LMFDB - Embedded newform 11.6.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,6,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	11.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:	$1.76422201794$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.54492.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 52x - 38 $ x^3 - x^2 - 52*x - 38
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-6.29828$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.18772 q^{2} -3.48600 q^{3} +35.0388 q^{4} -59.8722 q^{5} -28.5424 q^{6} +145.071 q^{7} +24.8808 q^{8} -230.848 q^{9} +O(q^{10})$	\(q+8.18772 q^{2} -3.48600 q^{3} +35.0388 q^{4} -59.8722 q^{5} -28.5424 q^{6} +145.071 q^{7} +24.8808 q^{8} -230.848 q^{9} -490.217 q^{10} +121.000 q^{11} -122.145 q^{12} +615.772 q^{13} +1187.80 q^{14} +208.715 q^{15} -917.524 q^{16} +1840.68 q^{17} -1890.12 q^{18} +366.633 q^{19} -2097.85 q^{20} -505.718 q^{21} +990.714 q^{22} -4516.38 q^{23} -86.7344 q^{24} +459.685 q^{25} +5041.77 q^{26} +1651.83 q^{27} +5083.12 q^{28} -1717.00 q^{29} +1708.90 q^{30} -2650.54 q^{31} -8308.62 q^{32} -421.806 q^{33} +15070.9 q^{34} -8685.74 q^{35} -8088.63 q^{36} +9660.61 q^{37} +3001.89 q^{38} -2146.58 q^{39} -1489.67 q^{40} -11154.8 q^{41} -4140.68 q^{42} +8368.48 q^{43} +4239.69 q^{44} +13821.4 q^{45} -36978.9 q^{46} -2221.22 q^{47} +3198.49 q^{48} +4238.64 q^{49} +3763.77 q^{50} -6416.60 q^{51} +21575.9 q^{52} +23707.9 q^{53} +13524.8 q^{54} -7244.54 q^{55} +3609.48 q^{56} -1278.08 q^{57} -14058.3 q^{58} +19517.8 q^{59} +7313.11 q^{60} +20937.3 q^{61} -21701.9 q^{62} -33489.4 q^{63} -38667.9 q^{64} -36867.6 q^{65} -3453.63 q^{66} -51707.7 q^{67} +64495.1 q^{68} +15744.1 q^{69} -71116.4 q^{70} -1398.38 q^{71} -5743.67 q^{72} +72466.6 q^{73} +79098.4 q^{74} -1602.46 q^{75} +12846.4 q^{76} +17553.6 q^{77} -17575.6 q^{78} +64632.2 q^{79} +54934.2 q^{80} +50337.7 q^{81} -91332.4 q^{82} -96790.3 q^{83} -17719.8 q^{84} -110205. q^{85} +68518.8 q^{86} +5985.47 q^{87} +3010.57 q^{88} -47614.1 q^{89} +113166. q^{90} +89330.7 q^{91} -158249. q^{92} +9239.79 q^{93} -18186.7 q^{94} -21951.2 q^{95} +28963.9 q^{96} -38399.6 q^{97} +34704.8 q^{98} -27932.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9}+O(q^{10}) $ 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9	\( 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9} - 414 q^{10} + 363 q^{11} + 992 q^{12} + 486 q^{13} - 1020 q^{14} + 1654 q^{15} + 1992 q^{16} + 1086 q^{17} - 3706 q^{18} + 1380 q^{19} - 3480 q^{20} - 908 q^{21} - 3066 q^{23} - 11748 q^{24} - 57 q^{25} + 12132 q^{26} - 2990 q^{27} + 23712 q^{28} - 3426 q^{29} + 2650 q^{30} - 4098 q^{31} - 12408 q^{32} + 4114 q^{33} + 25320 q^{34} - 24228 q^{35} + 4756 q^{36} + 17724 q^{37} - 9240 q^{38} - 6560 q^{39} - 15276 q^{40} + 5994 q^{41} - 47828 q^{42} - 26208 q^{43} + 10164 q^{44} + 18458 q^{45} - 16806 q^{46} - 17232 q^{47} + 61064 q^{48} + 48531 q^{49} + 41070 q^{50} - 22724 q^{51} - 35304 q^{52} + 50586 q^{53} + 18814 q^{54} + 2904 q^{55} - 42312 q^{56} + 20160 q^{57} - 29172 q^{58} - 3738 q^{59} - 13456 q^{60} + 18486 q^{61} - 19974 q^{62} - 12496 q^{63} - 20352 q^{64} - 7668 q^{65} - 24926 q^{66} - 47754 q^{67} - 12600 q^{68} + 35042 q^{69} - 123372 q^{70} + 39282 q^{71} - 95040 q^{72} + 15426 q^{73} + 153294 q^{74} - 21916 q^{75} + 103920 q^{76} + 10164 q^{77} + 124984 q^{78} + 125148 q^{79} + 118680 q^{80} - 86917 q^{81} - 255372 q^{82} - 143928 q^{83} + 343616 q^{84} - 104040 q^{85} + 243060 q^{86} - 19368 q^{87} - 68244 q^{88} - 106824 q^{89} + 103424 q^{90} - 109632 q^{91} - 336528 q^{92} - 16622 q^{93} - 74928 q^{94} - 22200 q^{95} - 76456 q^{96} + 9684 q^{97} + 3480 q^{98} - 847 q^{99}+O(q^{100}) \) 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9 - 414 * q^10 + 363 * q^11 + 992 * q^12 + 486 * q^13 - 1020 * q^14 + 1654 * q^15 + 1992 * q^16 + 1086 * q^17 - 3706 * q^18 + 1380 * q^19 - 3480 * q^20 - 908 * q^21 - 3066 * q^23 - 11748 * q^24 - 57 * q^25 + 12132 * q^26 - 2990 * q^27 + 23712 * q^28 - 3426 * q^29 + 2650 * q^30 - 4098 * q^31 - 12408 * q^32 + 4114 * q^33 + 25320 * q^34 - 24228 * q^35 + 4756 * q^36 + 17724 * q^37 - 9240 * q^38 - 6560 * q^39 - 15276 * q^40 + 5994 * q^41 - 47828 * q^42 - 26208 * q^43 + 10164 * q^44 + 18458 * q^45 - 16806 * q^46 - 17232 * q^47 + 61064 * q^48 + 48531 * q^49 + 41070 * q^50 - 22724 * q^51 - 35304 * q^52 + 50586 * q^53 + 18814 * q^54 + 2904 * q^55 - 42312 * q^56 + 20160 * q^57 - 29172 * q^58 - 3738 * q^59 - 13456 * q^60 + 18486 * q^61 - 19974 * q^62 - 12496 * q^63 - 20352 * q^64 - 7668 * q^65 - 24926 * q^66 - 47754 * q^67 - 12600 * q^68 + 35042 * q^69 - 123372 * q^70 + 39282 * q^71 - 95040 * q^72 + 15426 * q^73 + 153294 * q^74 - 21916 * q^75 + 103920 * q^76 + 10164 * q^77 + 124984 * q^78 + 125148 * q^79 + 118680 * q^80 - 86917 * q^81 - 255372 * q^82 - 143928 * q^83 + 343616 * q^84 - 104040 * q^85 + 243060 * q^86 - 19368 * q^87 - 68244 * q^88 - 106824 * q^89 + 103424 * q^90 - 109632 * q^91 - 336528 * q^92 - 16622 * q^93 - 74928 * q^94 - 22200 * q^95 - 76456 * q^96 + 9684 * q^97 + 3480 * q^98 - 847 * 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 $

$2$	8.18772	1.44740	0.723699	−	0.690116i	$-0.242440\pi$
$2$	8.18772	1.44740	0.723699	+	0.690116i	$0.242440\pi$
$3$	−3.48600	−0.223627	−0.111814	−	0.993729i	$-0.535666\pi$
$3$	−3.48600	−0.223627	−0.111814	+	0.993729i	$0.535666\pi$
$4$	35.0388	1.09496
$5$	−59.8722	−1.07103	−0.535514	−	0.844527i	$-0.679882\pi$
$5$	−59.8722	−1.07103	−0.535514	+	0.844527i	$0.679882\pi$
$6$	−28.5424	−0.323678
$7$	145.071	1.11902	0.559508	−	0.828825i	$-0.310990\pi$
$7$	145.071	1.11902	0.559508	+	0.828825i	$0.310990\pi$
$8$	24.8808	0.137448
$9$	−230.848	−0.949991
$10$	−490.217	−1.55020
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−122.145	−0.244863
$13$	615.772	1.01056	0.505279	−	0.862956i	$-0.331390\pi$
$13$	615.772	1.01056	0.505279	+	0.862956i	$0.331390\pi$
$14$	1187.80	1.61966
$15$	208.715	0.239511
$16$	−917.524	−0.896020
$17$	1840.68	1.54474	0.772369	−	0.635174i	$-0.219071\pi$
$17$	1840.68	1.54474	0.772369	+	0.635174i	$0.219071\pi$
$18$	−1890.12	−1.37502
$19$	366.633	0.232996	0.116498	−	0.993191i	$-0.462833\pi$
$19$	366.633	0.232996	0.116498	+	0.993191i	$0.462833\pi$
$20$	−2097.85	−1.17273
$21$	−505.718	−0.250242
$22$	990.714	0.436407
$23$	−4516.38	−1.78021	−0.890104	−	0.455757i	$-0.849369\pi$
$23$	−4516.38	−1.78021	−0.890104	+	0.455757i	$0.849369\pi$
$24$	−86.7344	−0.0307371
$25$	459.685	0.147099
$26$	5041.77	1.46268
$27$	1651.83	0.436071
$28$	5083.12	1.22528
