858$	2.98457e6	0.138409
$859$	1.05765e7	0.489058	0.244529	−	0.969642i	$-0.421367\pi$
$859$	1.05765e7	0.489058	0.244529	+	0.969642i	$0.421367\pi$
$860$	2.08723e6	0.0962332
$861$	−7.58701e6	−0.348789
$862$	−2.97840e7	−1.36526
$863$	−2.67144e7	−1.22101	−0.610503	−	0.792014i	$-0.709033\pi$
$863$	−2.67144e7	−1.22101	−0.610503	+	0.792014i	$0.709033\pi$
$864$	−610130.	−0.0278060
$865$	8.23502e6	0.374218
$866$	2.82364e7	1.27942
$867$	−2.17025e7	−0.980533
$868$	3.81694e6	0.171955
$869$	6.50199e6	0.292077
$870$	−5.09443e6	−0.228191
$871$	4.74268e6	0.211826
$872$	−1.00689e7	−0.448426
$873$	1.03566e7	0.459919
$874$	2.37657e6	0.105238
$875$	−554889.	−0.0245011
$876$	9.34151e6	0.411298
$877$	3.58779e7	1.57517	0.787587	−	0.616204i	$-0.211330\pi$
$877$	3.58779e7	1.57517	0.787587	+	0.616204i	$0.211330\pi$
$878$	−4.53379e7	−1.98484
$879$	−1.62356e7	−0.708756
$880$	−3.83901e6	−0.167114
$881$	8.91161e6	0.386827	0.193413	−	0.981117i	$-0.438044\pi$
$881$	8.91161e6	0.386827	0.193413	+	0.981117i	$0.438044\pi$
$882$	2.59121e7	1.12158
$883$	3.57476e7	1.54293	0.771464	−	0.636273i	$-0.219525\pi$
$883$	3.57476e7	1.54293	0.771464	+	0.636273i	$0.219525\pi$
$884$	3.26950e6	0.140718
$885$	1.01247e7	0.434534
$886$	9.33936e6	0.399699
$887$	2.89800e7	1.23677	0.618386	−	0.785874i	$-0.287787\pi$
$887$	2.89800e7	1.23677	0.618386	+	0.785874i	$0.287787\pi$
$888$	−3.52054e7	−1.49823
$889$	−1.21028e7	−0.513610
$890$	1.85177e7	0.783632
$891$	6.95446e6	0.293474
$892$	−1.38258e7	−0.581808
$893$	3.34579e6	0.140401
$894$	6.98607e7	2.92340
$895$	4.17259e6	0.174120
$896$	−7.67824e6	−0.319515
$897$	−3.63291e6	−0.150756
$898$	−4.80736e7	−1.98937
$899$	1.16277e7	0.479839
$900$	1.97857e6	0.0814228
$901$	−2.96308e7	−1.21600
$902$	7.78918e6	0.318768
$903$	5.18099e6	0.211443
$904$	8.59040e6	0.349617
$905$	1.77985e7	0.722373
$906$	5.04586e7	2.04228
$907$	−7.81143e6	−0.315291	−0.157646	−	0.987496i	$-0.550390\pi$
$907$	−7.81143e6	−0.315291	−0.157646	+	0.987496i	$0.550390\pi$
$908$	−1.31706e7	−0.530139
$909$	1.67522e7	0.672453
$910$	−986966.	−0.0395092
$911$	−4.46841e6	−0.178385	−0.0891923	−	0.996014i	$-0.528429\pi$
$911$	−4.46841e6	−0.178385	−0.0891923	+	0.996014i	$0.528429\pi$
$912$	1.01654e7	0.404702
$913$	4.60127e6	0.182684
$914$	−1.02706e6	−0.0406660
$915$	−2.06191e7	−0.814172
$916$	4.33204e6	0.170590
$917$	−8.39710e6	−0.329766
$918$	−1.45038e6	−0.0568035
$919$	−2.74698e7	−1.07292	−0.536459	−	0.843926i	$-0.680239\pi$
$919$	−2.74698e7	−1.07292	−0.536459	+	0.843926i	$0.680239\pi$
$920$	3.17681e6	0.123743
$921$	−5.38813e7	−2.09309
$922$	−2.28297e7	−0.884449
$923$	−304915.	−0.0117808
$924$	1.21065e6	0.0466486
$925$	7.68453e6	0.295300
$926$	4.55839e6	0.174696
