LMFDB - Embedded newform 1045.6.a.f.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:	$38$
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)

$f(q)$	$=$	$q-6.62298 q^{2} -27.0099 q^{3} +11.8638 q^{4} +25.0000 q^{5} +178.886 q^{6} +116.446 q^{7} +133.361 q^{8} +486.535 q^{9} +O(q^{10})$	\(q-6.62298 q^{2} -27.0099 q^{3} +11.8638 q^{4} +25.0000 q^{5} +178.886 q^{6} +116.446 q^{7} +133.361 q^{8} +486.535 q^{9} -165.574 q^{10} -121.000 q^{11} -320.441 q^{12} -620.902 q^{13} -771.220 q^{14} -675.248 q^{15} -1262.89 q^{16} +1063.99 q^{17} -3222.31 q^{18} -361.000 q^{19} +296.596 q^{20} -3145.20 q^{21} +801.380 q^{22} -1775.52 q^{23} -3602.08 q^{24} +625.000 q^{25} +4112.22 q^{26} -6577.86 q^{27} +1381.50 q^{28} +6822.51 q^{29} +4472.15 q^{30} +6352.29 q^{31} +4096.54 q^{32} +3268.20 q^{33} -7046.79 q^{34} +2911.15 q^{35} +5772.17 q^{36} +11247.6 q^{37} +2390.89 q^{38} +16770.5 q^{39} +3334.03 q^{40} +3052.66 q^{41} +20830.6 q^{42} +9533.60 q^{43} -1435.52 q^{44} +12163.4 q^{45} +11759.2 q^{46} +3387.34 q^{47} +34110.6 q^{48} -3247.29 q^{49} -4139.36 q^{50} -28738.3 q^{51} -7366.28 q^{52} -9152.84 q^{53} +43565.0 q^{54} -3025.00 q^{55} +15529.4 q^{56} +9750.58 q^{57} -45185.3 q^{58} +30919.6 q^{59} -8011.03 q^{60} -35258.9 q^{61} -42071.1 q^{62} +56655.2 q^{63} +13281.2 q^{64} -15522.6 q^{65} -21645.2 q^{66} +43760.8 q^{67} +12623.0 q^{68} +47956.7 q^{69} -19280.5 q^{70} -26162.8 q^{71} +64885.0 q^{72} +32979.8 q^{73} -74492.8 q^{74} -16881.2 q^{75} -4282.84 q^{76} -14090.0 q^{77} -111071. q^{78} +31332.8 q^{79} -31572.3 q^{80} +59439.5 q^{81} -20217.7 q^{82} +54205.1 q^{83} -37314.1 q^{84} +26599.8 q^{85} -63140.8 q^{86} -184275. q^{87} -16136.7 q^{88} -85868.8 q^{89} -80557.8 q^{90} -72301.7 q^{91} -21064.5 q^{92} -171575. q^{93} -22434.3 q^{94} -9025.00 q^{95} -110647. q^{96} +142949. q^{97} +21506.7 q^{98} -58870.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * 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 $

$2$	−6.62298	−1.17079	−0.585394	−	0.810749i	$-0.699060\pi$
$2$	−6.62298	−1.17079	−0.585394	+	0.810749i	$0.699060\pi$
$3$	−27.0099	−1.73269	−0.866343	−	0.499449i	$-0.833536\pi$
$3$	−27.0099	−1.73269	−0.866343	+	0.499449i	$0.833536\pi$
$4$	11.8638	0.370745
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	178.886	2.02861
$7$	116.446	0.898215	0.449107	−	0.893478i	$-0.351742\pi$
$7$	116.446	0.898215	0.449107	+	0.893478i	$0.351742\pi$
$8$	133.361	0.736724
$9$	486.535	2.00220
$10$	−165.574	−0.523592
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−320.441	−0.642385
$13$	−620.902	−1.01898	−0.509489	−	0.860477i	$-0.670166\pi$
$13$	−620.902	−1.01898	−0.509489	+	0.860477i	$0.670166\pi$
$14$	−771.220	−1.05162
$15$	−675.248	−0.774881
$16$	−1262.89	−1.23329
$17$	1063.99	0.892927	0.446463	−	0.894802i	$-0.352683\pi$
$17$	1063.99	0.892927	0.446463	+	0.894802i	$0.352683\pi$
$18$	−3222.31	−2.34415
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	296.596	0.165802
$21$	−3145.20	−1.55632
$22$	801.380	0.353006
$23$	−1775.52	−0.699853	−0.349926	−	0.936777i	$-0.613793\pi$
$23$	−1775.52	−0.699853	−0.349926	+	0.936777i	$0.613793\pi$
$24$	−3602.08	−1.27651
$25$	625.000	0.200000
$26$	4112.22	1.19301
$27$	−6577.86	−1.73650
$28$	1381.50	0.333008
$29$	6822.51	1.50643	0.753215	−	0.657774i	$-0.228502\pi$
$29$	6822.51	1.50643	0.753215	+	0.657774i	$0.228502\pi$
$30$	4472.15	0.907221
$31$	6352.29	1.18721	0.593603	−	0.804758i	$-0.297705\pi$
$31$	6352.29	1.18721	0.593603	+	0.804758i	$0.297705\pi$
$32$	4096.54	0.707200
$33$	3268.20	0.522425
$34$	−7046.79	−1.04543
$35$	2911.15	0.401694
$36$	5772.17	0.742306
$37$	11247.6	1.35069	0.675346	−	0.737501i	$-0.263994\pi$
$37$	11247.6	1.35069	0.675346	+	0.737501i	$0.263994\pi$
$38$	2390.89	0.268597
$39$	16770.5	1.76557
$40$	3334.03	0.329473
$41$	3052.66	0.283609	0.141804	−	0.989895i	$-0.454710\pi$
$41$	3052.66	0.283609	0.141804	+	0.989895i	$0.454710\pi$
$42$	20830.6	1.82213
$43$	9533.60	0.786296	0.393148	−	0.919475i	$-0.371386\pi$
$43$	9533.60	0.786296	0.393148	+	0.919475i	$0.371386\pi$
$44$	−1435.52	−0.111784
$45$	12163.4	0.895412
$46$	11759.2	0.819379
$47$	3387.34	0.223673	0.111837	−	0.993727i	$-0.464327\pi$
$47$	3387.34	0.223673	0.111837	+	0.993727i	$0.464327\pi$
$48$	34110.6	2.13691
$49$	−3247.29	−0.193210
$50$	−4139.36	−0.234158
$51$	−28738.3	−1.54716
$52$	−7366.28	−0.377781
$53$	−9152.84	−0.447575	−0.223788	−	0.974638i	$-0.571842\pi$
$53$	−9152.84	−0.447575	−0.223788	+	0.974638i	$0.571842\pi$
$54$	43565.0	2.03308
$55$	−3025.00	−0.134840
$56$	15529.4	0.661737
$57$	9750.58	0.397506
$58$	−45185.3	−1.76371
$59$	30919.6	1.15639	0.578195	−	0.815898i	$-0.303757\pi$
$59$	30919.6	1.15639	0.578195	+	0.815898i	$0.303757\pi$
$60$	−8011.03	−0.287283
$61$	−35258.9	−1.21323	−0.606617	−	0.794994i	$-0.707474\pi$
$61$	−35258.9	−1.21323	−0.606617	+	0.794994i	$0.707474\pi$
$62$	−42071.1	−1.38997
$63$	56655.2	1.79841
$64$	13281.2	0.405311
$65$	−15522.6	−0.455701
$66$	−21645.2	−0.611649
$67$	43760.8	1.19096	0.595481	−	0.803369i	$-0.296961\pi$
$67$	43760.8	1.19096	0.595481	+	0.803369i	$0.296961\pi$
$68$	12623.0	0.331048
$69$	47956.7	1.21263
$70$	−19280.5	−0.470298
$71$	−26162.8	−0.615939	−0.307970	−	0.951396i	$-0.599649\pi$
$71$	−26162.8	−0.615939	−0.307970	+	0.951396i	$0.599649\pi$
$72$	64885.0	1.47507
$73$	32979.8	0.724337	0.362169	−	0.932113i	$-0.382036\pi$
$73$	32979.8	0.724337	0.362169	+	0.932113i	$0.382036\pi$
$74$	−74492.8	−1.58138
$75$	−16881.2	−0.346537
$76$	−4282.84	−0.0850547
$77$	−14090.0	−0.270822
$78$	−111071.	−2.06711
$79$	31332.8	0.564848	0.282424	−	0.959290i	$-0.408862\pi$
$79$	31332.8	0.564848	0.282424	+	0.959290i	$0.408862\pi$
$80$	−31572.3	−0.551545
$81$	59439.5	1.00661