$29$	−1717.00	−0.379119	−0.189560	−	0.981869i	$-0.560706\pi$
$29$	−1717.00	−0.379119	−0.189560	+	0.981869i	$0.560706\pi$
$30$	1708.90	0.346667
$31$	−2650.54	−0.495371	−0.247685	−	0.968841i	$-0.579670\pi$
$31$	−2650.54	−0.495371	−0.247685	+	0.968841i	$0.579670\pi$
$32$	−8308.62	−1.43435
$33$	−421.806	−0.0674261
$34$	15070.9	2.23585
$35$	−8685.74	−1.19850
$36$	−8088.63	−1.04020
$37$	9660.61	1.16011	0.580057	−	0.814576i	$-0.303030\pi$
$37$	9660.61	1.16011	0.580057	+	0.814576i	$0.303030\pi$
$38$	3001.89	0.337238
$39$	−2146.58	−0.225988
$40$	−1489.67	−0.147211
$41$	−11154.8	−1.03634	−0.518170	−	0.855278i	$-0.673386\pi$
$41$	−11154.8	−1.03634	−0.518170	+	0.855278i	$0.673386\pi$
$42$	−4140.68	−0.362200
$43$	8368.48	0.690201	0.345100	−	0.938566i	$-0.387845\pi$
$43$	8368.48	0.690201	0.345100	+	0.938566i	$0.387845\pi$
$44$	4239.69	0.330144
$45$	13821.4	1.01747
$46$	−36978.9	−2.57667
$47$	−2221.22	−0.146672	−0.0733360	−	0.997307i	$-0.523365\pi$
$47$	−2221.22	−0.146672	−0.0733360	+	0.997307i	$0.523365\pi$
$48$	3198.49	0.200374
$49$	4238.64	0.252195
$50$	3763.77	0.212911
$51$	−6416.60	−0.345445
$52$	21575.9	1.10652
$53$	23707.9	1.15932	0.579659	−	0.814859i	$-0.303186\pi$
$53$	23707.9	1.15932	0.579659	+	0.814859i	$0.303186\pi$
$54$	13524.8	0.631168
$55$	−7244.54	−0.322927
$56$	3609.48	0.153807
$57$	−1278.08	−0.0521042
$58$	−14058.3	−0.548737
$59$	19517.8	0.729964	0.364982	−	0.931015i	$-0.381075\pi$
$59$	19517.8	0.729964	0.364982	+	0.931015i	$0.381075\pi$
$60$	7313.11	0.262255
$61$	20937.3	0.720436	0.360218	−	0.932868i	$-0.382702\pi$
$61$	20937.3	0.720436	0.360218	+	0.932868i	$0.382702\pi$
$62$	−21701.9	−0.716999
$63$	−33489.4	−1.06305
$64$	−38667.9	−1.18005
$65$	−36867.6	−1.08233
$66$	−3453.63	−0.0975924
$67$	−51707.7	−1.40724	−0.703619	−	0.710577i	$-0.748434\pi$
$67$	−51707.7	−1.40724	−0.703619	+	0.710577i	$0.748434\pi$
$68$	64495.1	1.69143
$69$	15744.1	0.398103
$70$	−71116.4	−1.73470
$71$	−1398.38	−0.0329216	−0.0164608	−	0.999865i	$-0.505240\pi$
$71$	−1398.38	−0.0329216	−0.0164608	+	0.999865i	$0.505240\pi$
$72$	−5743.67	−0.130574
$73$	72466.6	1.59159	0.795794	−	0.605567i	$-0.207054\pi$
$73$	72466.6	1.59159	0.795794	+	0.605567i	$0.207054\pi$
$74$	79098.4	1.67915
$75$	−1602.46	−0.0328954
$76$	12846.4	0.255122
$77$	17553.6	0.337396
$78$	−17575.6	−0.327095
$79$	64632.2	1.16515	0.582574	−	0.812777i	$-0.302045\pi$
$79$	64632.2	1.16515	0.582574	+	0.812777i	$0.302045\pi$
$80$	54934.2	0.959662
$81$	50337.7	0.852474
$82$	−91332.4	−1.50000
$83$	−96790.3	−1.54219	−0.771093	−	0.636723i	$-0.780290\pi$
$83$	−96790.3	−1.54219	−0.771093	+	0.636723i	$0.780290\pi$
$84$	−17719.8	−0.274006
$85$	−110205.	−1.65446
$86$	68518.8	0.998995
$87$	5985.47	0.0847814
$88$	3010.57	0.0414422
$89$	−47614.1	−0.637178	−0.318589	−	0.947893i	$-0.603209\pi$
$89$	−47614.1	−0.637178	−0.318589	+	0.947893i	$0.603209\pi$
$90$	113166.	1.47268
$91$	89330.7	1.13083
$92$	−158249.	−1.94926
$93$	9239.79	0.110778
$94$	−18186.7	−0.212293
$95$	−21951.2	−0.249545
$96$	28963.9	0.320759
$97$	−38399.6	−0.414378	−0.207189	−	0.978301i	$-0.566432\pi$
$97$	−38399.6	−0.414378	−0.207189	+	0.978301i	$0.566432\pi$
$98$	34704.8	0.365027
$99$	−27932.6	−0.286433
$100$	16106.8	0.161068
$101$	−41011.2	−0.400036	−0.200018	−	0.979792i	$-0.564100\pi$
$101$	−41011.2	−0.400036	−0.200018	+	0.979792i	$0.564100\pi$
$102$	−52537.3	−0.499997
$103$	−49634.4	−0.460988	−0.230494	−	0.973074i	$-0.574034\pi$
$103$	−49634.4	−0.460988	−0.230494	+	0.973074i	$0.574034\pi$
$104$	15320.9	0.138899
$105$	30278.5	0.268016
$106$	194113.	1.67800
$107$	−6791.34	−0.0573450	−0.0286725	−	0.999589i	$-0.509128\pi$
$107$	−6791.34	−0.0573450	−0.0286725	+	0.999589i	$0.509128\pi$
$108$	57878.3	0.477481
$109$	96780.7	0.780230	0.390115	−	0.920766i	$-0.372435\pi$
$109$	96780.7	0.780230	0.390115	+	0.920766i	$0.372435\pi$
$110$	−59316.3	−0.467404
$111$	−33676.9	−0.259433
$112$	−133106.	−1.00266
$113$	−212938.	−1.56876	−0.784379	−	0.620281i	$-0.787018\pi$
$113$	−212938.	−1.56876	−0.784379	+	0.620281i	$0.787018\pi$
$114$	−10464.6	−0.0754155
$115$	270406.	1.90665
$116$	−60161.7	−0.415121
$117$	−142149.	−0.960021
$118$	159806.	1.05655
$119$	267029.	1.72859
$120$	5192.98	0.0329203
$121$	14641.0	0.0909091
$122$	171428.	1.04276
$123$	38885.6	0.231754
$124$	−92871.8	−0.542412
$125$	159578.	0.913480
$126$	−274202.	−1.53866
$127$	−90363.9	−0.497148	−0.248574	−	0.968613i	$-0.579962\pi$
$127$	−90363.9	−0.497148	−0.248574	+	0.968613i	$0.579962\pi$
$128$	−50726.1	−0.273657
$129$	−29172.5	−0.154348
$130$	−301862.	−1.56657
$131$	65299.5	0.332454	0.166227	−	0.986088i	$-0.446842\pi$
$131$	65299.5	0.332454	0.166227	+	0.986088i	$0.446842\pi$
$132$	−14779.6	−0.0738290
$133$	53187.9	0.260726
$134$	−423368.	−2.03684
$135$	−98899.0	−0.467044
$136$	45797.4	0.212321
$137$	5322.74	0.0242289	0.0121145	−	0.999927i	$-0.496144\pi$
$137$	5322.74	0.0242289	0.0121145	+	0.999927i	$0.496144\pi$
$138$	128908.	0.576214
$139$	89967.1	0.394954	0.197477	−	0.980308i	$-0.436725\pi$
$139$	89967.1	0.394954	0.197477	+	0.980308i	$0.436725\pi$
$140$	−304338.	−1.31231
$141$	7743.18	0.0327998
$142$	−11449.6	−0.0476506
$143$	74508.4	0.304695
$144$	211808.	0.851211
$145$	102801.	0.406047
$146$	593336.	2.30366
$147$	−14775.9	−0.0563977
$148$	338496.	1.27028
$149$	66489.8	0.245352	0.122676	−	0.992447i	$-0.460852\pi$
$149$	66489.8	0.245352	0.122676	+	0.992447i	$0.460852\pi$
$150$	−13120.5	−0.0476127
$151$	−130866.	−0.467074	−0.233537	−	0.972348i	$-0.575030\pi$
$151$	−130866.	−0.467074	−0.233537	+	0.972348i	$0.575030\pi$
$152$	9122.12	0.0320248
$153$	−424916.	−1.46749
$154$	143724.	0.488346
$155$	158694.	0.530555
$156$	−75213.6	−0.247448
$157$	−163297.	−0.528723	−0.264362	−	0.964424i	$-0.585161\pi$
$157$	−163297.	−0.528723	−0.264362	+	0.964424i	$0.585161\pi$
$158$	529191.	1.68643
$159$	−82645.6	−0.259255
$160$	497456.	1.53622
$161$	−655197.	−1.99208
$162$	412151.	1.23387
$163$	−535758.	−1.57943	−0.789713	−	0.613477i	$-0.789771\pi$
$163$	−535758.	−1.57943	−0.789713	+	0.613477i	$0.789771\pi$
$164$	−390851.	−1.13475
$165$	25254.5	0.0722152
$166$	−792492.	−2.23216
$167$	553587.	1.53601	0.768005	−	0.640443i	$-0.221249\pi$
$167$	553587.	1.53601	0.768005	+	0.640443i	$0.221249\pi$
$168$	−12582.7	−0.0343953
$169$	7881.54	0.0212273
$170$	−902331.	−2.39466
$171$	−84636.5	−0.221344
$172$	293221.	0.755744
$173$	266973.	0.678190	0.339095	−	0.940752i	$-0.389879\pi$
$173$	266973.	0.678190	0.339095	+	0.940752i	$0.389879\pi$
$174$	49007.4	0.122712
$175$	66687.0	0.164606
$176$	−111020.	−0.270160
$177$	−68039.2	−0.163240
$178$	−389851.	−0.922250
