LMFDB - Embedded newform 165.6.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.307532.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 76x + 168 $ x^3 - x^2 - 76*x + 168
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$7.91848$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.91848 q^{2} -9.00000 q^{3} +66.3762 q^{4} -25.0000 q^{5} -89.2663 q^{6} +92.6461 q^{7} +340.959 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.91848 q^{2} -9.00000 q^{3} +66.3762 q^{4} -25.0000 q^{5} -89.2663 q^{6} +92.6461 q^{7} +340.959 q^{8} +81.0000 q^{9} -247.962 q^{10} +121.000 q^{11} -597.386 q^{12} +800.249 q^{13} +918.908 q^{14} +225.000 q^{15} +1257.76 q^{16} -117.742 q^{17} +803.397 q^{18} +831.422 q^{19} -1659.40 q^{20} -833.814 q^{21} +1200.14 q^{22} +2952.23 q^{23} -3068.63 q^{24} +625.000 q^{25} +7937.25 q^{26} -729.000 q^{27} +6149.49 q^{28} +5765.87 q^{29} +2231.66 q^{30} -61.7803 q^{31} +1564.36 q^{32} -1089.00 q^{33} -1167.83 q^{34} -2316.15 q^{35} +5376.47 q^{36} -10236.6 q^{37} +8246.44 q^{38} -7202.24 q^{39} -8523.98 q^{40} +9599.21 q^{41} -8270.17 q^{42} -17473.2 q^{43} +8031.52 q^{44} -2025.00 q^{45} +29281.7 q^{46} +18748.3 q^{47} -11319.8 q^{48} -8223.71 q^{49} +6199.05 q^{50} +1059.68 q^{51} +53117.5 q^{52} -9703.45 q^{53} -7230.57 q^{54} -3025.00 q^{55} +31588.5 q^{56} -7482.79 q^{57} +57188.6 q^{58} -24401.4 q^{59} +14934.6 q^{60} +33910.3 q^{61} -612.766 q^{62} +7504.33 q^{63} -24732.2 q^{64} -20006.2 q^{65} -10801.2 q^{66} -4989.24 q^{67} -7815.29 q^{68} -26570.1 q^{69} -22972.7 q^{70} -62961.6 q^{71} +27617.7 q^{72} -54232.5 q^{73} -101531. q^{74} -5625.00 q^{75} +55186.6 q^{76} +11210.2 q^{77} -71435.2 q^{78} -56996.4 q^{79} -31444.0 q^{80} +6561.00 q^{81} +95209.6 q^{82} +49685.9 q^{83} -55345.4 q^{84} +2943.56 q^{85} -173308. q^{86} -51892.8 q^{87} +41256.1 q^{88} -87990.1 q^{89} -20084.9 q^{90} +74139.9 q^{91} +195958. q^{92} +556.022 q^{93} +185954. q^{94} -20785.5 q^{95} -14079.3 q^{96} -44817.9 q^{97} -81566.7 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9	\( 3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9} - 175 q^{10} + 363 q^{11} - 657 q^{12} - 90 q^{13} - 784 q^{14} + 675 q^{15} - 415 q^{16} + 1934 q^{17} + 567 q^{18} + 2084 q^{19} - 1825 q^{20} - 828 q^{21} + 847 q^{22} + 1220 q^{23} - 2079 q^{24} + 1875 q^{25} + 17062 q^{26} - 2187 q^{27} + 11120 q^{28} + 4402 q^{29} + 1575 q^{30} - 10688 q^{31} + 12439 q^{32} - 3267 q^{33} - 4094 q^{34} - 2300 q^{35} + 5913 q^{36} - 8190 