$82$	−20217.7	−0.332046
$83$	54205.1	0.863664	0.431832	−	0.901954i	$-0.357867\pi$
$83$	54205.1	0.863664	0.431832	+	0.901954i	$0.357867\pi$
$84$	−37314.1	−0.576999
$85$	26599.8	0.399329
$86$	−63140.8	−0.920586
$87$	−184275.	−2.61017
$88$	−16136.7	−0.222131
$89$	−85868.8	−1.14911	−0.574553	−	0.818467i	$-0.694824\pi$
$89$	−85868.8	−1.14911	−0.574553	+	0.818467i	$0.694824\pi$
$90$	−80557.8	−1.04834
$91$	−72301.7	−0.915261
$92$	−21064.5	−0.259467
$93$	−171575.	−2.05706
$94$	−22434.3	−0.261874
$95$	−9025.00	−0.102598
$96$	−110647.	−1.22536
$97$	142949.	1.54259	0.771297	−	0.636475i	$-0.219608\pi$
$97$	142949.	1.54259	0.771297	+	0.636475i	$0.219608\pi$
$98$	21506.7	0.226208
$99$	−58870.8	−0.603687
$100$	7414.90	0.0741490
$101$	−80082.5	−0.781149	−0.390575	−	0.920571i	$-0.627724\pi$
$101$	−80082.5	−0.781149	−0.390575	+	0.920571i	$0.627724\pi$
$102$	190333.	1.81140
$103$	32201.1	0.299073	0.149537	−	0.988756i	$-0.452222\pi$
$103$	32201.1	0.299073	0.149537	+	0.988756i	$0.452222\pi$
$104$	−82804.4	−0.750706
$105$	−78630.0	−0.696009
$106$	60619.0	0.524016
$107$	45317.9	0.382658	0.191329	−	0.981526i	$-0.438720\pi$
$107$	45317.9	0.382658	0.191329	+	0.981526i	$0.438720\pi$
$108$	−78038.7	−0.643799
$109$	127164.	1.02517	0.512587	−	0.858635i	$-0.328687\pi$
$109$	127164.	1.02517	0.512587	+	0.858635i	$0.328687\pi$
$110$	20034.5	0.157869
$111$	−303797.	−2.34033
$112$	−147059.	−1.10776
$113$	−208549.	−1.53643	−0.768214	−	0.640193i	$-0.778854\pi$
$113$	−208549.	−1.53643	−0.768214	+	0.640193i	$0.778854\pi$
$114$	−64577.9	−0.465395
$115$	−44388.1	−0.312984
$116$	80941.1	0.558501
$117$	−302091.	−2.04020
$118$	−204780.	−1.35389
$119$	123898.	0.802040
$120$	−90052.0	−0.570874
$121$	14641.0	0.0909091
$122$	233519.	1.42044
$123$	−82452.2	−0.491405
$124$	75362.6	0.440151
$125$	15625.0	0.0894427
$126$	−375226.	−2.10555
$127$	−401.076	−0.00220657	−0.00110328	−	0.999999i	$-0.500351\pi$
$127$	−401.076	−0.00220657	−0.00110328	+	0.999999i	$0.500351\pi$
$128$	−219051.	−1.18173
$129$	−257502.	−1.36240
$130$	102806.	0.533529
$131$	279139.	1.42116	0.710580	−	0.703617i	$-0.248433\pi$
$131$	279139.	1.42116	0.710580	+	0.703617i	$0.248433\pi$
$132$	38773.4	0.193686
$133$	−42037.1	−0.206065
$134$	−289827.	−1.39436
$135$	−164447.	−0.776588
$136$	141895.	0.657841
$137$	173320.	0.788946	0.394473	−	0.918907i	$-0.370927\pi$
$137$	173320.	0.788946	0.394473	+	0.918907i	$0.370927\pi$
$138$	−317616.	−1.41973
$139$	−229502.	−1.00751	−0.503755	−	0.863847i	$-0.668048\pi$
$139$	−229502.	−1.00751	−0.503755	+	0.863847i	$0.668048\pi$
$140$	34537.5	0.148926
$141$	−91491.7	−0.387555
$142$	173275.	0.721134
$143$	75129.2	0.307233
$144$	−614441.	−2.46930
$145$	170563.	0.673696
$146$	−218424.	−0.848045
$147$	87708.9	0.334773
$148$	133440.	0.500762
$149$	312242.	1.15219	0.576097	−	0.817381i	$-0.304575\pi$
$149$	312242.	1.15219	0.576097	+	0.817381i	$0.304575\pi$
$150$	111804.	0.405722
$151$	−228059.	−0.813962	−0.406981	−	0.913437i	$-0.633418\pi$
$151$	−228059.	−0.813962	−0.406981	+	0.913437i	$0.633418\pi$
$152$	−48143.5	−0.169016
$153$	517669.	1.78782
$154$	93317.7	0.317075
$155$	158807.	0.530935
$156$	198963.	0.654576
$157$	−104821.	−0.339390	−0.169695	−	0.985497i	$-0.554278\pi$
$157$	−104821.	−0.339390	−0.169695	+	0.985497i	$0.554278\pi$
$158$	−207516.	−0.661317
$159$	247217.	0.775508
$160$	102414.	0.316270
$161$	−206753.	−0.628618
$162$	−393666.	−1.17853
$163$	30544.0	0.0900443	0.0450221	−	0.998986i	$-0.485664\pi$
$163$	30544.0	0.0900443	0.0450221	+	0.998986i	$0.485664\pi$
$164$	36216.3	0.105146
$165$	81705.0	0.233635
$166$	−358999.	−1.01117
$167$	350365.	0.972140	0.486070	−	0.873920i	$-0.338430\pi$
$167$	350365.	0.972140	0.486070	+	0.873920i	$0.338430\pi$
$168$	−419448.	−1.14658
$169$	14226.4	0.0383158
$170$	−176170.	−0.467530
$171$	−175639.	−0.459337
$172$	113105.	0.291515
$173$	−657723.	−1.67081	−0.835406	−	0.549633i	$-0.814767\pi$
$173$	−657723.	−1.67081	−0.835406	+	0.549633i	$0.814767\pi$
$174$	1.22045e6	3.05596
$175$	72778.9	0.179643
$176$	152810.	0.371852
$177$	−835137.	−2.00366
$178$	568707.	1.34536
$179$	590092.	1.37654	0.688268	−	0.725457i	$-0.258371\pi$
$179$	590092.	1.37654	0.688268	+	0.725457i	$0.258371\pi$
$180$	144304.	0.331969
$181$	668481.	1.51668	0.758338	−	0.651862i	$-0.226012\pi$
$181$	668481.	1.51668	0.758338	+	0.651862i	$0.226012\pi$
$182$	478852.	1.07158
$183$	952341.	2.10215
$184$	−236786.	−0.515599
$185$	281191.	0.604048
$186$	1.13634e6	2.40838
$187$	−128743.	−0.269228
$188$	40186.8	0.0829257
$189$	−765967.	−1.55975
$190$	59772.4	0.120120
$191$	−638762.	−1.26694	−0.633469	−	0.773768i	$-0.718370\pi$
$191$	−638762.	−1.26694	−0.633469	+	0.773768i	$0.718370\pi$
$192$	−358725.	−0.702277
$193$	334659.	0.646710	0.323355	−	0.946278i	$-0.395189\pi$
$193$	334659.	0.646710	0.323355	+	0.946278i	$0.395189\pi$
$194$	−946748.	−1.80605
$195$	419263.	0.789587
$196$	−38525.3	−0.0716317
$197$	−734146.	−1.34777	−0.673887	−	0.738835i	$-0.735376\pi$
$197$	−734146.	−1.34777	−0.673887	+	0.738835i	$0.735376\pi$
$198$	389900.	0.706789
$199$	−487057.	−0.871860	−0.435930	−	0.899981i	$-0.643581\pi$
$199$	−487057.	−0.871860	−0.435930	+	0.899981i	$0.643581\pi$
$200$	83350.9	0.147345
$201$	−1.18197e6	−2.06356
$202$	530385.	0.914561
$203$	794455.	1.35310
$204$	−340947.	−0.573602
$205$	76316.6	0.126834
$206$	−213267.	−0.350151
$207$	−863854.	−1.40125
$208$	784132.	1.25670
$209$	43681.0	0.0691714
$210$	520765.	0.814880
$211$	−599101.	−0.926391	−0.463195	−	0.886256i	$-0.653297\pi$
$211$	−599101.	−0.926391	−0.463195	+	0.886256i	$0.653297\pi$
$212$	−108588.	−0.165936
$213$	706654.	1.06723
$214$	−300140.	−0.448011
$215$	238340.	0.351642
$216$	−877233.	−1.27932
$217$	739700.	1.06637