$179$	3030.33	0.00706900	0.00353450	−	0.999994i	$-0.498875\pi$
$179$	3030.33	0.00706900	0.00353450	+	0.999994i	$0.498875\pi$
$180$	484284.	1.11409
$181$	761242.	1.72714	0.863568	−	0.504233i	$-0.168225\pi$
$181$	761242.	1.72714	0.863568	+	0.504233i	$0.168225\pi$
$182$	731415.	1.63676
$183$	−72987.3	−0.161109
$184$	−112371.	−0.244686
$185$	−578402.	−1.24251
$186$	75652.8	0.160340
$187$	222722.	0.465756
$188$	−77828.9	−0.160600
$189$	239634.	0.487970
$190$	−179730.	−0.361191
$191$	−430653.	−0.854170	−0.427085	−	0.904212i	$-0.640459\pi$
$191$	−430653.	−0.854170	−0.427085	+	0.904212i	$0.640459\pi$
$192$	134796.	0.263891
$193$	−272285.	−0.526175	−0.263088	−	0.964772i	$-0.584741\pi$
$193$	−272285.	−0.526175	−0.263088	+	0.964772i	$0.584741\pi$
$194$	−314405.	−0.599770
$195$	128521.	0.242039
$196$	148517.	0.276144
$197$	574550.	1.05478	0.527390	−	0.849623i	$-0.323171\pi$
$197$	574550.	1.05478	0.527390	+	0.849623i	$0.323171\pi$
$198$	−228704.	−0.414583
$199$	269926.	0.483183	0.241592	−	0.970378i	$-0.422331\pi$
$199$	269926.	0.483183	0.241592	+	0.970378i	$0.422331\pi$
$200$	11437.3	0.0202185
$201$	180253.	0.314697
$202$	−335788.	−0.579011
$203$	−249088.	−0.424240
$204$	−224830.	−0.378250
$205$	667863.	1.10995
$206$	−406393.	−0.667234
$207$	1.04260e6	1.69118
$208$	−564985.	−0.905480
$209$	44362.6	0.0702509
$210$	247912.	0.387926
$211$	−753372.	−1.16494	−0.582470	−	0.812853i	$-0.697913\pi$
$211$	−753372.	−1.16494	−0.582470	+	0.812853i	$0.697913\pi$
$212$	830695.	1.26941
$213$	4874.77	0.00736216
$214$	−55605.6	−0.0830011
$215$	−501040.	−0.739224
$216$	41098.9	0.0599371
$217$	−384517.	−0.554327
$218$	792414.	1.12930
$219$	−252619.	−0.355922
$220$	−253840.	−0.353593
$221$	1.13344e6	1.56105
$222$	−275737.	−0.375503
$223$	−997692.	−1.34349	−0.671745	−	0.740783i	$-0.734455\pi$
$223$	−997692.	−1.34349	−0.671745	+	0.740783i	$0.734455\pi$
$224$	−1.20534e6	−1.60506
$225$	−106117.	−0.139743
$226$	−1.74347e6	−2.27062
$227$	−495214.	−0.637864	−0.318932	−	0.947778i	$-0.603324\pi$
$227$	−495214.	−0.637864	−0.318932	+	0.947778i	$0.603324\pi$
$228$	−44782.5	−0.0570521
$229$	−221893.	−0.279611	−0.139806	−	0.990179i	$-0.544648\pi$
$229$	−221893.	−0.279611	−0.139806	+	0.990179i	$0.544648\pi$
$230$	2.21401e6	2.75968
$231$	−61191.9	−0.0754508
$232$	−42720.4	−0.0521093
$233$	619425.	0.747479	0.373739	−	0.927534i	$-0.378075\pi$
$233$	619425.	0.747479	0.373739	+	0.927534i	$0.378075\pi$
$234$	−1.16388e6	−1.38953
$235$	132989.	0.157090
$236$	683881.	0.799283
$237$	−225308.	−0.260559
$238$	2.18636e6	2.50195
$239$	−295471.	−0.334595	−0.167298	−	0.985906i	$-0.553504\pi$
$239$	−295471.	−0.334595	−0.167298	+	0.985906i	$0.553504\pi$
$240$	−191501.	−0.214606
$241$	693153.	0.768753	0.384376	−	0.923176i	$-0.374416\pi$
$241$	693153.	0.768753	0.384376	+	0.923176i	$0.374416\pi$
$242$	119876.	0.131582
$243$	−576873.	−0.626707
$244$	733616.	0.788850
$245$	−253777.	−0.270108
$246$	318385.	0.335440
$247$	225762.	0.235456
$248$	−65947.5	−0.0680878
$249$	337411.	0.344875
$250$	1.30658e6	1.32217
$251$	533816.	0.534820	0.267410	−	0.963583i	$-0.413832\pi$
$251$	533816.	0.534820	0.267410	+	0.963583i	$0.413832\pi$
$252$	−1.17343e6	−1.16400
$253$	−546482.	−0.536753
$254$	−739874.	−0.719571
$255$	384176.	0.369981
$256$	822041.	0.783960
$257$	−652296.	−0.616044	−0.308022	−	0.951379i	$-0.599667\pi$
$257$	−652296.	−0.616044	−0.308022	+	0.951379i	$0.599667\pi$
$258$	−238857.	−0.223402
$259$	1.40148e6	1.29818
$260$	−1.29180e6	−1.18512
$261$	396366.	0.360160
$262$	534654.	0.481193
$263$	−622045.	−0.554540	−0.277270	−	0.960792i	$-0.589430\pi$
$263$	−622045.	−0.554540	−0.277270	+	0.960792i	$0.589430\pi$
$264$	−10494.9	−0.00926759
$265$	−1.41944e6	−1.24166
$266$	435488.	0.377374
$267$	165983.	0.142490
$268$	−1.81177e6	−1.54087
$269$	−482862.	−0.406858	−0.203429	−	0.979090i	$-0.565209\pi$
$269$	−482862.	−0.406858	−0.203429	+	0.979090i	$0.565209\pi$
$270$	−809758.	−0.675998
$271$	−1.10678e6	−0.915460	−0.457730	−	0.889091i	$-0.651337\pi$
$271$	−1.10678e6	−0.915460	−0.457730	+	0.889091i	$0.651337\pi$
$272$	−1.68887e6	−1.38412
$273$	−311407.	−0.252884
$274$	43581.1	0.0350689
$275$	55621.9	0.0443521
$276$	551655.	0.435908
$277$	639062.	0.500430	0.250215	−	0.968190i	$-0.419499\pi$
$277$	639062.	0.500430	0.250215	+	0.968190i	$0.419499\pi$
$278$	736626.	0.571656
$279$	611872.	0.470598
$280$	−216108.	−0.164731
$281$	−257984.	−0.194907	−0.0974534	−	0.995240i	$-0.531070\pi$
$281$	−257984.	−0.194907	−0.0974534	+	0.995240i	$0.531070\pi$
$282$	63399.0	0.0474744
$283$	1.02991e6	0.764425	0.382213	−	0.924074i	$-0.375162\pi$
$283$	1.02991e6	0.764425	0.382213	+	0.924074i	$0.375162\pi$
$284$	−48997.7	−0.0360479
$285$	76521.8	0.0558050
$286$	610054.	0.441015
$287$	−1.61824e6	−1.15968
$288$	1.91803e6	1.36262
$289$	1.96823e6	1.38622
$290$	841704.	0.587712
$291$	133861.	0.0926662
$292$	2.53914e6	1.74273
$293$	877712.	0.597287	0.298644	−	0.954365i	$-0.403466\pi$
$293$	877712.	0.597287	0.298644	+	0.954365i	$0.403466\pi$
$294$	−120981.	−0.0816299
$295$	−1.16858e6	−0.781811
$296$	240363.	0.159455
$297$	199872.	0.131480
$298$	544400.	0.355122
$299$	−2.78106e6	−1.79900
$300$	−56148.4	−0.0360192
$301$	1.21403e6	0.772345
$302$	−1.07150e6	−0.676042
$303$	142965.	0.0894589
$304$	−336395.	−0.208769
$305$	−1.25356e6	−0.771606
$306$	−3.47909e6	−2.12404
$307$	−1.30925e6	−0.792826	−0.396413	−	0.918072i	$-0.629745\pi$
$307$	−1.30925e6	−0.792826	−0.396413	+	0.918072i	$0.629745\pi$
$308$	615057.	0.369436
$309$	173026.	0.103089
$310$	1.29934e6	0.767925
$311$	3.35930e6	1.96946	0.984731	−	0.174083i	$-0.0556962\pi$
$311$	3.35930e6	1.96946	0.984731	+	0.174083i	$0.0556962\pi$
$312$	−53408.6	−0.0310616
$313$	−3.00640e6	−1.73454	−0.867272	−	0.497835i	$-0.834129\pi$
$313$	−3.00640e6	−1.73454	−0.867272	+	0.497835i	$0.834129\pi$
$314$	−1.33703e6	−0.765273
$315$	2.00508e6	1.13856
$316$	2.26464e6	1.27579
$317$	2.10147e6	1.17456	0.587279	−	0.809385i	$-0.300199\pi$
$317$	2.10147e6	1.17456	0.587279	+	0.809385i	$0.300199\pi$
$318$	−676679.	−0.375245
$319$	−207757.	−0.114309
$320$	2.31513e6	1.26387
$321$	23674.6	0.0128239
$322$	−5.36457e6	−2.88333
$323$	674853.	0.359918
$324$	1.76377e6	0.933426
$325$	283061.	0.148652
$326$	−4.38663e6	−2.28606
$327$	−337378.	−0.174481
$328$	−277540.	−0.142443
$329$	−322235.	−0.164128
$330$	206777.	0.104524
$331$	1.23338e6	0.618766	0.309383	−	0.950938i	$-0.399878\pi$
$331$	1.23338e6	0.618766	0.309383	+	0.950938i	$0.399878\pi$
$332$	−3.39142e6	−1.68864
$333$	−2.23013e6	−1.10210
$334$	4.53261e6	2.22322
$335$	3.09585e6	1.50719