$927$	2.89379e7	1.10603
$928$	5.98270e6	0.228049
$929$	−2.25448e7	−0.857054	−0.428527	−	0.903529i	$-0.640967\pi$
$929$	−2.25448e7	−0.857054	−0.428527	+	0.903529i	$0.640967\pi$
$930$	−3.13911e7	−1.19014
$931$	−5.61205e6	−0.212201
$932$	−1.86385e7	−0.702862
$933$	−4.97836e7	−1.87233
$934$	−4.83651e7	−1.81412
$935$	−4.68433e6	−0.175234
$936$	−5.34972e6	−0.199591
$937$	−2.99038e7	−1.11270	−0.556350	−	0.830948i	$-0.687798\pi$
$937$	−2.99038e7	−1.11270	−0.556350	+	0.830948i	$0.687798\pi$
$938$	6.77205e6	0.251312
$939$	4.52174e7	1.67356
$940$	−2.94210e6	−0.108602
$941$	2.26665e7	0.834468	0.417234	−	0.908799i	$-0.363000\pi$
$941$	2.26665e7	0.834468	0.417234	+	0.908799i	$0.363000\pi$
$942$	9.65998e6	0.354690
$943$	−9.48121e6	−0.347204
$944$	−2.31641e7	−0.846029
$945$	124378.	0.00453069
$946$	−5.31904e6	−0.193244
$947$	1.20875e7	0.437986	0.218993	−	0.975726i	$-0.429723\pi$
$947$	1.20875e7	0.437986	0.218993	+	0.975726i	$0.429723\pi$
$948$	1.51394e7	0.547126
$949$	5.51320e6	0.198718
$950$	−1.50845e6	−0.0542277
$951$	−2.08413e7	−0.747265
$952$	−7.09675e6	−0.253786
$953$	−3.58778e7	−1.27966	−0.639828	−	0.768518i	$-0.720995\pi$
$953$	−3.58778e7	−1.27966	−0.639828	+	0.768518i	$0.720995\pi$
$954$	−3.18942e7	−1.13459
$955$	−1.95572e7	−0.693902
$956$	−1.65516e7	−0.585726
$957$	3.68806e6	0.130172
$958$	7.15170e6	0.251765
$959$	3.73138e6	0.131015
$960$	6.37574e6	0.223281
$961$	4.30191e7	1.50263
$962$	1.36683e7	0.476185
$963$	−5.22732e7	−1.81641
$964$	−1.05131e7	−0.364367
$965$	328915.	0.0113701
$966$	−5.18741e6	−0.178858
$967$	3.79193e7	1.30405	0.652026	−	0.758197i	$-0.273919\pi$
$967$	3.79193e7	1.30405	0.652026	+	0.758197i	$0.273919\pi$
$968$	1.88939e6	0.0648087
$969$	1.24037e7	0.424366
$970$	6.94310e6	0.236932
$971$	1.60742e7	0.547120	0.273560	−	0.961855i	$-0.411799\pi$
$971$	1.60742e7	0.547120	0.273560	+	0.961855i	$0.411799\pi$
$972$	1.66252e7	0.564417
$973$	2.97182e6	0.100633
$974$	−5.28409e7	−1.78473
$975$	2.30587e6	0.0776824
$976$	4.71739e7	1.58518
$977$	3.17636e7	1.06462	0.532308	−	0.846551i	$-0.321325\pi$
$977$	3.17636e7	1.06462	0.532308	+	0.846551i	$0.321325\pi$
$978$	3.54920e7	1.18654
$979$	−1.34057e7	−0.447026
$980$	4.93492e6	0.164140
$981$	−1.94526e7	−0.645364
$982$	3.85880e7	1.27695
$983$	−9.91800e6	−0.327371	−0.163686	−	0.986513i	$-0.552338\pi$
$983$	−9.91800e6	−0.327371	−0.163686	+	0.986513i	$0.552338\pi$
$984$	−2.75699e7	−0.907712
$985$	603198.	0.0198093
$986$	1.42219e7	0.465869
$987$	−7.30296e6	−0.238620
$988$	−762195.	−0.0248413
$989$	6.47449e6	0.210482
$990$	−5.04214e6	−0.163503
$991$	−2.96999e6	−0.0960662	−0.0480331	−	0.998846i	$-0.515295\pi$
$991$	−2.96999e6	−0.0960662	−0.0480331	+	0.998846i	$0.515295\pi$