$218$	−842204.	−1.20026
$219$	−890781.	−1.25505
$220$	−35888.1	−0.0499912
$221$	−660635.	−0.909873
$222$	2.01204e6	2.74003
$223$	−71915.1	−0.0968407	−0.0484204	−	0.998827i	$-0.515419\pi$
$223$	−71915.1	−0.0968407	−0.0484204	+	0.998827i	$0.515419\pi$
$224$	477027.	0.635218
$225$	304085.	0.400440
$226$	1.38122e6	1.79883
$227$	1.25207e6	1.61274	0.806368	−	0.591414i	$-0.201430\pi$
$227$	1.25207e6	1.61274	0.806368	+	0.591414i	$0.201430\pi$
$228$	115679.	0.147373
$229$	−862119.	−1.08637	−0.543186	−	0.839612i	$-0.682782\pi$
$229$	−862119.	−1.08637	−0.543186	+	0.839612i	$0.682782\pi$
$230$	293981.	0.366438
$231$	380569.	0.469249
$232$	909859.	1.10982
$233$	−403812.	−0.487292	−0.243646	−	0.969864i	$-0.578344\pi$
$233$	−403812.	−0.487292	−0.243646	+	0.969864i	$0.578344\pi$
$234$	2.00074e6	2.38864
$235$	84683.4	0.100030
$236$	366826.	0.428726
$237$	−846296.	−0.978704
$238$	−820572.	−0.939019
$239$	−1.46245e6	−1.65610	−0.828052	−	0.560652i	$-0.810551\pi$
$239$	−1.46245e6	−1.65610	−0.828052	+	0.560652i	$0.810551\pi$
$240$	852765.	0.955655
$241$	−1.10891e6	−1.22985	−0.614927	−	0.788584i	$-0.710815\pi$
$241$	−1.10891e6	−1.22985	−0.614927	+	0.788584i	$0.710815\pi$
$242$	−96967.0	−0.106435
$243$	−7033.26	−0.00764084
$244$	−418306.	−0.449800
$245$	−81182.2	−0.0864063
$246$	546079.	0.575331
$247$	224146.	0.233770
$248$	847151.	0.874644
$249$	−1.46407e6	−1.49646
$250$	−103484.	−0.104718
$251$	−1.30956e6	−1.31202	−0.656012	−	0.754751i	$-0.727758\pi$
$251$	−1.30956e6	−1.31202	−0.656012	+	0.754751i	$0.727758\pi$
$252$	672148.	0.666750
$253$	214838.	0.211014
$254$	2656.32	0.00258342
$255$	−718458.	−0.691912
$256$	1.02577e6	0.978249
$257$	429184.	0.405332	0.202666	−	0.979248i	$-0.435039\pi$
$257$	429184.	0.405332	0.202666	+	0.979248i	$0.435039\pi$
$258$	1.70543e6	1.59509
$259$	1.30974e6	1.21321
$260$	−184157.	−0.168949
$261$	3.31939e6	3.01618
$262$	−1.84873e6	−1.66388
$263$	1.66887e6	1.48776	0.743882	−	0.668312i	$-0.232983\pi$
$263$	1.66887e6	1.48776	0.743882	+	0.668312i	$0.232983\pi$
$264$	435852.	0.384883
$265$	−228821.	−0.200162
$266$	278411.	0.241258
$267$	2.31931e6	1.99104
$268$	519171.	0.441543
$269$	−914527.	−0.770576	−0.385288	−	0.922796i	$-0.625898\pi$
$269$	−914527.	−0.770576	−0.385288	+	0.922796i	$0.625898\pi$
$270$	1.08913e6	0.909220
$271$	465037.	0.384648	0.192324	−	0.981331i	$-0.438397\pi$
$271$	465037.	0.384648	0.192324	+	0.981331i	$0.438397\pi$
$272$	−1.34371e6	−1.10124
$273$	1.95286e6	1.58586
$274$	−1.14789e6	−0.923689
$275$	−75625.0	−0.0603023
$276$	568951.	0.449575
$277$	−2.07184e6	−1.62240	−0.811200	−	0.584769i	$-0.801185\pi$
$277$	−2.07184e6	−1.62240	−0.811200	+	0.584769i	$0.801185\pi$
$278$	1.51999e6	1.17958
$279$	3.09061e6	2.37703
$280$	388236.	0.295938
$281$	−1.50722e6	−1.13871	−0.569353	−	0.822093i	$-0.692806\pi$
$281$	−1.50722e6	−1.13871	−0.569353	+	0.822093i	$0.692806\pi$
$282$	605947.	0.453745
$283$	814416.	0.604478	0.302239	−	0.953232i	$-0.402266\pi$
$283$	814416.	0.604478	0.302239	+	0.953232i	$0.402266\pi$
$284$	−310391.	−0.228356
$285$	243764.	0.177770
$286$	−497579.	−0.359705
$287$	355471.	0.254741
$288$	1.99311e6	1.41596
$289$	−287779.	−0.202681
$290$	−1.12963e6	−0.788756
$291$	−3.86104e6	−2.67283
$292$	391267.	0.268544
$293$	155248.	0.105647	0.0528233	−	0.998604i	$-0.483178\pi$
$293$	155248.	0.105647	0.0528233	+	0.998604i	$0.483178\pi$
$294$	−580894.	−0.391948
$295$	772991.	0.517154
$296$	1.50000e6	0.995089
$297$	795922.	0.523575
$298$	−2.06797e6	−1.34898
$299$	1.10243e6	0.713134
$300$	−200276.	−0.128477
$301$	1.11015e6	0.706262
$302$	1.51043e6	0.952977
$303$	2.16302e6	1.35349
$304$	455904.	0.282937
$305$	−881474.	−0.542575
$306$	−3.42851e6	−2.09316
$307$	−619981.	−0.375433	−0.187717	−	0.982223i	$-0.560109\pi$
$307$	−619981.	−0.375433	−0.187717	+	0.982223i	$0.560109\pi$
$308$	−167161.	−0.100406
$309$	−869749.	−0.518200
$310$	−1.05178e6	−0.621612
$311$	−536005.	−0.314244	−0.157122	−	0.987579i	$-0.550222\pi$
$311$	−536005.	−0.314244	−0.157122	+	0.987579i	$0.550222\pi$
$312$	2.23654e6	1.30074
$313$	1.40002e6	0.807742	0.403871	−	0.914816i	$-0.367664\pi$
$313$	1.40002e6	0.807742	0.403871	+	0.914816i	$0.367664\pi$
$314$	694226.	0.397353
$315$	1.41638e6	0.804272
$316$	371727.	0.209414
$317$	2.65992e6	1.48669	0.743345	−	0.668908i	$-0.233238\pi$
$317$	2.65992e6	1.48669	0.743345	+	0.668908i	$0.233238\pi$
$318$	−1.63731e6	−0.907955
$319$	−825524.	−0.454206
$320$	332031.	0.181261
$321$	−1.22403e6	−0.663026
$322$	1.36932e6	0.735979
$323$	−384101.	−0.204851
$324$	705180.	0.373196
$325$	−388064.	−0.203796
$326$	−202292.	−0.105423
$327$	−3.43469e6	−1.77631
$328$	407107.	0.208941
$329$	394443.	0.200906
$330$	−541130.	−0.273538
$331$	−2.84073e6	−1.42515	−0.712574	−	0.701597i	$-0.752471\pi$
$331$	−2.84073e6	−1.42515	−0.712574	+	0.701597i	$0.752471\pi$
$332$	643080.	0.320199
$333$	5.47237e6	2.70436
$334$	−2.32046e6	−1.13817
$335$	1.09402e6	0.532614
$336$	3.97205e6	1.91940
$337$	3.63614e6	1.74408	0.872039	−	0.489436i	$-0.162797\pi$
$337$	3.63614e6	1.74408	0.872039	+	0.489436i	$0.162797\pi$
$338$	−94221.1	−0.0448597
$339$	5.63289e6	2.66215
$340$	315576.	0.148049
$341$	−768627.	−0.357956
$342$	1.16325e6	0.537786
$343$	−2.33525e6	−1.07176
$344$	1.27141e6	0.579283
$345$	1.19892e6	0.542303
$346$	4.35608e6	1.95617
$347$	3.65446e6	1.62929	0.814646	−	0.579958i	$-0.196931\pi$
$347$	3.65446e6	1.62929	0.814646	+	0.579958i	$0.196931\pi$
$348$	−2.18621e6	−0.967708
$349$	2.07097e6	0.910144	0.455072	−	0.890455i	$-0.349614\pi$
$349$	2.07097e6	0.910144	0.455072	+	0.890455i	$0.349614\pi$
$350$	−482013.	−0.210324
$351$	4.08421e6	1.76946
$352$	−495682.	−0.213229
$353$	−2.29634e6	−0.980843	−0.490421	−	0.871485i	$-0.663157\pi$