q^{37} + 13792 q^{38} + 810 q^{39} - 5775 q^{40} + 5974 q^{41} + 7056 q^{42} + 18868 q^{43} + 8833 q^{44} - 6075 q^{45} + 46220 q^{46} + 55500 q^{47} + 3735 q^{48} + 1907 q^{49} + 4375 q^{50} - 17406 q^{51} + 27330 q^{52} + 9206 q^{53} - 5103 q^{54} - 9075 q^{55} + 73248 q^{56} - 18756 q^{57} + 15366 q^{58} - 59196 q^{59} + 16425 q^{60} + 79902 q^{61} + 64616 q^{62} + 7452 q^{63} + 2129 q^{64} + 2250 q^{65} - 7623 q^{66} + 4468 q^{67} - 1218 q^{68} - 10980 q^{69} + 19600 q^{70} - 75164 q^{71} + 18711 q^{72} - 61290 q^{73} - 56766 q^{74} - 16875 q^{75} + 37816 q^{76} + 11132 q^{77} - 153558 q^{78} - 83564 q^{79} + 10375 q^{80} + 19683 q^{81} + 147410 q^{82} + 74764 q^{83} - 100080 q^{84} - 48350 q^{85} - 253432 q^{86} - 39618 q^{87} + 27951 q^{88} + 37342 q^{89} - 14175 q^{90} - 126488 q^{91} + 148164 q^{92} + 96192 q^{93} + 59252 q^{94} - 52100 q^{95} - 111951 q^{96} + 33486 q^{97} - 95249 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9 - 175 * q^10 + 363 * q^11 - 657 * q^12 - 90 * q^13 - 784 * q^14 + 675 * q^15 - 415 * q^16 + 1934 * q^17 + 567 * q^18 + 2084 * q^19 - 1825 * q^20 - 828 * q^21 + 847 * q^22 + 1220 * q^23 - 2079 * q^24 + 1875 * q^25 + 17062 * q^26 - 2187 * q^27 + 11120 * q^28 + 4402 * q^29 + 1575 * q^30 - 10688 * q^31 + 12439 * q^32 - 3267 * q^33 - 4094 * q^34 - 2300 * q^35 + 5913 * q^36 - 8190 * q^37 + 13792 * q^38 + 810 * q^39 - 5775 * q^40 + 5974 * q^41 + 7056 * q^42 + 18868 * q^43 + 8833 * q^44 - 6075 * q^45 + 46220 * q^46 + 55500 * q^47 + 3735 * q^48 + 1907 * q^49 + 4375 * q^50 - 17406 * q^51 + 27330 * q^52 + 9206 * q^53 - 5103 * q^54 - 9075 * q^55 + 73248 * q^56 - 18756 * q^57 + 15366 * q^58 - 59196 * q^59 + 16425 * q^60 + 79902 * q^61 + 64616 * q^62 + 7452 * q^63 + 2129 * q^64 + 2250 * q^65 - 7623 * q^66 + 4468 * q^67 - 1218 * q^68 - 10980 * q^69 + 19600 * q^70 - 75164 * q^71 + 18711 * q^72 - 61290 * q^73 - 56766 * q^74 - 16875 * q^75 + 37816 * q^76 + 11132 * q^77 - 153558 * q^78 - 83564 * q^79 + 10375 * q^80 + 19683 * q^81 + 147410 * q^82 + 74764 * q^83 - 100080 * q^84 - 48350 * q^85 - 253432 * q^86 - 39618 * q^87 + 27951 * q^88 + 37342 * q^89 - 14175 * q^90 - 126488 * q^91 + 148164 * q^92 + 96192 * q^93 + 59252 * q^94 - 52100 * q^95 - 111951 * q^96 + 33486 * q^97 - 95249 * q^98 + 29403 * 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 $

$2$	9.91848	1.75336	0.876678	−	0.481078i	$-0.159755\pi$
$2$	9.91848	1.75336	0.876678	+	0.481078i	$0.159755\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	66.3762	2.07426