$336$	464009.	0.224222
$337$	679319.	0.325836	0.162918	−	0.986640i	$-0.447909\pi$
$337$	679319.	0.325836	0.162918	+	0.986640i	$0.447909\pi$
$338$	64531.9	0.0307243
$339$	742301.	0.350817
$340$	−3.86146e6	−1.81157
$341$	−320715.	−0.149360
$342$	−692980.	−0.320373
$343$	−1.82331e6	−0.836805
$344$	208214.	0.0948668
$345$	−942635.	−0.426379
$346$	2.18590e6	0.981611
$347$	2.67540e6	1.19279	0.596397	−	0.802690i	$-0.296598\pi$
$347$	2.67540e6	1.19279	0.596397	+	0.802690i	$0.296598\pi$
$348$	209724.	0.0928324
$349$	−2.37636e6	−1.04435	−0.522177	−	0.852837i	$-0.674880\pi$
$349$	−2.37636e6	−1.04435	−0.522177	+	0.852837i	$0.674880\pi$
$350$	546015.	0.238251
$351$	1.01715e6	0.440675
$352$	−1.00534e6	−0.432472
$353$	638696.	0.272808	0.136404	−	0.990653i	$-0.456445\pi$
$353$	638696.	0.272808	0.136404	+	0.990653i	$0.456445\pi$
$354$	−557086.	−0.236273
$355$	83724.4	0.0352599
$356$	−1.66834e6	−0.697686
$357$	−930864.	−0.386559
$358$	24811.5	0.0102317
$359$	1.50842e6	0.617712	0.308856	−	0.951109i	$-0.400054\pi$
$359$	1.50842e6	0.617712	0.308856	+	0.951109i	$0.400054\pi$
$360$	343886.	0.139849
$361$	−2.34168e6	−0.945713
$362$	6.23284e6	2.49985
$363$	−51038.5	−0.0203297
$364$	3.13004e6	1.23822
$365$	−4.33874e6	−1.70463
$366$	−597600.	−0.233189
$367$	1.77368e6	0.687403	0.343701	−	0.939079i	$-0.388319\pi$
$367$	1.77368e6	0.687403	0.343701	+	0.939079i	$0.388319\pi$
$368$	4.14389e6	1.59510
$369$	2.57506e6	0.984513
$370$	−4.73580e6	−1.79841
$371$	3.43933e6	1.29729
$372$	323751.	0.121298
$373$	2.27176e6	0.845456	0.422728	−	0.906257i	$-0.361073\pi$
$373$	2.27176e6	0.845456	0.422728	+	0.906257i	$0.361073\pi$
$374$	1.82358e6	0.674135
$375$	−556290.	−0.204279
$376$	−55265.7	−0.0201598
$377$	−1.05728e6	−0.383122
$378$	1.96205e6	0.706287
$379$	−4.42409e6	−1.58207	−0.791035	−	0.611771i	$-0.790457\pi$
$379$	−4.42409e6	−1.58207	−0.791035	+	0.611771i	$0.790457\pi$
$380$	−769142.	−0.273242
$381$	315009.	0.111176
$382$	−3.52607e6	−1.23632
$383$	2.37588e6	0.827615	0.413807	−	0.910364i	$-0.364199\pi$
$383$	2.37588e6	0.827615	0.413807	+	0.910364i	$0.364199\pi$
$384$	176831.	0.0611971
$385$	−1.05097e6	−0.361360
$386$	−2.22939e6	−0.761586
$387$	−1.93185e6	−0.655684
$388$	−1.34547e6	−0.453728
$389$	−2.65905e6	−0.890949	−0.445474	−	0.895295i	$-0.646965\pi$
$389$	−2.65905e6	−0.890949	−0.445474	+	0.895295i	$0.646965\pi$
$390$	1.05229e6	0.350328
$391$	−8.31319e6	−2.74996
$392$	105461.	0.0346638
$393$	−227634.	−0.0743457
$394$	4.70425e6	1.52669
$395$	−3.86968e6	−1.24791
$396$	−978724.	−0.313633
$397$	2.15712e6	0.686907	0.343453	−	0.939170i	$-0.388403\pi$
$397$	2.15712e6	0.686907	0.343453	+	0.939170i	$0.388403\pi$
$398$	2.21008e6	0.699359
$399$	−185413.	−0.0583054
$400$	−421772.	−0.131804
$401$	−2.43031e6	−0.754744	−0.377372	−	0.926062i	$-0.623172\pi$
$401$	−2.43031e6	−0.754744	−0.377372	+	0.926062i	$0.623172\pi$
$402$	1.47586e6	0.455492
$403$	−1.63213e6	−0.500601
$404$	−1.43698e6	−0.438024
$405$	−3.01383e6	−0.913022
$406$	−2.03946e6	−0.614045
$407$	1.16893e6	0.349787
$408$	−159650.	−0.0474808
$409$	6.12831e6	1.81148	0.905738	−	0.423839i	$-0.139318\pi$
$409$	6.12831e6	1.81148	0.905738	+	0.423839i	$0.139318\pi$
$410$	5.46827e6	1.60654
$411$	−18555.1	−0.00541824
$412$	−1.73913e6	−0.504765
$413$	2.83147e6	0.816841
$414$	8.53649e6	2.44781
$415$	5.79505e6	1.65172
$416$	−5.11621e6	−1.44949
$417$	−313625.	−0.0883225
$418$	363229.	0.101681
$419$	−375626.	−0.104525	−0.0522626	−	0.998633i	$-0.516643\pi$
$419$	−375626.	−0.104525	−0.0522626	+	0.998633i	$0.516643\pi$
$420$	1.06092e6	0.293468
$421$	3.52333e6	0.968831	0.484416	−	0.874838i	$-0.339032\pi$
$421$	3.52333e6	0.968831	0.484416	+	0.874838i	$0.339032\pi$
$422$	−6.16840e6	−1.68613
$423$	512764.	0.139337
$424$	589870.	0.159346
$425$	846131.	0.227230
$426$	39913.3	0.0106560
$427$	3.03739e6	0.806178
$428$	−237960.	−0.0627906
$429$	−259736.	−0.0681380
$430$	−4.10237e6	−1.06995
$431$	3.15287e6	0.817548	0.408774	−	0.912636i	$-0.365956\pi$
$431$	3.15287e6	0.817548	0.408774	+	0.912636i	$0.365956\pi$
$432$	−1.51560e6	−0.390728
$433$	1.62168e6	0.415667	0.207833	−	0.978164i	$-0.433359\pi$
$433$	1.62168e6	0.415667	0.207833	+	0.978164i	$0.433359\pi$
$434$	−3.14832e6	−0.802333
$435$	−358364.	−0.0908032
$436$	3.39108e6	0.854322
$437$	−1.65586e6	−0.414781
$438$	−2.06837e6	−0.515161
$439$	−2.48145e6	−0.614533	−0.307266	−	0.951624i	$-0.599414\pi$
$439$	−2.48145e6	−0.614533	−0.307266	+	0.951624i	$0.599414\pi$
$440$	−180250.	−0.0443857
$441$	−978482.	−0.239583
$442$	9.28026e6	2.25946
$443$	3.75466e6	0.908994	0.454497	−	0.890748i	$-0.349819\pi$
$443$	3.75466e6	0.908994	0.454497	+	0.890748i	$0.349819\pi$
$444$	−1.18000e6	−0.284069
$445$	2.85076e6	0.682435
$446$	−8.16882e6	−1.94456
$447$	−231783.	−0.0548673
$448$	−5.60960e6	−1.32049
$449$	−4.80916e6	−1.12578	−0.562890	−	0.826532i	$-0.690311\pi$
$449$	−4.80916e6	−1.12578	−0.562890	+	0.826532i	$0.690311\pi$
$450$	−868859.	−0.202264
$451$	−1.34973e6	−0.312468
$452$	−7.46108e6	−1.71773
$453$	456200.	0.104450
$454$	−4.05467e6	−0.923244
$455$	−5.34843e6	−1.21115
$456$	−31799.7	−0.00716162
$457$	7.09951e6	1.59015	0.795075	−	0.606512i	$-0.207432\pi$
$457$	7.09951e6	1.59015	0.795075	+	0.606512i	$0.207432\pi$
$458$	−1.81680e6	−0.404709
$459$	3.04049e6	0.673616
$460$	9.47469e6	2.08771
$461$	8.12745e6	1.78116	0.890578	−	0.454830i	$-0.150300\pi$
$461$	8.12745e6	1.78116	0.890578	+	0.454830i	$0.150300\pi$
$462$	−501022.	−0.109207
$463$	−2.67361e6	−0.579623	−0.289812	−	0.957084i	$-0.593593\pi$
$463$	−2.67361e6	−0.579623	−0.289812	+	0.957084i	$0.593593\pi$
$464$	1.57539e6	0.339699
$465$	−553207.	−0.118647
$466$	5.07168e6	1.08190
$467$	−4.32733e6	−0.918180	−0.459090	−	0.888390i	$-0.651825\pi$
$467$	−4.32733e6	−0.918180	−0.459090	+	0.888390i	$0.651825\pi$
$468$	−4.98075e6	−1.05119
$469$	−7.50129e6	−1.57472
$470$	1.08888e6	0.227371
$471$	569253.	0.118237
$472$	485618.	0.100332
$473$	1.01259e6	0.208103
$474$	−1.84476e6	−0.377133
$475$	168536.	0.0342735
$476$	9.35637e6	1.89274
$477$	−5.47291e6	−1.10134
$478$	−2.41923e6	−0.484293
$479$	1.55878e6	0.310417	0.155208	−	0.987882i	$-0.450395\pi$
$479$	1.55878e6	0.310417	0.155208	+	0.987882i	$0.450395\pi$
$480$	−1.73413e6	−0.343541
$481$	5.94873e6	1.17236
$482$	5.67535e6	1.11269
$483$	2.28402e6	0.445483
$484$	513003.	0.0995420
$485$	2.29907e6	0.443810
$486$	−4.72328e6	−0.907095
$487$	−7.63818e6	−1.45938	−0.729689	−	0.683779i	$-0.760335\pi$
$487$	−7.63818e6	−1.45938	−0.729689	+	0.683779i	$0.760335\pi$
$488$	520935.	0.0990225
$489$	1.86765e6	0.353202
$490$	−2.07786e6	−0.390954