$353$	−2.29634e6	−0.980843	−0.490421	+	0.871485i	$0.663157\pi$
$354$	5.53109e6	2.34586
$355$	−654069.	−0.275456
$356$	−1.01873e6	−0.426025
$357$	−3.34647e6	−1.38968
$358$	−3.90817e6	−1.61163
$359$	1.48606e6	0.608554	0.304277	−	0.952584i	$-0.401585\pi$
$359$	1.48606e6	0.608554	0.304277	+	0.952584i	$0.401585\pi$
$360$	1.62213e6	0.659672
$361$	130321.	0.0526316
$362$	−4.42734e6	−1.77571
$363$	−395452.	−0.157517
$364$	−857775.	−0.339328
$365$	824495.	0.323933
$366$	−6.30733e6	−2.46118
$367$	−3.42280e6	−1.32653	−0.663263	−	0.748386i	$-0.730829\pi$
$367$	−3.42280e6	−1.32653	−0.663263	+	0.748386i	$0.730829\pi$
$368$	2.24229e6	0.863124
$369$	1.48523e6	0.567842
$370$	−1.86232e6	−0.707213
$371$	−1.06581e6	−0.402019
$372$	−2.03554e6	−0.762643
$373$	−2.23012e6	−0.829958	−0.414979	−	0.909831i	$-0.636211\pi$
$373$	−2.23012e6	−0.829958	−0.414979	+	0.909831i	$0.636211\pi$
$374$	852662.	0.315208
$375$	−422030.	−0.154976
$376$	451740.	0.164785
$377$	−4.23611e6	−1.53502
$378$	5.07298e6	1.82614
$379$	2.10157e6	0.751528	0.375764	−	0.926715i	$-0.377380\pi$
$379$	2.10157e6	0.751528	0.375764	+	0.926715i	$0.377380\pi$
$380$	−107071.	−0.0380376
$381$	10833.0	0.00382329
$382$	4.23051e6	1.48332
$383$	3.14641e6	1.09602	0.548010	−	0.836471i	$-0.315385\pi$
$383$	3.14641e6	1.09602	0.548010	+	0.836471i	$0.315385\pi$
$384$	5.91654e6	2.04757
$385$	−352250.	−0.121115
$386$	−2.21644e6	−0.757160
$387$	4.63843e6	1.57432
$388$	1.69592e6	0.571909
$389$	−3.51131e6	−1.17651	−0.588254	−	0.808676i	$-0.700184\pi$
$389$	−3.51131e6	−1.17651	−0.588254	+	0.808676i	$0.700184\pi$
$390$	−2.77677e6	−0.924439
$391$	−1.88914e6	−0.624917
$392$	−433063.	−0.142343
$393$	−7.53953e6	−2.46242
$394$	4.86223e6	1.57796
$395$	783320.	0.252608
$396$	−698433.	−0.223814
$397$	−81861.5	−0.0260677	−0.0130339	−	0.999915i	$-0.504149\pi$
$397$	−81861.5	−0.0260677	−0.0130339	+	0.999915i	$0.504149\pi$
$398$	3.22577e6	1.02076
$399$	1.13542e6	0.357045
$400$	−789308.	−0.246659
$401$	550387.	0.170926	0.0854628	−	0.996341i	$-0.472763\pi$
$401$	550387.	0.170926	0.0854628	+	0.996341i	$0.472763\pi$
$402$	7.82819e6	2.41600
$403$	−3.94415e6	−1.20974
$404$	−950085.	−0.289607
$405$	1.48599e6	0.450171
$406$	−5.26166e6	−1.58419
$407$	−1.36096e6	−0.407249
$408$	−3.83258e6	−1.13983
$409$	2.82527e6	0.835127	0.417563	−	0.908648i	$-0.362884\pi$
$409$	2.82527e6	0.835127	0.417563	+	0.908648i	$0.362884\pi$
$410$	−505443.	−0.148495
$411$	−4.68136e6	−1.36700
$412$	382028.	0.110880
$413$	3.60047e6	1.03869
$414$	5.72129e6	1.64056
$415$	1.35513e6	0.386242
$416$	−2.54355e6	−0.720622
$417$	6.19882e6	1.74570
$418$	−289298.	−0.0809851
$419$	−5.59670e6	−1.55739	−0.778695	−	0.627403i	$-0.784118\pi$
$419$	−5.59670e6	−1.55739	−0.778695	+	0.627403i	$0.784118\pi$
$420$	−932854.	−0.258042
$421$	2.21018e6	0.607746	0.303873	−	0.952713i	$-0.401720\pi$
$421$	2.21018e6	0.607746	0.303873	+	0.952713i	$0.401720\pi$
$422$	3.96783e6	1.08461
$423$	1.64806e6	0.447839
$424$	−1.22063e6	−0.329740
$425$	664995.	0.178585
$426$	−4.68015e6	−1.24950
$427$	−4.10577e6	−1.08974
$428$	537645.	0.141868
$429$	−2.02923e6	−0.532339
$430$	−1.57852e6	−0.411698
$431$	−5.61981e6	−1.45723	−0.728615	−	0.684924i	$-0.759836\pi$
$431$	−5.61981e6	−1.45723	−0.728615	+	0.684924i	$0.759836\pi$
$432$	8.30713e6	2.14162
$433$	−1.60197e6	−0.410616	−0.205308	−	0.978697i	$-0.565820\pi$
$433$	−1.60197e6	−0.410616	−0.205308	+	0.978697i	$0.565820\pi$
$434$	−4.89902e6	−1.24849
$435$	−4.60688e6	−1.16730
$436$	1.50865e6	0.380078
$437$	640964.	0.160557
$438$	5.89962e6	1.46940
$439$	3.80034e6	0.941155	0.470577	−	0.882359i	$-0.344046\pi$
$439$	3.80034e6	0.941155	0.470577	+	0.882359i	$0.344046\pi$
$440$	−403418.	−0.0993399
$441$	−1.57992e6	−0.386846
$442$	4.37537e6	1.06527
$443$	4.20137e6	1.01714	0.508570	−	0.861020i	$-0.330174\pi$
$443$	4.20137e6	1.01714	0.508570	+	0.861020i	$0.330174\pi$
$444$	−3.60420e6	−0.867664
$445$	−2.14672e6	−0.513896
$446$	476292.	0.113380
$447$	−8.43363e6	−1.99639
$448$	1.54655e6	0.364056
$449$	−1.56367e6	−0.366041	−0.183021	−	0.983109i	$-0.558587\pi$
$449$	−1.56367e6	−0.366041	−0.183021	+	0.983109i	$0.558587\pi$
$450$	−2.01394e6	−0.468831
$451$	−369372.	−0.0855112
$452$	−2.47419e6	−0.569623
$453$	6.15984e6	1.41034
$454$	−8.29242e6	−1.88817
$455$	−1.80754e6	−0.409317
$456$	1.30035e6	0.292852
$457$	3.86704e6	0.866141	0.433070	−	0.901360i	$-0.357430\pi$
$457$	3.86704e6	0.866141	0.433070	+	0.901360i	$0.357430\pi$
$458$	5.70980e6	1.27191
$459$	−6.99879e6	−1.55057
$460$	−526613.	−0.116037
$461$	5.78333e6	1.26744	0.633718	−	0.773564i	$-0.281528\pi$
$461$	5.78333e6	1.26744	0.633718	+	0.773564i	$0.281528\pi$
$462$	−2.52050e6	−0.549392
$463$	−4.57745e6	−0.992365	−0.496182	−	0.868218i	$-0.665265\pi$
$463$	−4.57745e6	−0.992365	−0.496182	+	0.868218i	$0.665265\pi$
$464$	−8.61609e6	−1.85787
$465$	−4.28937e6	−0.919944
$466$	2.67444e6	0.570516
$467$	4.37465e6	0.928219	0.464110	−	0.885778i	$-0.346374\pi$
$467$	4.37465e6	0.928219	0.464110	+	0.885778i	$0.346374\pi$
$468$	−3.58395e6	−0.756394
$469$	5.09577e6	1.06974
$470$	−560857.	−0.117114
$471$	2.83120e6	0.588056
$472$	4.12349e6	0.851941
$473$	−1.15357e6	−0.237077
$474$	5.60500e6	1.14585
$475$	−225625.	−0.0458831
$476$	1.46990e6	0.297352
$477$	−4.45318e6	−0.896136
$478$	9.68580e6	1.93895
$479$	7.47630e6	1.48884	0.744419	−	0.667712i	$-0.232726\pi$
$479$	7.47630e6	1.48884	0.744419	+	0.667712i	$0.232726\pi$
$480$	−2.76618e6	−0.547996
$481$	−6.98368e6	−1.37633
$482$	7.34429e6	1.43990
$483$	5.58438e6	1.08920
$484$	173698.	0.0337041
$485$	3.57372e6	0.689869
$486$	46581.1	0.00894580
$487$	−1.86709e6	−0.356733	−0.178367	−	0.983964i	$-0.557081\pi$
$487$	−1.86709e6	−0.356733	−0.178367	+	0.983964i	$0.557081\pi$
$488$	−4.70218e6	−0.893819