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−89.2663	−1.01230
$7$	92.6461	0.714631	0.357315	−	0.933984i	$-0.383692\pi$
$7$	92.6461	0.714631	0.357315	+	0.933984i	$0.383692\pi$
$8$	340.959	1.88355
$9$	81.0000	0.333333
$10$	−247.962	−0.784124
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−597.386	−1.19757
$13$	800.249	1.31331	0.656654	−	0.754192i	$-0.271971\pi$
$13$	800.249	1.31331	0.656654	+	0.754192i	$0.271971\pi$
$14$	918.908	1.25300
$15$	225.000	0.258199
$16$	1257.76	1.22828
$17$	−117.742	−0.0988122	−0.0494061	−	0.998779i	$-0.515733\pi$
$17$	−117.742	−0.0988122	−0.0494061	+	0.998779i	$0.515733\pi$
$18$	803.397	0.584452
$19$	831.422	0.528369	0.264185	−	0.964472i	$-0.414897\pi$
$19$	831.422	0.528369	0.264185	+	0.964472i	$0.414897\pi$
$20$	−1659.40	−0.927635
$21$	−833.814	−0.412592
$22$	1200.14	0.528657
$23$	2952.23	1.16367	0.581837	−	0.813306i	$-0.302334\pi$
$23$	2952.23	1.16367	0.581837	+	0.813306i	$0.302334\pi$
$24$	−3068.63	−1.08747
$25$	625.000	0.200000
$26$	7937.25	2.30270
$27$	−729.000	−0.192450
$28$	6149.49	1.48233
$29$	5765.87	1.27312	0.636560	−	0.771227i	$-0.280357\pi$
$29$	5765.87	1.27312	0.636560	+	0.771227i	$0.280357\pi$
$30$	2231.66	0.452714
$31$	−61.7803	−0.0115464	−0.00577319	−	0.999983i	$-0.501838\pi$
$31$	−61.7803	−0.0115464	−0.00577319	+	0.999983i	$0.501838\pi$
$32$	1564.36	0.270061
$33$	−1089.00	−0.174078
$34$	−1167.83	−0.173253
$35$	−2316.15	−0.319593
$36$	5376.47	0.691419
$37$	−10236.6	−1.22928	−0.614640	−	0.788808i	$-0.710699\pi$
$37$	−10236.6	−1.22928	−0.614640	+	0.788808i	$0.710699\pi$
$38$	8246.44	0.926419
$39$	−7202.24	−0.758239
$40$	−8523.98	−0.842350
$41$	9599.21	0.891818	0.445909	−	0.895078i	$-0.352881\pi$
$41$	9599.21	0.891818	0.445909	+	0.895078i	$0.352881\pi$
$42$	−8270.17	−0.723421
$43$	−17473.2	−1.44113	−0.720563	−	0.693389i	$-0.756117\pi$
$43$	−17473.2	−1.44113	−0.720563	+	0.693389i	$0.756117\pi$
$44$	8031.52	0.625412
$45$	−2025.00	−0.149071
$46$	29281.7	2.04033
$47$	18748.3	1.23799	0.618995	−	0.785395i	$-0.287540\pi$
$47$	18748.3	1.23799	0.618995	+	0.785395i	$0.287540\pi$
$48$	−11319.8	−0.709148
$49$	−8223.71	−0.489303
$50$	6199.05	0.350671
$51$	1059.68	0.0570493
$52$	53117.5	2.72414
$53$	−9703.45	−0.474500	−0.237250	−	0.971449i	$-0.576246\pi$
$53$	−9703.45	−0.474500	−0.237250	+	0.971449i	$0.576246\pi$
$54$	−7230.57	−0.337433
$55$	−3025.00	−0.134840
$56$	31588.5	1.34604
$57$	−7482.79	−0.305054
$58$	57188.6	2.23223
$59$	−24401.4	−0.912609	−0.456305	−	0.889824i	$-0.650827\pi$