$491$	3.60872e6	0.675537	0.337768	−	0.941229i	$-0.390328\pi$
$491$	3.60872e6	0.675537	0.337768	+	0.941229i	$0.390328\pi$
$492$	1.36251e6	0.253761
$493$	−3.16045e6	−0.585640
$494$	1.84848e6	0.340798
$495$	1.67239e6	0.306778
$496$	2.43194e6	0.443862
$497$	−202865.	−0.0368397
$498$	2.76263e6	0.499171
$499$	−8.46131e6	−1.52120	−0.760599	−	0.649221i	$-0.775095\pi$
$499$	−8.46131e6	−1.52120	−0.760599	+	0.649221i	$0.775095\pi$
$500$	5.59143e6	1.00023
$501$	−1.92980e6	−0.343494
$502$	4.37074e6	0.774098
$503$	−8.28353e6	−1.45981	−0.729904	−	0.683550i	$-0.760435\pi$
$503$	−8.28353e6	−1.45981	−0.729904	+	0.683550i	$0.760435\pi$
$504$	−833241.	−0.146115
$505$	2.45543e6	0.428449
$506$	−4.47444e6	−0.776896
$507$	−27475.1	−0.00474700
$508$	−3.16624e6	−0.544358
$509$	−7.60138e6	−1.30046	−0.650232	−	0.759736i	$-0.725328\pi$
$509$	−7.60138e6	−1.30046	−0.650232	+	0.759736i	$0.725328\pi$
$510$	3.14553e6	0.535511
$511$	1.05128e7	1.78101
$512$	8.35388e6	1.40836
$513$	605618.	0.101603
$514$	−5.34082e6	−0.891661
$515$	2.97172e6	0.493731
$516$	−1.02217e6	−0.169005
$517$	−268768.	−0.0442233
$518$	1.14749e7	1.87899
$519$	−930667.	−0.151662
$520$	−917295.	−0.148765
$521$	9.60432e6	1.55015	0.775073	−	0.631872i	$-0.217713\pi$
$521$	9.60432e6	1.55015	0.775073	+	0.631872i	$0.217713\pi$
$522$	3.24534e6	0.521295
$523$	−9.97831e6	−1.59515	−0.797577	−	0.603217i	$-0.793885\pi$
$523$	−9.97831e6	−1.59515	−0.797577	+	0.603217i	$0.793885\pi$
$524$	2.28802e6	0.364025
$525$	−232471.	−0.0368104
$526$	−5.09313e6	−0.802640
$527$	−4.87879e6	−0.765218
$528$	387018.	0.0604151
$529$	1.39613e7	2.16914
$530$	−1.16220e7	−1.79718
$531$	−4.50565e6	−0.693459
$532$	1.86364e6	0.285485
$533$	−6.86881e6	−1.04728
$534$	1.35902e6	0.206240
$535$	406612.	0.0614181
$536$	−1.28653e6	−0.193422
$537$	−10563.8	−0.00158082
$538$	−3.95354e6	−0.588885
$539$	512876.	0.0760397
$540$	−3.46530e6	−0.511395
$541$	−4.34177e6	−0.637784	−0.318892	−	0.947791i	$-0.603311\pi$
$541$	−4.34177e6	−0.637784	−0.318892	+	0.947791i	$0.603311\pi$
$542$	−9.06203e6	−1.32503
$543$	−2.65369e6	−0.386234
$544$	−1.52935e7	−2.21569
$545$	−5.79448e6	−0.835647
$546$	−2.54971e6	−0.366024
$547$	1.14668e7	1.63860	0.819302	−	0.573363i	$-0.194361\pi$
$547$	1.14668e7	1.63860	0.819302	+	0.573363i	$0.194361\pi$
$548$	186503.	0.0265298
$549$	−4.83332e6	−0.684407
$550$	455417.	0.0641951
$551$	−629511.	−0.0883332
$552$	391726.	0.0547185
$553$	9.37627e6	1.30382
$554$	5.23246e6	0.724322
$555$	2.01631e6	0.277860
$556$	3.15234e6	0.432460
$557$	−1.57100e6	−0.214555	−0.107278	−	0.994229i	$-0.534213\pi$
$557$	−1.57100e6	−0.214555	−0.107278	+	0.994229i	$0.534213\pi$
$558$	5.00983e6	0.681142
$559$	5.15307e6	0.697488
$560$	7.96938e6	1.07388
$561$	−776409.	−0.104156
$562$	−2.11230e6	−0.282108
$563$	−850908.	−0.113139	−0.0565694	−	0.998399i	$-0.518016\pi$
$563$	−850908.	−0.113139	−0.0565694	+	0.998399i	$0.518016\pi$
$564$	271312.	0.0359146
$565$	1.27490e7	1.68018
$566$	8.43265e6	1.10643
$567$	7.30255e6	0.953931
$568$	−34792.9	−0.00452501
$569$	−1.19642e7	−1.54919	−0.774595	−	0.632458i	$-0.782046\pi$
$569$	−1.19642e7	−1.54919	−0.774595	+	0.632458i	$0.782046\pi$
$570$	626539.	0.0807721
$571$	−7.97842e6	−1.02406	−0.512032	−	0.858967i	$-0.671107\pi$
$571$	−7.97842e6	−1.02406	−0.512032	+	0.858967i	$0.671107\pi$
$572$	2.61068e6	0.333629
$573$	1.50126e6	0.191016
$574$	−1.32497e7	−1.67852
$575$	−2.07611e6	−0.261867
$576$	8.92640e6	1.12104
$577$	5.90743e6	0.738685	0.369342	−	0.929293i	$-0.379583\pi$
$577$	5.90743e6	0.738685	0.369342	+	0.929293i	$0.379583\pi$
$578$	1.61153e7	2.00641
$579$	949186.	0.117667
$580$	3.60202e6	0.444606
$581$	−1.40415e7	−1.72573
$582$	1.09602e6	0.134125
$583$	2.86865e6	0.349548
$584$	1.80303e6	0.218761
$585$	8.51081e6	1.02821
$586$	7.18646e6	0.864512
$587$	1.34766e6	0.161430	0.0807151	−	0.996737i	$-0.474280\pi$
$587$	1.34766e6	0.161430	0.0807151	+	0.996737i	$0.474280\pi$
$588$	−517730.	−0.0617533
$589$	−971777.	−0.115419
$590$	−9.56797e6	−1.13159
$591$	−2.00288e6	−0.235877
$592$	−8.86385e6	−1.03948
$593$	1.05883e7	1.23649	0.618243	−	0.785987i	$-0.287845\pi$
$593$	1.05883e7	1.23649	0.618243	+	0.785987i	$0.287845\pi$
$594$	1.63650e6	0.190304
$595$	−1.59876e7	−1.85136
$596$	2.32972e6	0.268651
$597$	−940962.	−0.108053
$598$	−2.27705e7	−2.60388
$599$	3.48377e6	0.396718	0.198359	−	0.980129i	$-0.436439\pi$
$599$	3.48377e6	0.396718	0.198359	+	0.980129i	$0.436439\pi$
$600$	−39870.5	−0.00452141
$601$	−6.41433e6	−0.724378	−0.362189	−	0.932105i	$-0.617970\pi$
$601$	−6.41433e6	−0.724378	−0.362189	+	0.932105i	$0.617970\pi$
$602$	9.94010e6	1.11789
$603$	1.19366e7	1.33686
$604$	−4.58540e6	−0.511428
$605$	−876589.	−0.0973661
$606$	1.17056e6	0.129483
$607$	−700912.	−0.0772132	−0.0386066	−	0.999254i	$-0.512292\pi$
$607$	−700912.	−0.0772132	−0.0386066	+	0.999254i	$0.512292\pi$
$608$	−3.04622e6	−0.334197
$609$	868320.	0.0948717
$610$	−1.02638e7	−1.11682
$611$	−1.36776e6	−0.148221
$612$	−1.48885e7	−1.60684
$613$	−1.17591e7	−1.26393	−0.631966	−	0.774996i	$-0.717752\pi$
$613$	−1.17591e7	−1.26393	−0.631966	+	0.774996i	$0.717752\pi$
$614$	−1.07198e7	−1.14753
$615$	−2.32817e6	−0.248214
$616$	436747.	0.0463744
$617$	−1.00683e6	−0.106474	−0.0532371	−	0.998582i	$-0.516954\pi$
$617$	−1.00683e6	−0.106474	−0.0532371	+	0.998582i	$0.516954\pi$
$618$	1.41669e6	0.149212
$619$	1.27458e7	1.33703	0.668513	−	0.743700i	$-0.266931\pi$
$619$	1.27458e7	1.33703	0.668513	+	0.743700i	$0.266931\pi$
$620$	5.56044e6	0.580938
$621$	−7.46031e6	−0.776297
$622$	2.75050e7	2.85060
$623$	−6.90744e6	−0.713012
$624$	1.96954e6	0.202490
$625$	−1.09908e7	−1.12546
$626$	−2.46155e7	−2.51058
$627$	−154648.	−0.0157100
$628$	−5.72172e6	−0.578932
$629$	1.77821e7	1.79207
$630$	1.64171e7	1.64795
$631$	1.41284e7	1.41260	0.706299	−	0.707913i	$-0.250363\pi$
$631$	1.41284e7	1.41260	0.706299	+	0.707913i	$0.250363\pi$
$632$	1.60810e6	0.160148
$633$	2.62626e6	0.260512
$634$	1.72062e7	1.70005
$635$	5.41029e6	0.532459
$636$	−2.89580e6	−0.283874
$637$	2.61004e6	0.254858
$638$	−1.70106e6	−0.165450
$639$	322814.	0.0312752
$640$	3.03708e6	0.293094
$641$	−4.36680e6	−0.419777	−0.209888	−	0.977725i	$-0.567310\pi$
$641$	−4.36680e6	−0.419777	−0.209888	+	0.977725i	$0.567310\pi$
$642$	193841.	0.0185613
$643$	7.81597e6	0.745513	0.372757	−	0.927929i	$-0.378413\pi$
$643$	7.81597e6	0.745513	0.372757	+	0.927929i	$0.378413\pi$
$644$	−2.29573e7	−2.18125
$645$	1.74662e6	0.165310
$646$	5.52551e6	0.520944
$647$	2.01624e7	1.89357	0.946786	−	0.321863i	$-0.104309\pi$
$647$	2.01624e7	1.89357	0.946786	+	0.321863i	$0.104309\pi$
$648$	1.25244e6	0.117171
$649$	2.36166e6	0.220092