$489$	−824989.	−0.156019
$490$	537668.	0.101163
$491$	3.50392e6	0.655919	0.327960	−	0.944692i	$-0.393639\pi$
$491$	3.50392e6	0.655919	0.327960	+	0.944692i	$0.393639\pi$
$492$	−978199.	−0.182186
$493$	7.25909e6	1.34513
$494$	−1.48451e6	−0.273695
$495$	−1.47177e6	−0.269977
$496$	−8.02226e6	−1.46417
$497$	−3.04655e6	−0.553246
$498$	9.69653e6	1.75204
$499$	−3.52220e6	−0.633231	−0.316616	−	0.948554i	$-0.602547\pi$
$499$	−3.52220e6	−0.633231	−0.316616	+	0.948554i	$0.602547\pi$
$500$	185372.	0.0331604
$501$	−9.46332e6	−1.68441
$502$	8.67320e6	1.53610
$503$	8.04944e6	1.41855	0.709277	−	0.704930i	$-0.249022\pi$
$503$	8.04944e6	1.41855	0.709277	+	0.704930i	$0.249022\pi$
$504$	7.55561e6	1.32493
$505$	−2.00206e6	−0.349341
$506$	−1.42287e6	−0.247052
$507$	−384254.	−0.0663893
$508$	−4758.30	−0.000818074 0
$509$	−4.95948e6	−0.848481	−0.424240	−	0.905550i	$-0.639459\pi$
$509$	−4.95948e6	−0.848481	−0.424240	+	0.905550i	$0.639459\pi$
$510$	4.75833e6	0.810082
$511$	3.84037e6	0.650610
$512$	215982.	0.0364118
$513$	2.37461e6	0.398381
$514$	−2.84248e6	−0.474558
$515$	805027.	0.133750
$516$	−3.05496e6	−0.505104
$517$	−409868.	−0.0674400
$518$	−8.67440e6	−1.42041
$519$	1.77650e7	2.89499
$520$	−2.07011e6	−0.335726
$521$	1.09227e6	0.176293	0.0881466	−	0.996108i	$-0.471906\pi$
$521$	1.09227e6	0.176293	0.0881466	+	0.996108i	$0.471906\pi$
$522$	−2.19843e7	−3.53131
$523$	6.76684e6	1.08176	0.540881	−	0.841099i	$-0.318091\pi$
$523$	6.76684e6	1.08176	0.540881	+	0.841099i	$0.318091\pi$
$524$	3.31166e6	0.526888
$525$	−1.96575e6	−0.311265
$526$	−1.10529e7	−1.74186
$527$	6.75879e6	1.06009
$528$	−4.12738e6	−0.644303
$529$	−3.28386e6	−0.510206
$530$	1.51548e6	0.234347
$531$	1.50435e7	2.31533
$532$	−498721.	−0.0763974
$533$	−1.89541e6	−0.288991
$534$	−1.53607e7	−2.33109
$535$	1.13295e6	0.171130
$536$	5.83600e6	0.877411
$537$	−1.59383e7	−2.38510
$538$	6.05689e6	0.902182
$539$	392922.	0.0582551
$540$	−1.95097e6	−0.287916
$541$	1.02740e7	1.50920	0.754601	−	0.656184i	$-0.227831\pi$
$541$	1.02740e7	1.50920	0.754601	+	0.656184i	$0.227831\pi$
$542$	−3.07993e6	−0.450342
$543$	−1.80556e7	−2.62792
$544$	4.35869e6	0.631478
$545$	3.17910e6	0.458472
$546$	−1.29338e7	−1.85671
$547$	5.26079e6	0.751766	0.375883	−	0.926667i	$-0.377339\pi$
$547$	5.26079e6	0.751766	0.375883	+	0.926667i	$0.377339\pi$
$548$	2.05624e6	0.292498
$549$	−1.71547e7	−2.42914
$550$	500863.	0.0706012
$551$	−2.46293e6	−0.345599
$552$	6.39557e6	0.893371
$553$	3.64858e6	0.507354
$554$	1.37218e7	1.89949
$555$	−7.59494e6	−1.04663
$556$	−2.72277e6	−0.373529
$557$	−5.91357e6	−0.807628	−0.403814	−	0.914841i	$-0.632316\pi$
$557$	−5.91357e6	−0.807628	−0.403814	+	0.914841i	$0.632316\pi$
$558$	−2.04691e7	−2.78300
$559$	−5.91943e6	−0.801218
$560$	−3.67647e6	−0.495406
$561$	3.47734e6	0.466487
$562$	9.98231e6	1.33318
$563$	8.51779e6	1.13255	0.566273	−	0.824218i	$-0.308385\pi$
$563$	8.51779e6	1.13255	0.566273	+	0.824218i	$0.308385\pi$
$564$	−1.08544e6	−0.143684
$565$	−5.21373e6	−0.687111
$566$	−5.39386e6	−0.707716
$567$	6.92150e6	0.904154
$568$	−3.48910e6	−0.453777
$569$	−533438.	−0.0690722	−0.0345361	−	0.999403i	$-0.510995\pi$
$569$	−533438.	−0.0690722	−0.0345361	+	0.999403i	$0.510995\pi$
$570$	−1.61445e6	−0.208131
$571$	−3.91272e6	−0.502213	−0.251107	−	0.967959i	$-0.580794\pi$
$571$	−3.91272e6	−0.502213	−0.251107	+	0.967959i	$0.580794\pi$
$572$	891320.	0.113905
$573$	1.72529e7	2.19521
$574$	−2.35428e6	−0.298248
$575$	−1.10970e6	−0.139971
$576$	6.46179e6	0.811515
$577$	−1.31074e7	−1.63900	−0.819498	−	0.573083i	$-0.805747\pi$
$577$	−1.31074e7	−1.63900	−0.819498	+	0.573083i	$0.805747\pi$
$578$	1.90595e6	0.237297
$579$	−9.03911e6	−1.12055
$580$	2.02353e6	0.249769
$581$	6.31197e6	0.775755
$582$	2.55716e7	3.12932
$583$	1.10749e6	0.134949
$584$	4.39823e6	0.533637
$585$	−7.55227e6	−0.912405
$586$	−1.02820e6	−0.123690
$587$	9.19668e6	1.10163	0.550815	−	0.834627i	$-0.314317\pi$
$587$	9.19668e6	1.10163	0.550815	+	0.834627i	$0.314317\pi$
$588$	1.04056e6	0.124115
$589$	−2.29318e6	−0.272364
$590$	−5.11950e6	−0.605477
$591$	1.98292e7	2.33527
$592$	−1.42045e7	−1.66580
$593$	7.84595e6	0.916239	0.458119	−	0.888891i	$-0.348523\pi$
$593$	7.84595e6	0.916239	0.458119	+	0.888891i	$0.348523\pi$
$594$	−5.27137e6	−0.612996
$595$	3.09744e6	0.358683
$596$	3.70439e6	0.427170
$597$	1.31554e7	1.51066
$598$	−7.30134e6	−0.834929
$599$	−5.89447e6	−0.671240	−0.335620	−	0.941998i	$-0.608946\pi$
$599$	−5.89447e6	−0.671240	−0.335620	+	0.941998i	$0.608946\pi$
$600$	−2.25130e6	−0.255303
$601$	6.52145e6	0.736475	0.368238	−	0.929732i	$-0.379961\pi$
$601$	6.52145e6	0.736475	0.368238	+	0.929732i	$0.379961\pi$
$602$	−7.35251e6	−0.826884
$603$	2.12912e7	2.38455
$604$	−2.70565e6	−0.301772
$605$	366025.	0.0406558
$606$	−1.43256e7	−1.58465
$607$	−5.20969e6	−0.573905	−0.286952	−	0.957945i	$-0.592642\pi$
$607$	−5.20969e6	−0.573905	−0.286952	+	0.957945i	$0.592642\pi$
$608$	−1.47885e6	−0.162243
$609$	−2.14582e7	−2.34450
$610$	5.83798e6	0.635240
$611$	−2.10320e6	−0.227918
$612$	6.14154e6	0.662825
$613$	−4.26778e6	−0.458724	−0.229362	−	0.973341i	$-0.573664\pi$
$613$	−4.26778e6	−0.458724	−0.229362	+	0.973341i	$0.573664\pi$
$614$	4.10612e6	0.439553
$615$	−2.06130e6	−0.219763
$616$	−1.87906e6	−0.199521
$617$	−1.74105e6	−0.184119	−0.0920596	−	0.995753i	$-0.529345\pi$
$617$	−1.74105e6	−0.184119	−0.0920596	+	0.995753i	$0.529345\pi$
$618$	5.76033e6	0.606703
$619$	5.27339e6	0.553176	0.276588	−	0.960989i	$-0.410796\pi$
$619$	5.27339e6	0.553176	0.276588	+	0.960989i	$0.410796\pi$
$620$	1.88406e6	0.196841
$621$	1.16791e7	1.21530
$622$	3.54995e6	0.367914
$623$	−9.99909e6	−1.03214
$624$	−2.11793e7	−2.17746
$625$	390625.	0.0400000
$626$	−9.27228e6	−0.945695
$627$	−1.17982e6	−0.119852