$59$	−24401.4	−0.912609	−0.456305	+	0.889824i	$0.650827\pi$
$60$	14934.6	0.535571
$61$	33910.3	1.16683	0.583413	−	0.812175i	$-0.301717\pi$
$61$	33910.3	1.16683	0.583413	+	0.812175i	$0.301717\pi$
$62$	−612.766	−0.0202449
$63$	7504.33	0.238210
$64$	−24732.2	−0.754768
$65$	−20006.2	−0.587329
$66$	−10801.2	−0.305220
$67$	−4989.24	−0.135784	−0.0678918	−	0.997693i	$-0.521627\pi$
$67$	−4989.24	−0.135784	−0.0678918	+	0.997693i	$0.521627\pi$
$68$	−7815.29	−0.204962
$69$	−26570.1	−0.671847
$70$	−22972.7	−0.560360
$71$	−62961.6	−1.48228	−0.741140	−	0.671351i	$-0.765714\pi$
$71$	−62961.6	−1.48228	−0.741140	+	0.671351i	$0.765714\pi$
$72$	27617.7	0.627851
$73$	−54232.5	−1.19111	−0.595556	−	0.803314i	$-0.703068\pi$
$73$	−54232.5	−1.19111	−0.595556	+	0.803314i	$0.703068\pi$
$74$	−101531.	−2.15537
$75$	−5625.00	−0.115470
$76$	55186.6	1.09597
$77$	11210.2	0.215469
$78$	−71435.2	−1.32946
$79$	−56996.4	−1.02750	−0.513748	−	0.857941i	$-0.671743\pi$
$79$	−56996.4	−1.02750	−0.513748	+	0.857941i	$0.671743\pi$
$80$	−31444.0	−0.549304
$81$	6561.00	0.111111
$82$	95209.6	1.56367
$83$	49685.9	0.791659	0.395830	−	0.918324i	$-0.370457\pi$
$83$	49685.9	0.791659	0.395830	+	0.918324i	$0.370457\pi$
$84$	−55345.4	−0.855822
$85$	2943.56	0.0441902
$86$	−173308.	−2.52681
$87$	−51892.8	−0.735037
$88$	41256.1	0.567912
$89$	−87990.1	−1.17749	−0.588747	−	0.808317i	$-0.700379\pi$
$89$	−87990.1	−1.17749	−0.588747	+	0.808317i	$0.700379\pi$
$90$	−20084.9	−0.261375
$91$	74139.9	0.938531
$92$	195958.	2.41376
$93$	556.022	0.00666630
$94$	185954.	2.17064
$95$	−20785.5	−0.236294
$96$	−14079.3	−0.155920
$97$	−44817.9	−0.483640	−0.241820	−	0.970321i	$-0.577744\pi$
$97$	−44817.9	−0.483640	−0.241820	+	0.970321i	$0.577744\pi$
$98$	−81566.7	−0.857921
$99$	9801.00	0.100504
$100$	41485.1	0.414851
$101$	82871.7	0.808356	0.404178	−	0.914680i	$-0.367558\pi$
$101$	82871.7	0.808356	0.404178	+	0.914680i	$0.367558\pi$
$102$	10510.4	0.100028
$103$	153697.	1.42749	0.713744	−	0.700406i	$-0.246998\pi$
$103$	153697.	1.42749	0.713744	+	0.700406i	$0.246998\pi$
$104$	272852.	2.47368
$105$	20845.4	0.184517
$106$	−96243.5	−0.831968
$107$	41662.3	0.351790	0.175895	−	0.984409i	$-0.443718\pi$
$107$	41662.3	0.351790	0.175895	+	0.984409i	$0.443718\pi$
$108$	−48388.2	−0.399191
$109$	39745.0	0.320417	0.160209	−	0.987083i	$-0.448783\pi$
$109$	39745.0	0.320417	0.160209	+	0.987083i	$0.448783\pi$
$110$	−30003.4	−0.236422
$111$	92129.3	0.709725
$112$	116526.	0.877768
$113$	−191157.	−1.40829	−0.704147	−	0.710054i	$-0.748671\pi$