$650$	2.31762e6	0.215159
$651$	1.34043e6	0.123963
$652$	−1.87723e7	−1.72941
$653$	324619.	0.0297914	0.0148957	−	0.999889i	$-0.495258\pi$
$653$	324619.	0.0297914	0.0148957	+	0.999889i	$0.495258\pi$
$654$	−2.76235e6	−0.252543
$655$	−3.90963e6	−0.356067
$656$	1.02348e7	0.928581
$657$	−1.67288e7	−1.51199
$658$	−2.63837e6	−0.237559
$659$	−1.07107e7	−0.960740	−0.480370	−	0.877066i	$-0.659498\pi$
$659$	−1.07107e7	−0.960740	−0.480370	+	0.877066i	$0.659498\pi$
$660$	884886.	0.0790729
$661$	−1.11064e7	−0.988712	−0.494356	−	0.869260i	$-0.664596\pi$
$661$	−1.11064e7	−0.988712	−0.494356	+	0.869260i	$0.664596\pi$
$662$	1.00986e7	0.895601
$663$	−3.95116e6	−0.349093
$664$	−2.40822e6	−0.211971
$665$	−3.18448e6	−0.279244
$666$	−1.82597e7	−1.59517
$667$	7.75464e6	0.674912
$668$	1.93970e7	1.68187
$669$	3.47795e6	0.300441
$670$	2.53480e7	2.18151
$671$	2.53341e6	0.217219
$672$	4.20182e6	0.358934
$673$	−1.38137e7	−1.17564	−0.587818	−	0.808993i	$-0.700013\pi$
$673$	−1.38137e7	−1.17564	−0.587818	+	0.808993i	$0.700013\pi$
$674$	5.56208e6	0.471615
$675$	759323.	0.0641457
$676$	276160.	0.0232431
$677$	2.29090e6	0.192103	0.0960514	−	0.995376i	$-0.469379\pi$
$677$	2.29090e6	0.192103	0.0960514	+	0.995376i	$0.469379\pi$
$678$	6.07775e6	0.507772
$679$	−5.57067e6	−0.463695
$680$	−2.74200e6	−0.227402
$681$	1.72632e6	0.142644
$682$	−2.62593e6	−0.216183
$683$	4.40512e6	0.361332	0.180666	−	0.983545i	$-0.442175\pi$
$683$	4.40512e6	0.361332	0.180666	+	0.983545i	$0.442175\pi$
$684$	−2.96556e6	−0.242363
$685$	−318685.	−0.0259498
$686$	−1.49287e7	−1.21119
$687$	773519.	0.0625287
$688$	−7.67828e6	−0.618434
$689$	1.45986e7	1.17156
$690$	−7.71803e6	−0.617140
$691$	−5.86199e6	−0.467035	−0.233518	−	0.972353i	$-0.575024\pi$
$691$	−5.86199e6	−0.467035	−0.233518	+	0.972353i	$0.575024\pi$
$692$	9.35440e6	0.742592
$693$	−4.05221e6	−0.320523
$694$	2.19054e7	1.72645
$695$	−5.38653e6	−0.423007
$696$	148923.	0.0116530
$697$	−2.05324e7	−1.60087
$698$	−1.94569e7	−1.51160
$699$	−2.15932e6	−0.167157
$700$	2.33663e6	0.180238
$701$	−8.02106e6	−0.616505	−0.308253	−	0.951305i	$-0.599744\pi$
$701$	−8.02106e6	−0.616505	−0.308253	+	0.951305i	$0.599744\pi$
$702$	8.32816e6	0.637832
$703$	3.54190e6	0.270301
$704$	−4.67881e6	−0.355799
$705$	−463602.	−0.0351295
$706$	5.22946e6	0.394862
$707$	−5.94954e6	−0.447646
$708$	−2.38401e6	−0.178741
$709$	2.17891e7	1.62788	0.813941	−	0.580948i	$-0.197318\pi$
$709$	2.17891e7	1.62788	0.813941	+	0.580948i	$0.197318\pi$
$710$	685512.	0.0510351
$711$	−1.49202e7	−1.10688
$712$	−1.18468e6	−0.0875789
$713$	1.19709e7	0.881863
$714$	−7.62165e6	−0.559505
$715$	−4.46098e6	−0.326336
$716$	106179.	0.00774029
$717$	1.03001e6	0.0748246
$718$	1.23505e7	0.894076
$719$	1.03483e7	0.746531	0.373266	−	0.927724i	$-0.378238\pi$
$719$	1.03483e7	0.746531	0.373266	+	0.927724i	$0.378238\pi$
$720$	−1.26814e7	−0.911670
$721$	−7.20052e6	−0.515853
$722$	−1.91730e7	−1.36882
$723$	−2.41633e6	−0.171914
$724$	2.66730e7	1.89115
$725$	−789280.	−0.0557682
$726$	−417889.	−0.0294252
$727$	−2.03348e7	−1.42693	−0.713466	−	0.700690i	$-0.752876\pi$
$727$	−2.03348e7	−1.42693	−0.713466	+	0.700690i	$0.752876\pi$
$728$	2.22262e6	0.155430
$729$	−1.02211e7	−0.712325
$730$	−3.55244e7	−2.46729
$731$	1.54037e7	1.06618
$732$	−2.55739e6	−0.176408
$733$	4.78280e6	0.328793	0.164396	−	0.986394i	$-0.447432\pi$
$733$	4.78280e6	0.328793	0.164396	+	0.986394i	$0.447432\pi$
$734$	1.45224e7	0.994946
$735$	884668.	0.0604034
$736$	3.75249e7	2.55344
$737$	−6.25663e6	−0.424298
$738$	2.10839e7	1.42498
$739$	−1.08737e7	−0.732429	−0.366215	−	0.930530i	$-0.619346\pi$
$739$	−1.08737e7	−0.732429	−0.366215	+	0.930530i	$0.619346\pi$
$740$	−2.02665e7	−1.36050
$741$	−787008.	−0.0526543
$742$	2.81603e7	1.87770
$743$	−1.01036e7	−0.671434	−0.335717	−	0.941963i	$-0.608979\pi$
$743$	−1.01036e7	−0.671434	−0.335717	+	0.941963i	$0.608979\pi$
$744$	229893.	0.0152263
$745$	−3.98089e6	−0.262778
$746$	1.86006e7	1.22371
$747$	2.23438e7	1.46506
$748$	7.80390e6	0.509986
$749$	−985227.	−0.0641700
$750$	−4.55475e6	−0.295673
$751$	9.91947e6	0.641784	0.320892	−	0.947116i	$-0.396017\pi$
$751$	9.91947e6	0.641784	0.320892	+	0.947116i	$0.396017\pi$
$752$	2.03802e6	0.131421
$753$	−1.86088e6	−0.119600
$754$	−8.65673e6	−0.554530
$755$	7.83526e6	0.500249
$756$	8.39647e6	0.534309
$757$	−1.33506e7	−0.846759	−0.423380	−	0.905952i	$-0.639156\pi$
$757$	−1.33506e7	−0.846759	−0.423380	+	0.905952i	$0.639156\pi$
$758$	−3.62232e7	−2.28988
$759$	1.90504e6	0.120033
$760$	−546162.	−0.0342995
$761$	1.28109e7	0.801898	0.400949	−	0.916100i	$-0.368680\pi$
$761$	1.28109e7	0.801898	0.400949	+	0.916100i	$0.368680\pi$
$762$	2.57920e6	0.160916
$763$	1.40401e7	0.873089
$764$	−1.50896e7	−0.935284
$765$	2.54407e7	1.57172
$766$	1.94531e7	1.19789
$767$	1.20185e7	0.737671
$768$	−2.86564e6	−0.175315
$769$	1.90629e7	1.16245	0.581224	−	0.813743i	$-0.302574\pi$
$769$	1.90629e7	1.16245	0.581224	+	0.813743i	$0.302574\pi$
$770$	−8.60508e6	−0.523032
$771$	2.27390e6	0.137764
$772$	−9.54054e6	−0.576142
$773$	−2.34434e6	−0.141115	−0.0705574	−	0.997508i	$-0.522478\pi$
$773$	−2.34434e6	−0.141115	−0.0705574	+	0.997508i	$0.522478\pi$
$774$	−1.58174e7	−0.949037
$775$	−1.21841e6	−0.0728686
$776$	−955410.	−0.0569555
$777$	−4.88555e6	−0.290309
$778$	−2.17716e7	−1.28956
$779$	−4.08972e6	−0.241463
$780$	4.50321e6	0.265024
$781$	−169204.	−0.00992623
$782$	−6.80661e7	−3.98028
$783$	−2.83620e6	−0.165323
$784$	−3.88906e6	−0.225972
$785$	9.77694e6	0.566277
$786$	−1.86381e6	−0.107608
$787$	−1.52283e7	−0.876425	−0.438212	−	0.898871i	$-0.644388\pi$
$787$	−1.52283e7	−0.876425	−0.438212	+	0.898871i	$0.644388\pi$
$788$	2.01315e7	1.15494
$789$	2.16845e6	0.124010
$790$	−3.16838e7	−1.80622
$791$	−3.08911e7	−1.75547
$792$	−694984.	−0.0393697
$793$	1.28926e7	0.728042
$794$	1.76619e7	0.994228
$795$	4.94818e6	0.277669
$796$	9.45788e6	0.529068
$797$	−2.70618e7	−1.50907	−0.754537	−	0.656257i	$-0.772139\pi$
$797$	−2.70618e7	−1.50907	−0.754537	+	0.656257i	$0.772139\pi$
$798$	−1.51811e6	−0.0843911
$799$	−4.08855e6	−0.226570
$800$	−3.81935e6	−0.210991
$801$	1.09916e7	0.605313
$802$	−1.98987e7	−1.09242
$803$	8.76846e6	0.479882
$804$	6.31585e6	0.344581
$805$	3.92281e7	2.13357
$806$	−1.33634e7	−0.724569
$807$	1.68326e6	0.0909844
$808$	−1.02039e6	−0.0549842
$809$	−2.25663e6	−0.121224	−0.0606121	−	0.998161i	$-0.519305\pi$
$809$	−2.25663e6	−0.121224	−0.0606121	+	0.998161i	$0.519305\pi$
$810$	−2.46764e7	−1.32151
$811$	4.49121e6	0.239779	0.119890	−	0.992787i	$-0.461746\pi$
$811$	4.49121e6	0.239779	0.119890	+	0.992787i	$0.461746\pi$
$812$	−8.72773e6	−0.464527