$628$	−1.24358e6	−0.125827
$629$	1.19674e7	1.20607
$630$	−9.38065e6	−0.941633
$631$	172545.	0.0172516	0.00862581	−	0.999963i	$-0.497254\pi$
$631$	172545.	0.0172516	0.00862581	+	0.999963i	$0.497254\pi$
$632$	4.17858e6	0.416137
$633$	1.61817e7	1.60514
$634$	−1.76166e7	−1.74060
$635$	−10026.9	−0.000986807 0
$636$	2.93295e6	0.287515
$637$	2.01625e6	0.196877
$638$	5.46743e6	0.531779
$639$	−1.27291e7	−1.23323
$640$	−5.47627e6	−0.528488
$641$	9.99227e6	0.960548	0.480274	−	0.877119i	$-0.340537\pi$
$641$	9.99227e6	0.960548	0.480274	+	0.877119i	$0.340537\pi$
$642$	8.10675e6	0.776263
$643$	−2.04909e7	−1.95449	−0.977247	−	0.212106i	$-0.931968\pi$
$643$	−2.04909e7	−1.95449	−0.977247	+	0.212106i	$0.931968\pi$
$644$	−2.45288e6	−0.233057
$645$	−6.43754e6	−0.609286
$646$	2.54389e6	0.239838
$647$	6.20629e6	0.582869	0.291435	−	0.956591i	$-0.405867\pi$
$647$	6.20629e6	0.582869	0.291435	+	0.956591i	$0.405867\pi$
$648$	7.92693e6	0.741596
$649$	−3.74128e6	−0.348665
$650$	2.57014e6	0.238601
$651$	−1.99792e7	−1.84768
$652$	362368.	0.0333835
$653$	3.91787e6	0.359557	0.179778	−	0.983707i	$-0.442462\pi$
$653$	3.91787e6	0.359557	0.179778	+	0.983707i	$0.442462\pi$
$654$	2.27478e7	2.07968
$655$	6.97849e6	0.635562
$656$	−3.85518e6	−0.349772
$657$	1.60458e7	1.45027
$658$	−2.61238e6	−0.235219
$659$	−1.51693e7	−1.36066	−0.680332	−	0.732904i	$-0.738165\pi$
$659$	−1.51693e7	−1.36066	−0.680332	+	0.732904i	$0.738165\pi$
$660$	969334.	0.0866191
$661$	−1.45683e7	−1.29690	−0.648449	−	0.761258i	$-0.724582\pi$
$661$	−1.45683e7	−1.29690	−0.648449	+	0.761258i	$0.724582\pi$
$662$	1.88141e7	1.66855
$663$	1.78437e7	1.57652
$664$	7.22886e6	0.636282
$665$	−1.05093e6	−0.0921549
$666$	−3.62434e7	−3.16623
$667$	−1.21135e7	−1.05428
$668$	4.15667e6	0.360416
$669$	1.94242e6	0.167795
$670$	−7.24566e6	−0.623579
$671$	4.26633e6	0.365804
$672$	−1.28844e7	−1.10063
$673$	−9.74500e6	−0.829362	−0.414681	−	0.909967i	$-0.636107\pi$
$673$	−9.74500e6	−0.829362	−0.414681	+	0.909967i	$0.636107\pi$
$674$	−2.40821e7	−2.04195
$675$	−4.11116e6	−0.347301
$676$	168780.	0.0142054
$677$	1.30358e7	1.09312	0.546559	−	0.837420i	$-0.315937\pi$
$677$	1.30358e7	1.09312	0.546559	+	0.837420i	$0.315937\pi$
$678$	−3.73065e7	−3.11681
$679$	1.66459e7	1.38558
$680$	3.54738e6	0.294195
$681$	−3.38182e7	−2.79437
$682$	5.09060e6	0.419091
$683$	5.76665e6	0.473011	0.236506	−	0.971630i	$-0.423998\pi$
$683$	5.76665e6	0.473011	0.236506	+	0.971630i	$0.423998\pi$
$684$	−2.08375e6	−0.170297
$685$	4.33300e6	0.352827
$686$	1.54663e7	1.25480
$687$	2.32858e7	1.88234
$688$	−1.20399e7	−0.969733
$689$	5.68302e6	0.456069
$690$	−7.94041e6	−0.634921
$691$	1.12170e7	0.893681	0.446840	−	0.894614i	$-0.352549\pi$
$691$	1.12170e7	0.893681	0.446840	+	0.894614i	$0.352549\pi$
$692$	−7.80311e6	−0.619445
$693$	−6.85528e6	−0.542240
$694$	−2.42034e7	−1.90756
$695$	−5.73755e6	−0.450572
$696$	−2.45752e7	−1.92298
$697$	3.24801e6	0.253242
$698$	−1.37160e7	−1.06559
$699$	1.09069e7	0.844324
$700$	863436.	0.0666017
$701$	−2.60532e6	−0.200247	−0.100124	−	0.994975i	$-0.531924\pi$
$701$	−2.60532e6	−0.200247	−0.100124	+	0.994975i	$0.531924\pi$
$702$	−2.70496e7	−2.07166
$703$	−4.06039e6	−0.309870
$704$	−1.60703e6	−0.122206
$705$	−2.28729e6	−0.173320
$706$	1.52086e7	1.14836
$707$	−9.32530e6	−0.701640
$708$	−9.90793e6	−0.742847
$709$	6.11919e6	0.457170	0.228585	−	0.973524i	$-0.426590\pi$
$709$	6.11919e6	0.457170	0.228585	+	0.973524i	$0.426590\pi$
$710$	4.33189e6	0.322501
$711$	1.52445e7	1.13094
$712$	−1.14516e7	−0.846575
$713$	−1.12786e7	−0.830870
$714$	2.21636e7	1.62703
$715$	1.87823e6	0.137399
$716$	7.00076e6	0.510343
$717$	3.95007e7	2.86951
$718$	−9.84212e6	−0.712488
$719$	−3.66180e6	−0.264163	−0.132082	−	0.991239i	$-0.542166\pi$
$719$	−3.66180e6	−0.264163	−0.132082	+	0.991239i	$0.542166\pi$
$720$	−1.53610e7	−1.10431
$721$	3.74969e6	0.268632
$722$	−863113.	−0.0616204
$723$	2.99516e7	2.13095
$724$	7.93075e6	0.562300
$725$	4.26407e6	0.301286
$726$	2.61907e6	0.184419
$727$	−9.33056e6	−0.654744	−0.327372	−	0.944896i	$-0.606163\pi$
$727$	−9.33056e6	−0.654744	−0.327372	+	0.944896i	$0.606163\pi$
$728$	−9.64225e6	−0.674295
$729$	−1.42538e7	−0.993373
$730$	−5.46061e6	−0.379257
$731$	1.01437e7	0.702105
$732$	1.12984e7	0.779363
$733$	5.44908e6	0.374596	0.187298	−	0.982303i	$-0.440027\pi$
$733$	5.44908e6	0.374596	0.187298	+	0.982303i	$0.440027\pi$
$734$	2.26691e7	1.55308
$735$	2.19272e6	0.149715
$736$	−7.27351e6	−0.494936
$737$	−5.29505e6	−0.359089
$738$	−9.83663e6	−0.664822
$739$	−3.23116e6	−0.217644	−0.108822	−	0.994061i	$-0.534708\pi$
$739$	−3.23116e6	−0.217644	−0.108822	+	0.994061i	$0.534708\pi$
$740$	3.33600e6	0.223948
$741$	−6.05415e6	−0.405049
$742$	7.05886e6	0.470679
$743$	−1.92563e7	−1.27968	−0.639840	−	0.768508i	$-0.720999\pi$
$743$	−1.92563e7	−1.27968	−0.639840	+	0.768508i	$0.720999\pi$
$744$	−2.28815e7	−1.51548
$745$	7.80605e6	0.515277
$746$	1.47700e7	0.971705
$747$	2.63727e7	1.72923
$748$	−1.52739e6	−0.0998147
$749$	5.27710e6	0.343709
$750$	2.79509e6	0.181444
$751$	1.10117e7	0.712452	0.356226	−	0.934400i	$-0.384063\pi$
$751$	1.10117e7	0.712452	0.356226	+	0.934400i	$0.384063\pi$
$752$	−4.27784e6	−0.275855
$753$	3.53711e7	2.27333
$754$	2.80557e7	1.79718
$755$	−5.70147e6	−0.364015
$756$	−9.08731e6	−0.578270
$757$	1.71765e7	1.08942	0.544709	−	0.838625i	$-0.316640\pi$
$757$	1.71765e7	1.08942	0.544709	+	0.838625i	$0.316640\pi$
$758$	−1.39186e7	−0.879880
$759$	−5.80276e6	−0.365620
$760$	−1.20359e6	−0.0755863
$761$	−2.38537e7	−1.49312	−0.746558	−	0.665320i	$-0.768295\pi$
$761$	−2.38537e7	−1.49312	−0.746558	+	0.665320i	$0.768295\pi$
$762$	−71746.9	−0.00447626
$763$	1.48078e7	0.920826
$764$	−7.57817e6	−0.469711
$765$	1.29417e7	0.799538