$113$	−191157.	−1.40829	−0.704147	+	0.710054i	$0.748671\pi$
$114$	−74217.9	−0.534868
$115$	−73805.8	−0.520411
$116$	382716.	2.64078
$117$	64820.1	0.437769
$118$	−242025.	−1.60013
$119$	−10908.4	−0.0706143
$120$	76715.9	0.486331
$121$	14641.0	0.0909091
$122$	336338.	2.04586
$123$	−86392.9	−0.514891
$124$	−4100.74	−0.0239501
$125$	−15625.0	−0.0894427
$126$	74431.5	0.417667
$127$	−212879.	−1.17118	−0.585590	−	0.810608i	$-0.699137\pi$
$127$	−212879.	−1.17118	−0.585590	+	0.810608i	$0.699137\pi$
$128$	−295366.	−1.59344
$129$	157259.	0.832035
$130$	−198431.	−1.02980
$131$	−146592.	−0.746333	−0.373166	−	0.927764i	$-0.621728\pi$
$131$	−146592.	−0.746333	−0.373166	+	0.927764i	$0.621728\pi$
$132$	−72283.7	−0.361082
$133$	77027.9	0.377589
$134$	−49485.7	−0.238077
$135$	18225.0	0.0860663
$136$	−40145.4	−0.186118
$137$	335075.	1.52525	0.762623	−	0.646843i	$-0.223911\pi$
$137$	335075.	1.52525	0.762623	+	0.646843i	$0.223911\pi$
$138$	−263535.	−1.17799
$139$	30053.6	0.131935	0.0659674	−	0.997822i	$-0.478987\pi$
$139$	30053.6	0.131935	0.0659674	+	0.997822i	$0.478987\pi$
$140$	−153737.	−0.662917
$141$	−168735.	−0.714754
$142$	−624483.	−2.59896
$143$	96830.1	0.395977
$144$	101879.	0.409427
$145$	−144147.	−0.569357
$146$	−537904.	−2.08844
$147$	74013.4	0.282499
$148$	−679466.	−2.54984
$149$	240256.	0.886559	0.443280	−	0.896383i	$-0.353815\pi$
$149$	240256.	0.886559	0.443280	+	0.896383i	$0.353815\pi$
$150$	−55791.4	−0.202460
$151$	37997.8	0.135617	0.0678087	−	0.997698i	$-0.478399\pi$
$151$	37997.8	0.135617	0.0678087	+	0.997698i	$0.478399\pi$
$152$	283481.	0.995211
$153$	−9537.13	−0.0329374
$154$	111188.	0.377794
$155$	1544.51	0.00516369
$156$	−478057.	−1.57278
$157$	−260511.	−0.843483	−0.421742	−	0.906716i	$-0.638581\pi$
$157$	−260511.	−0.843483	−0.421742	+	0.906716i	$0.638581\pi$
$158$	−565318.	−1.80157
$159$	87331.1	0.273953
$160$	−39109.0	−0.120775
$161$	273513.	0.831597
$162$	65075.1	0.194817
$163$	−364741.	−1.07527	−0.537633	−	0.843179i	$-0.680681\pi$
$163$	−364741.	−1.07527	−0.537633	+	0.843179i	$0.680681\pi$
$164$	637159.	1.84986
$165$	27225.0	0.0778499
$166$	492809.	1.38806
$167$	70995.9	0.196989	0.0984945	−	0.995138i	$-0.468597\pi$
$167$	70995.9	0.196989	0.0984945	+	0.995138i	$0.468597\pi$
$168$	−284297.	−0.777139
$169$	269105.	0.724778
$170$	29195.6	0.0774811
$171$	67345.2	0.176123
$172$	−1.15981e6	−2.98927
$173$	295710.	0.751192	0.375596	−	0.926783i	$-0.377438\pi$
$173$	295710.	0.751192	0.375596	+	0.926783i	$0.377438\pi$
$174$	−514698.	−1.28878