$813$	3.85825e6	0.204722
$814$	9.57091e6	0.506282
$815$	3.20770e7	1.69161
$816$	5.88739e6	0.309526
$817$	3.06816e6	0.160814
$818$	5.01769e7	2.62193
$819$	−2.06218e7	−1.07428
$820$	2.34011e7	1.21535
$821$	592581.	0.0306825	0.0153412	−	0.999882i	$-0.495117\pi$
$821$	592581.	0.0306825	0.0153412	+	0.999882i	$0.495117\pi$
$822$	−151924.	−0.00784236
$823$	−1.14748e7	−0.590533	−0.295266	−	0.955415i	$-0.595408\pi$
$823$	−1.14748e7	−0.590533	−0.295266	+	0.955415i	$0.595408\pi$
$824$	−1.23494e6	−0.0633620
$825$	−193898.	−0.00991833
$826$	2.31833e7	1.18229
$827$	−8.47060e6	−0.430676	−0.215338	−	0.976540i	$-0.569085\pi$
$827$	−8.47060e6	−0.430676	−0.215338	+	0.976540i	$0.569085\pi$
$828$	3.65313e7	1.85178
$829$	−1.58876e7	−0.802919	−0.401460	−	0.915877i	$-0.631497\pi$
$829$	−1.58876e7	−0.802919	−0.401460	+	0.915877i	$0.631497\pi$
$830$	4.74483e7	2.39070
$831$	−2.22777e6	−0.111910
$832$	−2.38106e7	−1.19251
$833$	7.80197e6	0.389576
$834$	−2.56788e6	−0.127838
$835$	−3.31445e7	−1.64511
$836$	1.55441e6	0.0769221
$837$	−4.37825e6	−0.216017
$838$	−3.07552e6	−0.151290
$839$	2.66963e7	1.30932	0.654659	−	0.755924i	$-0.272812\pi$
$839$	2.66963e7	1.30932	0.654659	+	0.755924i	$0.272812\pi$
$840$	753352.	0.0368383
$841$	−1.75631e7	−0.856268
$842$	2.88480e7	1.40228
$843$	899333.	0.0435864
$844$	−2.63972e7	−1.27556
$845$	−471886.	−0.0227350
$846$	4.19837e6	0.201676
$847$	2.12399e6	0.101729
$848$	−2.17525e7	−1.03877
$849$	−3.59028e6	−0.170946
$850$	6.92789e6	0.328892
$851$	−4.36310e7	−2.06524
$852$	170806.	0.00806128
$853$	3.58773e6	0.168829	0.0844146	−	0.996431i	$-0.473098\pi$
$853$	3.58773e6	0.168829	0.0844146	+	0.996431i	$0.473098\pi$
$854$	2.48693e7	1.16686
$855$	5.06738e6	0.237065
$856$	−168974.	−0.00788197
$857$	−6.00941e6	−0.279499	−0.139749	−	0.990187i	$-0.544630\pi$
$857$	−6.00941e6	−0.279499	−0.139749	+	0.990187i	$0.544630\pi$
$858$	−2.12665e6	−0.0986228
$859$	−1.74629e7	−0.807484	−0.403742	−	0.914873i	$-0.632291\pi$
$859$	−1.74629e7	−0.807484	−0.403742	+	0.914873i	$0.632291\pi$
$860$	−1.75558e7	−0.809422
$861$	5.64118e6	0.259336
$862$	2.58149e7	1.18332
$863$	2.34431e6	0.107149	0.0535746	−	0.998564i	$-0.482939\pi$
$863$	2.34431e6	0.107149	0.0535746	+	0.998564i	$0.482939\pi$
$864$	−1.37245e7	−0.625476
$865$	−1.59842e7	−0.726360
$866$	1.32779e7	0.601635
$867$	−6.86126e6	−0.309996
$868$	−1.34730e7	−0.606968
$869$	7.82050e6	0.351306
$870$	−2.93418e6	−0.131428
$871$	−3.18401e7	−1.42210
$872$	2.40798e6	0.107241
$873$	8.86445e6	0.393655
$874$	−1.35577e7	−0.600354
$875$	2.31502e7	1.02220
$876$	−8.85145e6	−0.389721
$877$	1.98979e7	0.873591	0.436796	−	0.899561i	$-0.356113\pi$
$877$	1.98979e7	0.873591	0.436796	+	0.899561i	$0.356113\pi$
$878$	−2.03175e7	−0.889474
$879$	−3.05971e6	−0.133570
$880$	6.64704e6	0.289349
$881$	2.32718e7	1.01016	0.505081	−	0.863072i	$-0.331463\pi$
$881$	2.32718e7	1.01016	0.505081	+	0.863072i	$0.331463\pi$
$882$	−8.01154e6	−0.346772
$883$	−2.71777e7	−1.17304	−0.586518	−	0.809936i	$-0.699502\pi$
$883$	−2.71777e7	−1.17304	−0.586518	+	0.809936i	$0.699502\pi$
$884$	3.97142e7	1.70929
$885$	4.07366e6	0.174834
$886$	3.07421e7	1.31568
$887$	−1.39671e7	−0.596069	−0.298034	−	0.954555i	$-0.596331\pi$
$887$	−1.39671e7	−0.596069	−0.298034	+	0.954555i	$0.596331\pi$
$888$	−837907.	−0.0356585
$889$	−1.31092e7	−0.556316
$890$	2.33413e7	0.987755
$891$	6.09086e6	0.257030
$892$	−3.49579e7	−1.47107
$893$	−814374.	−0.0341740
$894$	−1.89778e6	−0.0794149
$895$	−181433.	−0.00757109
$896$	−7.35889e6	−0.306226
$897$	9.69477e6	0.402306
$898$	−3.93761e7	−1.62945
$899$	4.55099e6	0.187805
$900$	−3.71822e6	−0.153013
$901$	4.36385e7	1.79084
$902$	−1.10512e7	−0.452266
$903$	−4.23209e6	−0.172717
$904$	−5.29805e6	−0.215623
$905$	−4.55773e7	−1.84981
$906$	3.73524e6	0.151181
$907$	1.77875e7	0.717954	0.358977	−	0.933346i	$-0.383126\pi$
$907$	1.77875e7	0.717954	0.358977	+	0.933346i	$0.383126\pi$
$908$	−1.73517e7	−0.698437
$909$	9.46734e6	0.380031
$910$	−4.37914e7	−1.75302
$911$	30398.8	0.00121356	0.000606780	−	1.00000i	$-0.499807\pi$
$911$	30398.8	0.00121356	0.000606780		1.00000i	$0.499807\pi$
$912$	1.17267e6	0.0466864
$913$	−1.17116e7	−0.464987
$914$	5.81288e7	2.30158
$915$	4.36991e6	0.172552
$916$	−7.77486e6	−0.306164
$917$	9.47308e6	0.372021
$918$	2.48947e7	0.974990
$919$	−4.10055e6	−0.160160	−0.0800798	−	0.996788i	$-0.525518\pi$
$919$	−4.10055e6	−0.160160	−0.0800798	+	0.996788i	$0.525518\pi$
$920$	6.72790e6	0.262066
$921$	4.56406e6	0.177297
$922$	6.65453e7	2.57804
$923$	−861085.	−0.0332692
$924$	−2.14409e6	−0.0826158
$925$	4.44084e6	0.170652
$926$	−2.18908e7	−0.838946
$927$	1.14580e7	0.437935
$928$	1.42659e7	0.543788
$929$	−1.46532e7	−0.557048	−0.278524	−	0.960429i	$-0.589845\pi$
$929$	−1.46532e7	−0.557048	−0.278524	+	0.960429i	$0.589845\pi$
$930$	−4.52950e6	−0.171729
$931$	1.55403e6	0.0587604
$932$	2.17039e7	0.818461
$933$	−1.17105e7	−0.440425
$934$	−3.54310e7	−1.32897
$935$	−1.33349e7	−0.498838
$936$	−3.53679e6	−0.131953
$937$	−3.97538e7	−1.47921	−0.739604	−	0.673042i	$-0.764987\pi$
$937$	−3.97538e7	−1.47921	−0.739604	+	0.673042i	$0.764987\pi$
$938$	−6.14185e7	−2.27925
$939$	1.04803e7	0.387891
$940$	4.65979e6	0.172007
$941$	5.32850e6	0.196169	0.0980847	−	0.995178i	$-0.468728\pi$
$941$	5.32850e6	0.196169	0.0980847	+	0.995178i	$0.468728\pi$
$942$	4.66088e6	0.171136
$943$	5.03793e7	1.84490
$944$	−1.79081e7	−0.654062
$945$	−1.43474e7	−0.522629
$946$	8.29077e6	0.301208
$947$	3.11430e7	1.12846	0.564230	−	0.825618i	$-0.309173\pi$
$947$	3.11430e7	1.12846	0.564230	+	0.825618i	$0.309173\pi$
$948$	−7.89452e6	−0.285302
$949$	4.46229e7	1.60839
$950$	1.37993e6	0.0496074
$951$	−7.32571e6	−0.262663
$952$	6.64389e6	0.237591
$953$	4.87227e7	1.73780	0.868899	−	0.494990i	$-0.164828\pi$
$953$	4.87227e7	1.73780	0.868899	+	0.494990i	$0.164828\pi$
$954$	−4.48106e7	−1.59408
$955$	2.57842e7	0.914839
$956$	−1.03529e7	−0.366369
$957$	724242.	0.0255625
$958$	1.27628e7	0.449297
$959$	772177.	0.0271125
$960$	−8.07056e6	−0.282635
$961$	−2.16038e7	−0.754608
$962$	4.87065e7	1.69687
$963$	1.56776e6	0.0544773
$964$	2.42873e7	0.841755
$965$	1.63023e7	0.563548
$966$	1.87009e7	0.644792
$967$	4.85436e7	1.66942	0.834711	−	0.550688i	$-0.185635\pi$
$967$	4.85436e7	1.66942	0.834711	+	0.550688i	$0.185635\pi$
$968$	364279.	0.0124953
$969$	−2.35254e6	−0.0804873
$970$	1.88241e7	0.642370
$971$	−3.15035e7	−1.07229	−0.536143	−	0.844127i	$-0.680119\pi$
$971$	−3.15035e7	−1.07229	−0.536143	+	0.844127i	$0.680119\pi$
$972$	−2.02129e7	−0.686221
$973$	1.30516e7	0.441960
$974$	−6.25393e7	−2.11230
$975$	−986751.	−0.0332427