$766$	−2.08386e7	−1.28321
$767$	−1.91981e7	−1.17834
$768$	−2.77059e7	−1.69500
$769$	1.97081e6	0.120179	0.0600896	−	0.998193i	$-0.480861\pi$
$769$	1.97081e6	0.120179	0.0600896	+	0.998193i	$0.480861\pi$
$770$	2.33294e6	0.141800
$771$	−1.15922e7	−0.702314
$772$	3.97034e6	0.239764
$773$	1.16336e7	0.700270	0.350135	−	0.936699i	$-0.386136\pi$
$773$	1.16336e7	0.700270	0.350135	+	0.936699i	$0.386136\pi$
$774$	−3.07202e7	−1.84320
$775$	3.97018e6	0.237441
$776$	1.90639e7	1.13647
$777$	−3.53760e7	−2.10212
$778$	2.32553e7	1.37744
$779$	−1.10201e6	−0.0650643
$780$	4.97406e6	0.292735
$781$	3.16569e6	0.185713
$782$	1.25117e7	0.731646
$783$	−4.48775e7	−2.61592
$784$	4.10097e6	0.238285
$785$	−2.62052e6	−0.151780
$786$	4.99341e7	2.88298
$787$	−7.33115e6	−0.421925	−0.210963	−	0.977494i	$-0.567660\pi$
$787$	−7.33115e6	−0.421925	−0.210963	+	0.977494i	$0.567660\pi$
$788$	−8.70979e6	−0.499680
$789$	−4.50761e7	−2.57783
$790$	−5.18791e6	−0.295750
$791$	−2.42847e7	−1.38004
$792$	−7.85109e6	−0.444751
$793$	2.18924e7	1.23626
$794$	542167.	0.0305198
$795$	6.18043e6	0.346818
$796$	−5.77836e6	−0.323238
$797$	1.70621e6	0.0951452	0.0475726	−	0.998868i	$-0.484851\pi$
$797$	1.70621e6	0.0951452	0.0475726	+	0.998868i	$0.484851\pi$
$798$	−7.51985e6	−0.418024
$799$	3.60410e6	0.199724
$800$	2.56034e6	0.141440
$801$	−4.17782e7	−2.30074
$802$	−3.64520e6	−0.200118
$803$	−3.99055e6	−0.218396
$804$	−1.40227e7	−0.765056
$805$	−5.16882e6	−0.281127
$806$	2.61220e7	1.41635
$807$	2.47013e7	1.33517
$808$	−1.06799e7	−0.575492
$809$	1.89173e7	1.01622	0.508110	−	0.861292i	$-0.330345\pi$
$809$	1.89173e7	1.01622	0.508110	+	0.861292i	$0.330345\pi$
$810$	−9.84165e6	−0.527055
$811$	3.50938e7	1.87361	0.936803	−	0.349856i	$-0.113769\pi$
$811$	3.50938e7	1.87361	0.936803	+	0.349856i	$0.113769\pi$
$812$	9.42529e6	0.501654
$813$	−1.25606e7	−0.666475
$814$	9.01363e6	0.476803
$815$	763599.	0.0402690
$816$	3.62934e7	1.90810
$817$	−3.44163e6	−0.180389
$818$	−1.87117e7	−0.977756
$819$	−3.51773e7	−1.83254
$820$	905407.	0.0470229
$821$	−1.07886e7	−0.558606	−0.279303	−	0.960203i	$-0.590103\pi$
$821$	−1.07886e7	−0.558606	−0.279303	+	0.960203i	$0.590103\pi$
$822$	3.10045e7	1.60046
$823$	1.19216e7	0.613528	0.306764	−	0.951786i	$-0.400754\pi$
$823$	1.19216e7	0.613528	0.306764	+	0.951786i	$0.400754\pi$
$824$	4.29438e6	0.220335
$825$	2.04262e6	0.104485
$826$	−2.38459e7	−1.21608
$827$	−5.70664e6	−0.290146	−0.145073	−	0.989421i	$-0.546342\pi$
$827$	−5.70664e6	−0.290146	−0.145073	+	0.989421i	$0.546342\pi$
$828$	−1.02486e7	−0.519505
$829$	−2.96355e7	−1.49770	−0.748852	−	0.662738i	$-0.769395\pi$
$829$	−2.96355e7	−1.49770	−0.748852	+	0.662738i	$0.769395\pi$
$830$	−8.97497e6	−0.452208
$831$	5.59603e7	2.81111
$832$	−8.24635e6	−0.413003
$833$	−3.45509e6	−0.172523
$834$	−4.10547e7	−2.04384
$835$	8.75911e6	0.434754
$836$	518224.	0.0256450
$837$	−4.17845e7	−2.06159
$838$	3.70668e7	1.82337
$839$	−1.06236e7	−0.521034	−0.260517	−	0.965469i	$-0.583893\pi$
$839$	−1.06236e7	−0.521034	−0.260517	+	0.965469i	$0.583893\pi$
$840$	−1.04862e7	−0.512767
$841$	2.60355e7	1.26933
$842$	−1.46380e7	−0.711542
$843$	4.07100e7	1.97302
$844$	−7.10764e6	−0.343455
$845$	355660.	0.0171354
$846$	−1.09151e7	−0.524324
$847$	1.70489e6	0.0816559
$848$	1.15590e7	0.551991
$849$	−2.19973e7	−1.04737
$850$	−4.40425e6	−0.209086
$851$	−1.99704e7	−0.945286
$852$	8.38363e6	0.395670
$853$	8.08775e6	0.380588	0.190294	−	0.981727i	$-0.439056\pi$
$853$	8.08775e6	0.380588	0.190294	+	0.981727i	$0.439056\pi$
$854$	2.71924e7	1.27586
$855$	−4.39098e6	−0.205422
$856$	6.04366e6	0.281913
$857$	1.70739e7	0.794110	0.397055	−	0.917795i	$-0.370032\pi$
$857$	1.70739e7	0.794110	0.397055	+	0.917795i	$0.370032\pi$
$858$	1.34396e7	0.623256
$859$	3.83723e7	1.77433	0.887165	−	0.461452i	$-0.152671\pi$
$859$	3.83723e7	1.77433	0.887165	+	0.461452i	$0.152671\pi$
$860$	2.82763e6	0.130370
$861$	−9.60124e6	−0.441387
$862$	3.72198e7	1.70611
$863$	9.42187e6	0.430636	0.215318	−	0.976544i	$-0.430921\pi$
$863$	9.42187e6	0.430636	0.215318	+	0.976544i	$0.430921\pi$
$864$	−2.69465e7	−1.22806
$865$	−1.64431e7	−0.747210
$866$	1.06098e7	0.480744
$867$	7.77288e6	0.351183
$868$	8.77568e6	0.395350
$869$	−3.79127e6	−0.170308
$870$	3.05113e7	1.36667
$871$	−2.71712e7	−1.21356
$872$	1.69588e7	0.755271
$873$	6.95497e7	3.08859
$874$	−4.24509e6	−0.187979
$875$	1.81947e6	0.0803388
$876$	−1.05681e7	−0.465303
$877$	−3.16635e7	−1.39014	−0.695071	−	0.718941i	$-0.744627\pi$
$877$	−3.16635e7	−1.39014	−0.695071	+	0.718941i	$0.744627\pi$
$878$	−2.51696e7	−1.10189
$879$	−4.19322e6	−0.183052
$880$	3.82025e6	0.166297
$881$	−1.51043e7	−0.655631	−0.327816	−	0.944742i	$-0.606312\pi$
$881$	−1.51043e7	−0.655631	−0.327816	+	0.944742i	$0.606312\pi$
$882$	1.04638e7	0.452915
$883$	6.26536e6	0.270423	0.135212	−	0.990817i	$-0.456829\pi$
$883$	6.26536e6	0.270423	0.135212	+	0.990817i	$0.456829\pi$
$884$	−7.83766e6	−0.337331
$885$	−2.08784e7	−0.896065
$886$	−2.78256e7	−1.19086
$887$	−8.33898e6	−0.355880	−0.177940	−	0.984041i	$-0.556943\pi$
$887$	−8.33898e6	−0.355880	−0.177940	+	0.984041i	$0.556943\pi$
$888$	−4.05148e7	−1.72418
$889$	−46703.8	−0.00198197
$890$	1.42177e7	0.601663
$891$	−7.19217e6	−0.303505
$892$	−853189.	−0.0359032
$893$	−1.22283e6	−0.0513141
$894$	5.58557e7	2.33735
$895$	1.47523e7	0.615605
$896$	−2.55076e7	−1.06145
$897$	−2.97764e7	−1.23564
$898$	1.03562e7	0.428557
$899$	4.33386e7	1.78844
$900$	3.60761e6	0.148461
$901$	−9.73854e6	−0.399652
$902$	2.44634e6	0.100115
$903$	−2.99851e7	−1.22373
$904$	−2.78124e7	−1.13192
$905$	1.67120e7	0.678278
$906$	−4.07965e7	−1.65121
$907$	−2.96271e7	−1.19583	−0.597917	−	0.801558i	$-0.704005\pi$
$907$	−2.96271e7	−1.19583	−0.597917	+	0.801558i	$0.704005\pi$
$908$	1.48543e7	0.597914