$175$	57903.8	0.142926
$176$	152189.	0.370341
$177$	219613.	0.526895
$178$	−872727.	−2.06457
$179$	−567691.	−1.32428	−0.662139	−	0.749381i	$-0.730351\pi$
$179$	−567691.	−1.32428	−0.662139	+	0.749381i	$0.730351\pi$
$180$	−134412.	−0.309212
$181$	−361118.	−0.819319	−0.409660	−	0.912239i	$-0.634352\pi$
$181$	−361118.	−0.819319	−0.409660	+	0.912239i	$0.634352\pi$
$182$	735355.	1.64558
$183$	−305192.	−0.673668
$184$	1.00659e6	2.19184
$185$	255915.	0.549751
$186$	5514.90	0.0116884
$187$	−14246.8	−0.0297930
$188$	1.24444e6	2.56791
$189$	−67539.0	−0.137531
$190$	−206161.	−0.414307
$191$	334871.	0.664193	0.332096	−	0.943245i	$-0.392244\pi$
$191$	334871.	0.664193	0.332096	+	0.943245i	$0.392244\pi$
$192$	222590.	0.435765
$193$	−286645.	−0.553926	−0.276963	−	0.960881i	$-0.589328\pi$
$193$	−286645.	−0.553926	−0.276963	+	0.960881i	$0.589328\pi$
$194$	−444525.	−0.847992
$195$	180056.	0.339095
$196$	−545858.	−1.01494
$197$	402554.	0.739024	0.369512	−	0.929226i	$-0.379525\pi$
$197$	402554.	0.739024	0.369512	+	0.929226i	$0.379525\pi$
$198$	97211.0	0.176219
$199$	506857.	0.907304	0.453652	−	0.891179i	$-0.350121\pi$
$199$	506857.	0.907304	0.453652	+	0.891179i	$0.350121\pi$
$200$	213100.	0.376710
$201$	44903.2	0.0783948
$202$	821961.	1.41734
$203$	534185.	0.909812
$204$	70337.6	0.118335
$205$	−239980.	−0.398833
$206$	1.52444e6	2.50289
$207$	239131.	0.387891
$208$	1.00652e6	1.61311
$209$	100602.	0.159309
$210$	206754.	0.323524
$211$	166764.	0.257867	0.128934	−	0.991653i	$-0.458845\pi$
$211$	166764.	0.257867	0.128934	+	0.991653i	$0.458845\pi$
$212$	−644078.	−0.984235
$213$	566655.	0.855794
$214$	413227.	0.616813
$215$	436831.	0.644492
$216$	−248559.	−0.362490
$217$	−5723.70	−0.00825140
$218$	394209.	0.561805
$219$	488093.	0.687689
$220$	−200788.	−0.279693
$221$	−94223.2	−0.129771
$222$	913782.	1.24440
$223$	556053.	0.748780	0.374390	−	0.927271i	$-0.377852\pi$
$223$	556053.	0.748780	0.374390	+	0.927271i	$0.377852\pi$
$224$	144932.	0.192994
$225$	50625.0	0.0666667
$226$	−1.89598e6	−2.46924
$227$	507849.	0.654139	0.327069	−	0.945000i	$-0.393939\pi$
$227$	507849.	0.654139	0.327069	+	0.945000i	$0.393939\pi$
$228$	−496679.	−0.632760
$229$	−627193.	−0.790337	−0.395169	−	0.918609i	$-0.629314\pi$
$229$	−627193.	−0.790337	−0.395169	+	0.918609i	$0.629314\pi$
$230$	−732042.	−0.912465
$231$	−100892.	−0.124401
$232$	1.96593e6	2.39799
$233$	955870.	1.15348	0.576738	−	0.816929i	$-0.304325\pi$
$233$	955870.	1.15348	0.576738	+	0.816929i	$0.304325\pi$