$976$	−1.92104e7	−0.645525
$977$	−5.35354e7	−1.79434	−0.897170	−	0.441684i	$-0.854381\pi$
$977$	−5.35354e7	−1.79434	−0.897170	+	0.441684i	$0.854381\pi$
$978$	1.52918e7	0.511225
$979$	−5.76131e6	−0.192116
$980$	−8.89204e6	−0.295758
$981$	−2.23416e7	−0.741211
$982$	2.95472e7	0.977771
$983$	−5.40925e7	−1.78547	−0.892736	−	0.450580i	$-0.851217\pi$
$983$	−5.40925e7	−1.78547	−0.892736	+	0.450580i	$0.851217\pi$
$984$	967505.	0.0318541
$985$	−3.43996e7	−1.12970
$986$	−2.58769e7	−0.847655
$987$	1.12331e6	0.0367035
$988$	7.91044e6	0.257815
$989$	−3.77952e7	−1.22870
$990$	1.36930e7	0.444029
$991$	2.31007e7	0.747208	0.373604	−	0.927588i	$-0.378122\pi$
$991$	2.31007e7	0.747208	0.373604	+	0.927588i	$0.378122\pi$
$992$	2.20223e7	0.710533
$993$	−4.29956e6	−0.138373
$994$	−1.66100e6	−0.0533218
$995$	−1.61611e7	−0.517502
$996$	1.18225e7	0.377625
$997$	−4.54061e7	−1.44669	−0.723346	−	0.690486i	$-0.757397\pi$
$997$	−4.54061e7	−1.44669	−0.723346	+	0.690486i	$0.757397\pi$
$998$	−6.92788e7	−2.20178
$999$	1.59577e7	0.505891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.6.a.b.1.3	✓	3
3.2	odd	2		99.6.a.g.1.1		3
4.3	odd	2		176.6.a.i.1.3		3
5.2	odd	4		275.6.b.b.199.5		6
5.3	odd	4		275.6.b.b.199.2		6
5.4	even	2		275.6.a.b.1.1		3
7.6	odd	2		539.6.a.e.1.3		3
8.3	odd	2		704.6.a.t.1.1		3
8.5	even	2		704.6.a.q.1.3		3
11.10	odd	2		121.6.a.d.1.1		3
33.32	even	2		1089.6.a.r.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.6.a.b.1.3	✓	3	1.1	even	1	trivial
99.6.a.g.1.1		3	3.2	odd	2
121.6.a.d.1.1		3	11.10	odd	2
176.6.a.i.1.3		3	4.3	odd	2
275.6.a.b.1.1		3	5.4	even	2
275.6.b.b.199.2		6	5.3	odd	4
275.6.b.b.199.5		6	5.2	odd	4
539.6.a.e.1.3		3	7.6	odd	2
704.6.a.q.1.3		3	8.5	even	2
704.6.a.t.1.1		3	8.3	odd	2
1089.6.a.r.1.3		3	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q+8.18772 q^{2} -3.48600 q^{3} +35.0388 q^{4} -59.8722 q^{5} -28.5424 q^{6} +145.071 q^{7} +24.8808 q^{8} -230.848 q^{9} +O(q^{10})\)	\(q+8.18772 q^{2} -3.48600 q^{3} +35.0388 q^{4} -59.8722 q^{5} -28.5424 q^{6} +145.071 q^{7} +24.8808 q^{8} -230.848 q^{9} -490.217 q^{10} +121.000 q^{11} -122.145 q^{12} +615.772 q^{13} +1187.80 q^{14} +208.715 q^{15} -917.524 q^{16} +1840.68 q^{17} -1890.12 q^{18} +366.633 q^{19} -2097.85 q^{20} -505.718 q^{21} +990.714 q^{22} -4516.38 q^{23} -86.7344 q^{24} +459.685 q^{25} +5041.77 q^{26} +1651.83 q^{27} +5083.12 q^{28} -1717.00 q^{29} +1708.90 q^{30} -2650.54 q^{31} -8308.62 q^{32} -421.806 q^{33} +15070.9 q^{34} -8685.74 q^{35} -8088.63 q^{36} +9660.61 q^{37} +3001.89 q^{38} -2146.58 q^{39} -1489.67 q^{40} -11154.8 q^{41} -4140.68 q^{42} +8368.48 q^{43} +4239.69 q^{44} +13821.4 q^{45} -36978.9 q^{46} -2221.22 q^{47} +3198.49 q^{48} +4238.64 q^{49} +3763.77 q^{50} -6416.60 q^{51} +21575.9 q^{52} +23707.9 q^{53} +13524.8 q^{54} -7244.54 q^{55} +3609.48 q^{56} -1278.08 q^{57} -14058.3 q^{58} +19517.8 q^{59} +7313.11 q^{60} +20937.3 q^{61} -21701.9 q^{62} -33489.4 q^{63} -38667.9 q^{64} -36867.6 q^{65} -3453.63 q^{66} -51707.7 q^{67} +64495.1 q^{68} +15744.1 q^{69} -71116.4 q^{70} -1398.38 q^{71} -5743.67 q^{72} +72466.6 q^{73} +79098.4 q^{74} -1602.46 q^{75} +12846.4 q^{76} +17553.6 q^{77} -17575.6 q^{78} +64632.2 q^{79} +54934.2 q^{80} +50337.7 q^{81} -91332.4 q^{82} -96790.3 q^{83} -17719.8 q^{84} -110205. q^{85} +68518.8 q^{86} +5985.47 q^{87} +3010.57 q^{88} -47614.1 q^{89} +113166. q^{90} +89330.7 q^{91} -158249. q^{92} +9239.79 q^{93} -18186.7 q^{94} -21951.2 q^{95} +28963.9 q^{96} -38399.6 q^{97} +34704.8 q^{98} -27932.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9}+O(q^{10}) \) 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9	\( 3 q + 34 q^{3} + 84 q^{4} + 24 q^{5} - 206 q^{6} + 84 q^{7} - 564 q^{8} - 7 q^{9} - 414 q^{10} + 363 q^{11} + 992 q^{12} + 486 q^{13} - 1020 q^{14} + 1654 q^{15} + 1992 q^{16} + 1086 q^{17} - 3706 q^{18} + 1380 q^{19} - 3480 q^{20} - 908 q^{21} - 3066 q^{23} - 11748 q^{24} - 57 q^{25} + 12132 q^{26} - 2990 q^{27} + 23712 q^{28} - 3426 q^{29} + 2650 q^{30} - 4098 q^{31} - 12408 q^{32} + 4114 q^{33} + 25320 q^{34} - 24228 q^{35} + 4756 q^{36} + 17724 q^{37} - 9240 q^{38} - 6560 q^{39} - 15276 q^{40} + 5994 q^{41} - 47828 q^{42} - 26208 q^{43} + 10164 q^{44} + 18458 q^{45} - 16806 q^{46} - 17232 q^{47} + 61064 q^{48} + 48531 q^{49} + 41070 q^{50} - 22724 q^{51} - 35304 q^{52} + 50586 q^{53} + 18814 q^{54} + 2904 q^{55} - 42312 q^{56} + 20160 q^{57} - 29172 q^{58} - 3738 q^{59} - 13456 q^{60} + 18486 q^{61} - 19974 q^{62} - 12496 q^{63} - 20352 q^{64} - 7668 q^{65} - 24926 q^{66} - 47754 q^{67} - 12600 q^{68} + 35042 q^{69} - 123372 q^{70} + 39282 q^{71} - 95040 q^{72} + 15426 q^{73} + 153294 q^{74} - 21916 q^{75} + 103920 q^{76} + 10164 q^{77} + 124984 q^{78} + 125148 q^{79} + 118680 q^{80} - 86917 q^{81} - 255372 q^{82} - 143928 q^{83} + 343616 q^{84} - 104040 q^{85} + 243060 q^{86} - 19368 q^{87} - 68244 q^{88} - 106824 q^{89} + 103424 q^{90} - 109632 q^{91} - 336528 q^{92} - 16622 q^{93} - 74928 q^{94} - 22200 q^{95} - 76456 q^{96} + 9684 q^{97} + 3480 q^{98} - 847 q^{99}+O(q^{100}) \) 3 * q + 34 * q^3 + 84 * q^4 + 24 * q^5 - 206 * q^6 + 84 * q^7 - 564 * q^8 - 7 * q^9 - 414 * q^10 + 363 * q^11 + 992 * q^12 + 486 * q^13 - 1020 * q^14 + 1654 * q^15 + 1992 * q^16 + 1086 * q^17 - 3706 * q^18 + 1380 * q^19 - 3480 * q^20 - 908 * q^21 - 3066 * q^23 - 11748 * q^24 - 57 * q^25 + 12132 * q^26 - 2990 * q^27 + 23712 * q^28 - 3426 * q^29 + 2650 * q^30 - 4098 * q^31 - 12408 * q^32 + 4114 * q^33 + 25320 * q^34 - 24228 * q^35 + 4756 * q^36 + 17724 * q^37 - 9240 * q^38 - 6560 * q^39 - 15276 * q^40 + 5994 * q^41 - 47828 * q^42 - 26208 * q^43 + 10164 * q^44 + 18458 * q^45 - 16806 * q^46 - 17232 * q^47 + 61064 * q^48 + 48531 * q^49 + 41070 * q^50 - 22724 * q^51 - 35304 * q^52 + 50586 * q^53 + 18814 * q^54 + 2904 * q^55 - 42312 * q^56 + 20160 * q^57 - 29172 * q^58 - 3738 * q^59 - 13456 * q^60 + 18486 * q^61 - 19974 * q^62 - 12496 * q^63 - 20352 * q^64 - 7668 * q^65 - 24926 * q^66 - 47754 * q^67 - 12600 * q^68 + 35042 * q^69 - 123372 * q^70 + 39282 * q^71 - 95040 * q^72 + 15426 * q^73 + 153294 * q^74 - 21916 * q^75 + 103920 * q^76 + 10164 * q^77 + 124984 * q^78 + 125148 * q^79 + 118680 * q^80 - 86917 * q^81 - 255372 * q^82 - 143928 * q^83 + 343616 * q^84 - 104040 * q^85 + 243060 * q^86 - 19368 * q^87 - 68244 * q^88 - 106824 * q^89 + 103424 * q^90 - 109632 * q^91 - 336528 * q^92 - 16622 * q^93 - 74928 * q^94 - 22200 * q^95 - 76456 * q^96 + 9684 * q^97 + 3480 * q^98 - 847 * q^99

Introduction

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