$992$	3.68645e7	1.18940
$993$	−3.43335e7	−1.10496
$994$	−435386.	−0.0139768
$995$	−3.14659e6	−0.100759
$996$	1.07137e7	0.342209
$997$	−1.99638e7	−0.636070	−0.318035	−	0.948079i	$-0.603023\pi$
$997$	−1.99638e7	−0.636070	−0.318035	+	0.948079i	$0.603023\pi$
$998$	6.66951e7	2.11967
$999$	−1.72248e6	−0.0546061

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.g.1.9	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.g.1.9	✓	39	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)

\(f(q)\)	\(=\)	\(q-6.68564 q^{2} -22.1881 q^{3} +12.6977 q^{4} -25.0000 q^{5} +148.342 q^{6} +35.5129 q^{7} +129.048 q^{8} +249.314 q^{9} +O(q^{10})\)	\(q-6.68564 q^{2} -22.1881 q^{3} +12.6977 q^{4} -25.0000 q^{5} +148.342 q^{6} +35.5129 q^{7} +129.048 q^{8} +249.314 q^{9} +167.141 q^{10} -121.000 q^{11} -281.739 q^{12} -166.277 q^{13} -237.426 q^{14} +554.704 q^{15} -1269.09 q^{16} -1548.54 q^{17} -1666.82 q^{18} +361.000 q^{19} -317.443 q^{20} -787.966 q^{21} +808.962 q^{22} -984.692 q^{23} -2863.34 q^{24} +625.000 q^{25} +1111.67 q^{26} -140.093 q^{27} +450.933 q^{28} +1373.70 q^{29} -3708.55 q^{30} +8464.53 q^{31} +4355.17 q^{32} +2684.77 q^{33} +10353.0 q^{34} -887.823 q^{35} +3165.72 q^{36} +12295.3 q^{37} -2413.51 q^{38} +3689.39 q^{39} -3226.20 q^{40} +9628.61 q^{41} +5268.05 q^{42} -6575.14 q^{43} -1536.42 q^{44} -6232.85 q^{45} +6583.29 q^{46} +9268.12 q^{47} +28158.9 q^{48} -15545.8 q^{49} -4178.52 q^{50} +34359.2 q^{51} -2111.34 q^{52} +19134.7 q^{53} +936.612 q^{54} +3025.00 q^{55} +4582.87 q^{56} -8009.92 q^{57} -9184.06 q^{58} +18252.5 q^{59} +7043.47 q^{60} -37171.3 q^{61} -56590.8 q^{62} +8853.86 q^{63} +11494.0 q^{64} +4156.93 q^{65} -17949.4 q^{66} -28522.7 q^{67} -19662.9 q^{68} +21848.5 q^{69} +5935.66 q^{70} +1833.77 q^{71} +32173.5 q^{72} -33156.6 q^{73} -82201.6 q^{74} -13867.6 q^{75} +4583.88 q^{76} -4297.06 q^{77} -24665.9 q^{78} -53735.5 q^{79} +31727.4 q^{80} -57474.9 q^{81} -64373.4 q^{82} -38027.0 q^{83} -10005.4 q^{84} +38713.4 q^{85} +43959.0 q^{86} -30479.9 q^{87} -15614.8 q^{88} +110791. q^{89} +41670.5 q^{90} -5904.99 q^{91} -12503.3 q^{92} -187812. q^{93} -61963.3 q^{94} -9025.00 q^{95} -96633.2 q^{96} +41540.4 q^{97} +103934. q^{98} -30167.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9}+O(q^{10}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9	\( 39 q + 12 q^{2} + 27 q^{3} + 670 q^{4} - 975 q^{5} + 69 q^{6} - 251 q^{7} + 270 q^{8} + 3666 q^{9} - 300 q^{10} - 4719 q^{11} + 872 q^{12} - 717 q^{13} + 2647 q^{14} - 675 q^{15} + 15078 q^{16} + 2155 q^{17} + 3293 q^{18} + 14079 q^{19} - 16750 q^{20} + 6891 q^{21} - 1452 q^{22} + 1296 q^{23} - 3138 q^{24} + 24375 