$234$	642917.	0.767565
$235$	−468707.	−0.553646
$236$	−1.61967e6	−1.89298
$237$	512968.	0.593225
$238$	−108194.	−0.123812
$239$	−509255.	−0.576687	−0.288344	−	0.957527i	$-0.593105\pi$
$239$	−509255.	−0.576687	−0.288344	+	0.957527i	$0.593105\pi$
$240$	282996.	0.317141
$241$	−666125.	−0.738776	−0.369388	−	0.929275i	$-0.620433\pi$
$241$	−666125.	−0.738776	−0.369388	+	0.929275i	$0.620433\pi$
$242$	145216.	0.159396
$243$	−59049.0	−0.0641500
$244$	2.25083e6	2.42030
$245$	205593.	0.218823
$246$	−856886.	−0.902787
$247$	665344.	0.693911
$248$	−21064.6	−0.0217482
$249$	−447173.	−0.457065
$250$	−154976.	−0.156825
$251$	505010.	0.505960	0.252980	−	0.967472i	$-0.418589\pi$
$251$	505010.	0.505960	0.252980	+	0.967472i	$0.418589\pi$
$252$	498109.	0.494109
$253$	357220.	0.350861
$254$	−2.11144e6	−2.05349
$255$	−26492.0	−0.0255132
$256$	−2.13815e6	−2.03909
$257$	−2.02669e6	−1.91405	−0.957027	−	0.290000i	$-0.906345\pi$
$257$	−2.02669e6	−1.91405	−0.957027	+	0.290000i	$0.906345\pi$
$258$	1.55977e6	1.45885
$259$	−948379.	−0.878482
$260$	−1.32794e6	−1.21827
$261$	467035.	0.424374
$262$	−1.45397e6	−1.30859
$263$	1.57349e6	1.40273	0.701366	−	0.712801i	$-0.252574\pi$
$263$	1.57349e6	1.40273	0.701366	+	0.712801i	$0.252574\pi$
$264$	−371305.	−0.327884
$265$	242586.	0.212203
$266$	764000.	0.662048
$267$	791911.	0.679826
$268$	−331167.	−0.281650
$269$	−1.55958e6	−1.31409	−0.657046	−	0.753850i	$-0.728194\pi$
$269$	−1.55958e6	−1.31409	−0.657046	+	0.753850i	$0.728194\pi$
$270$	180764.	0.150905
$271$	1.35274e6	1.11890	0.559451	−	0.828864i	$-0.311012\pi$
$271$	1.35274e6	1.11890	0.559451	+	0.828864i	$0.311012\pi$
$272$	−148092.	−0.121369
$273$	−667259.	−0.541861
$274$	3.32343e6	2.67430
$275$	75625.0	0.0603023
$276$	−1.76362e6	−1.39358
$277$	2.47205e6	1.93579	0.967895	−	0.251353i	$-0.0808755\pi$
$277$	2.47205e6	1.93579	0.967895	+	0.251353i	$0.0808755\pi$
$278$	298086.	0.231328
$279$	−5004.20	−0.00384879
$280$	−789714.	−0.601970
$281$	769611.	0.581441	0.290721	−	0.956808i	$-0.406105\pi$
$281$	769611.	0.581441	0.290721	+	0.956808i	$0.406105\pi$
$282$	−1.67359e6	−1.25322
$283$	2.52887e6	1.87698	0.938490	−	0.345305i	$-0.112225\pi$
$283$	2.52887e6	1.87698	0.938490	+	0.345305i	$0.112225\pi$
$284$	−4.17915e6	−3.07463
$285$	187070.	0.136424
$286$	960407.	0.694289
$287$	889329.	0.637320
$288$	126713.	0.0900204
$289$	−1.40599e6	−0.990236
$290$	−1.42972e6	−0.998285
$291$	403361.	0.279229
$292$	−3.59975e6	−2.47067
$293$	2.06542e6	1.40553	0.702764	−	0.711423i	$-0.251949\pi$