$909$	−3.89630e7	−1.56402
$910$	1.19713e7	0.479224
$911$	2.02864e7	0.809857	0.404929	−	0.914348i	$-0.367296\pi$
$911$	2.02864e7	0.809857	0.404929	+	0.914348i	$0.367296\pi$
$912$	−1.23139e7	−0.490241
$913$	−6.55881e6	−0.260404
$914$	−2.56113e7	−1.01407
$915$	2.38085e7	0.940112
$916$	−1.02280e7	−0.402767
$917$	3.25047e7	1.27651
$918$	4.63528e7	1.81539
$919$	2.36811e7	0.924939	0.462469	−	0.886635i	$-0.346963\pi$
$919$	2.36811e7	0.924939	0.462469	+	0.886635i	$0.346963\pi$
$920$	−5.91965e6	−0.230583
$921$	1.67456e7	0.650508
$922$	−3.83029e7	−1.48390
$923$	1.62445e7	0.627628
$924$	4.51501e6	0.173972
$925$	7.02977e6	0.270139
$926$	3.03164e7	1.16185
$927$	1.56670e7	0.598805
$928$	2.79487e7	1.06535
$929$	3.71435e7	1.41203	0.706015	−	0.708197i	$-0.250491\pi$
$929$	3.71435e7	1.41203	0.706015	+	0.708197i	$0.250491\pi$
$930$	2.84084e7	1.07706
$931$	1.17227e6	0.0443255
$932$	−4.79076e6	−0.180661
$933$	1.44774e7	0.544487
$934$	−2.89732e7	−1.08675
$935$	−3.21857e6	−0.120402
$936$	−4.02872e7	−1.50307
$937$	−2.99554e7	−1.11462	−0.557310	−	0.830305i	$-0.688166\pi$
$937$	−2.99554e7	−1.11462	−0.557310	+	0.830305i	$0.688166\pi$
$938$	−3.37492e7	−1.25244
$939$	−3.78143e7	−1.39956
$940$	1.00467e6	0.0370855
$941$	−371413.	−0.0136736	−0.00683680	−	0.999977i	$-0.502176\pi$
$941$	−371413.	−0.0136736	−0.00683680	+	0.999977i	$0.502176\pi$
$942$	−1.87510e7	−0.688489
$943$	−5.42007e6	−0.198484
$944$	−3.90482e7	−1.42617
$945$	−1.91492e7	−0.697542
$946$	7.64004e6	0.277567
$947$	7.70493e6	0.279186	0.139593	−	0.990209i	$-0.455421\pi$
$947$	7.70493e6	0.279186	0.139593	+	0.990209i	$0.455421\pi$
$948$	−1.00403e7	−0.362849
$949$	−2.04772e7	−0.738083
$950$	1.49431e6	0.0537194
$951$	−7.18442e7	−2.57597
$952$	1.65232e7	0.590883
$953$	−792077.	−0.0282511	−0.0141255	−	0.999900i	$-0.504496\pi$
$953$	−792077.	−0.0282511	−0.0141255	+	0.999900i	$0.504496\pi$
$954$	2.94933e7	1.04919
$955$	−1.59690e7	−0.566592
$956$	−1.73503e7	−0.613992
$957$	2.22973e7	0.786997
$958$	−4.95153e7	−1.74311
$959$	2.01825e7	0.708643
$960$	−8.96813e6	−0.314068
$961$	1.17225e7	0.409460
$962$	4.62527e7	1.61139
$963$	2.20488e7	0.766159
$964$	−1.31559e7	−0.455962
$965$	8.36648e6	0.289217
$966$	−3.69852e7	−1.27522
$967$	−1.10121e7	−0.378706	−0.189353	−	0.981909i	$-0.560639\pi$
$967$	−1.10121e7	−0.378706	−0.189353	+	0.981909i	$0.560639\pi$
$968$	1.95254e6	0.0669750
$969$	1.03745e7	0.354943
$970$	−2.36687e7	−0.807690
$971$	5.41202e7	1.84209	0.921047	−	0.389453i	$-0.127336\pi$
$971$	5.41202e7	1.84209	0.921047	+	0.389453i	$0.127336\pi$
$972$	−83441.4	−0.00283280
$973$	−2.67246e7	−0.904960
$974$	1.23657e7	0.417659
$975$	1.04816e7	0.353114
$976$	4.45282e7	1.49627
$977$	−2.57676e7	−0.863650	−0.431825	−	0.901957i	$-0.642130\pi$
$977$	−2.57676e7	−0.863650	−0.431825	+	0.901957i	$0.642130\pi$
$978$	5.46389e6	0.182665
$979$	1.03901e7	0.346469
$980$	−963132.	−0.0320347
$981$	6.18697e7	2.05261
$982$	−2.32064e7	−0.767943
$983$	−2.72028e7	−0.897905	−0.448953	−	0.893556i	$-0.648203\pi$
$983$	−2.72028e7	−0.897905	−0.448953	+	0.893556i	$0.648203\pi$
$984$	−1.09959e7	−0.362030
$985$	−1.83537e7	−0.602743
$986$	−4.80768e7	−1.57487
$987$	−1.06539e7	−0.348108
$988$	2.65923e6	0.0866689
$989$	−1.69271e7	−0.550291
$990$	9.74749e6	0.316086
$991$	3.69342e6	0.119466	0.0597331	−	0.998214i	$-0.480975\pi$
$991$	3.69342e6	0.119466	0.0597331	+	0.998214i	$0.480975\pi$
$992$	2.60224e7	0.839593
$993$	7.67278e7	2.46933
$994$	2.01773e7	0.647733
$995$	−1.21764e7	−0.389908
$996$	−1.73695e7	−0.554804
$997$	−4.26438e7	−1.35868	−0.679341	−	0.733823i	$-0.737734\pi$
$997$	−4.26438e7	−1.35868	−0.679341	+	0.733823i	$0.737734\pi$
$998$	2.33274e7	0.741380
$999$	−7.39854e7	−2.34548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.9	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.9	✓	38	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)

\(f(q)\)	\(=\)	\(q-6.62298 q^{2} -27.0099 q^{3} +11.8638 q^{4} +25.0000 q^{5} +178.886 q^{6} +116.446 q^{7} +133.361 q^{8} +486.535 q^{9} +O(q^{10})\)	\(q-6.62298 q^{2} -27.0099 q^{3} +11.8638 q^{4} +25.0000 q^{5} +178.886 q^{6} +116.446 q^{7} +133.361 q^{8} +486.535 q^{9} -165.574 q^{10} -121.000 q^{11} -320.441 q^{12} -620.902 q^{13} -771.220 q^{14} -675.248 q^{15} -1262.89 q^{16} +1063.99 q^{17} -3222.31 q^{18} -361.000 q^{19} +296.596 q^{20} -3145.20 q^{21} +801.380 q^{22} -1775.52 q^{23} -3602.08 q^{24} +625.000 q^{25} +4112.22 q^{26} -6577.86 q^{27} +1381.50 q^{28} +6822.51 q^{29} +4472.15 q^{30} +6352.29 q^{31} +4096.54 q^{32} +3268.20 q^{33} -7046.79 q^{34} +2911.15 q^{35} +5772.17 q^{36} +11247.6 q^{37} +2390.89 q^{38} +16770.5 q^{39} +3334.03 q^{40} +3052.66 q^{41} +20830.6 q^{42} +9533.60 q^{43} -1435.52 q^{44} +12163.4 q^{45} +11759.2 q^{46} +3387.34 q^{47} +34110.6 q^{48} -3247.29 q^{49} -4139.36 q^{50} -28738.3 q^{51} -7366.28 q^{52} -9152.84 q^{53} +43565.0 q^{54} -3025.00 q^{55} +15529.4 q^{56} +9750.58 q^{57} -45185.3 q^{58} +30919.6 q^{59} -8011.03 q^{60} -35258.9 q^{61} -42071.1 q^{62} +56655.2 q^{63} +13281.2 q^{64} -15522.6 q^{65} -21645.2 q^{66} +43760.8 q^{67} +12623.0 q^{68} +47956.7 q^{69} -19280.5 q^{70} -26162.8 q^{71} +64885.0 q^{72} +32979.8 q^{73} -74492.8 q^{74} -16881.2 q^{75} -4282.84 q^{76} -14090.0 q^{77} -111071. q^{78} +31332.8 q^{79} -31572.3 q^{80} +59439.5 q^{81} -20217.7 q^{82} +54205.1 q^{83} -37314.1 q^{84} +26599.8 q^{85} -63140.8 q^{86} -184275. q^{87} -16136.7 q^{88} -85868.8 q^{89} -80557.8 q^{90} -72301.7 q^{91} -21064.5 q^{92} -171575. q^{93} -22434.3 q^{94} -9025.00 q^{95} -110647. q^{96} +142949. q^{97} +21506.7 q^{98} -58870.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

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