q^{25} + 2585 q^{26} + 3846 q^{27} - 20901 q^{28} - 7635 q^{29} - 1725 q^{30} + 9595 q^{31} - 43 q^{32} - 3267 q^{33} - 28383 q^{34} + 6275 q^{35} + 80573 q^{36} - 28965 q^{37} + 4332 q^{38} + 21358 q^{39} - 6750 q^{40} + 19627 q^{41} + 12478 q^{42} + 3711 q^{43} - 81070 q^{44} - 91650 q^{45} + 37459 q^{46} + 38450 q^{47} - 12259 q^{48} + 78758 q^{49} + 7500 q^{50} - 68114 q^{51} - 50322 q^{52} + 20631 q^{53} - 124732 q^{54} + 117975 q^{55} + 94893 q^{56} + 9747 q^{57} - 148140 q^{58} + 170405 q^{59} - 21800 q^{60} - 22345 q^{61} + 246390 q^{62} - 151688 q^{63} + 340312 q^{64} + 17925 q^{65} - 8349 q^{66} - 16408 q^{67} - 32276 q^{68} + 93536 q^{69} - 66175 q^{70} + 119338 q^{71} + 135668 q^{72} - 141606 q^{73} + 71843 q^{74} + 16875 q^{75} + 241870 q^{76} + 30371 q^{77} + 708290 q^{78} + 14727 q^{79} - 376950 q^{80} + 441659 q^{81} - 219870 q^{82} + 384909 q^{83} + 877024 q^{84} - 53875 q^{85} + 250290 q^{86} - 77038 q^{87} - 32670 q^{88} + 443394 q^{89} - 82325 q^{90} - 207088 q^{91} - 237112 q^{92} + 396718 q^{93} + 409516 q^{94} - 351975 q^{95} + 100332 q^{96} - 152942 q^{97} + 895680 q^{98} - 443586 q^{99}+O(q^{100}) \) 39 * q + 12 * q^2 + 27 * q^3 + 670 * q^4 - 975 * q^5 + 69 * q^6 - 251 * q^7 + 270 * q^8 + 3666 * q^9 - 300 * q^10 - 4719 * q^11 + 872 * q^12 - 717 * q^13 + 2647 * q^14 - 675 * q^15 + 15078 * q^16 + 2155 * q^17 + 3293 * q^18 + 14079 * q^19 - 16750 * q^20 + 6891 * q^21 - 1452 * q^22 + 1296 * q^23 - 3138 * q^24 + 24375 * q^25 + 2585 * q^26 + 3846 * q^27 - 20901 * q^28 - 7635 * q^29 - 1725 * q^30 + 9595 * q^31 - 43 * q^32 - 3267 * q^33 - 28383 * q^34 + 6275 * q^35 + 80573 * q^36 - 28965 * q^37 + 4332 * q^38 + 21358 * q^39 - 6750 * q^40 + 19627 * q^41 + 12478 * q^42 + 3711 * q^43 - 81070 * q^44 - 91650 * q^45 + 37459 * q^46 + 38450 * q^47 - 12259 * q^48 + 78758 * q^49 + 7500 * q^50 - 68114 * q^51 - 50322 * q^52 + 20631 * q^53 - 124732 * q^54 + 117975 * q^55 + 94893 * q^56 + 9747 * q^57 - 148140 * q^58 + 170405 * q^59 - 21800 * q^60 - 22345 * q^61 + 246390 * q^62 - 151688 * q^63 + 340312 * q^64 + 17925 * q^65 - 8349 * q^66 - 16408 * q^67 - 32276 * q^68 + 93536 * q^69 - 66175 * q^70 + 119338 * q^71 + 135668 * q^72 - 141606 * q^73 + 71843 * q^74 + 16875 * q^75 + 241870 * q^76 + 30371 * q^77 + 708290 * q^78 + 14727 * q^79 - 376950 * q^80 + 441659 * q^81 - 219870 * q^82 + 384909 * q^83 + 877024 * q^84 - 53875 * q^85 + 250290 * q^86 - 77038 * q^87 - 32670 * q^88 + 443394 * q^89 - 82325 * q^90 - 207088 * q^91 - 237112 * q^92 + 396718 * q^93 + 409516 * q^94 - 351975 * q^95 + 100332 * q^96 - 152942 * q^97 + 895680 * q^98 - 443586 * q^99

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