$293$	2.06542e6	1.40553	0.702764	+	0.711423i	$0.251949\pi$
$294$	734100.	0.495321
$295$	610035.	0.408131
$296$	−3.49026e6	−2.31541
$297$	−88209.0	−0.0580259
$298$	2.38297e6	1.55445
$299$	2.36252e6	1.52826
$300$	−373366.	−0.239514
$301$	−1.61883e6	−1.02987
$302$	376880.	0.237786
$303$	−745845.	−0.466704
$304$	1.04573e6	0.648986
$305$	−847756.	−0.521821
$306$	−94593.9	−0.0577510
$307$	−2.17085e6	−1.31457	−0.657286	−	0.753641i	$-0.728296\pi$
$307$	−2.17085e6	−1.31457	−0.657286	+	0.753641i	$0.728296\pi$
$308$	744088.	0.446939
$309$	−1.38327e6	−0.824161
$310$	15319.2	0.00905379
$311$	−198576.	−0.116420	−0.0582098	−	0.998304i	$-0.518539\pi$
$311$	−198576.	−0.116420	−0.0582098	+	0.998304i	$0.518539\pi$
$312$	−2.45567e6	−1.42818
$313$	−483762.	−0.279107	−0.139554	−	0.990215i	$-0.544567\pi$
$313$	−483762.	−0.279107	−0.139554	+	0.990215i	$0.544567\pi$
$314$	−2.58387e6	−1.47893
$315$	−187608.	−0.106531
$316$	−3.78321e6	−2.13129
$317$	−1.68099e6	−0.939542	−0.469771	−	0.882788i	$-0.655664\pi$
$317$	−1.68099e6	−0.939542	−0.469771	+	0.882788i	$0.655664\pi$
$318$	866191.	0.480337
$319$	697670.	0.383860
$320$	618306.	0.337542
$321$	−374961.	−0.203106
$322$	2.71283e6	1.45809
$323$	−97893.6	−0.0522093
$324$	435494.	0.230473
$325$	500155.	0.262662
$326$	−3.61768e6	−1.88532
$327$	−357705.	−0.184993
$328$	3.27294e6	1.67979
$329$	1.73696e6	0.884706
$330$	270031.	0.136499
$331$	−1.18881e6	−0.596407	−0.298204	−	0.954502i	$-0.596387\pi$
$331$	−1.18881e6	−0.596407	−0.298204	+	0.954502i	$0.596387\pi$
$332$	3.29796e6	1.64210
$333$	−829164.	−0.409760
$334$	704171.	0.345392
$335$	124731.	0.0607243
$336$	−1.04874e6	−0.506779
$337$	1.78561e6	0.856470	0.428235	−	0.903667i	$-0.359135\pi$
$337$	1.78561e6	0.856470	0.428235	+	0.903667i	$0.359135\pi$
$338$	2.66911e6	1.27079
$339$	1.72041e6	0.813079
$340$	195382.	0.0916617
$341$	−7475.41	−0.00348136
$342$	667961.	0.308806
$343$	−2.31900e6	−1.06430
$344$	−5.95766e6	−2.71444
$345$	664253.	0.300459
$346$	2.93299e6	1.31711
$347$	2.71689e6	1.21129	0.605645	−	0.795735i	$-0.292915\pi$
$347$	2.71689e6	1.21129	0.605645	+	0.795735i	$0.292915\pi$
$348$	−3.44445e6	−1.52465
$349$	−1.87050e6	−0.822044	−0.411022	−	0.911626i	$-0.634828\pi$
$349$	−1.87050e6	−0.822044	−0.411022	+	0.911626i	$0.634828\pi$
$350$	574317.	0.250600
$351$	−583381.	−0.252746
$352$	189288.	0.0814265
$353$	−4.27952e6	−1.82793	−0.913963	−	0.405798i	$-0.866994\pi$
$353$	−4.27952e6	−1.82793	−0.913963	+	0.405798i	$0.866994\pi$
$354$	2.17822e6	0.923835
$355$	1.57404e6	0.662896
$356$	−5.84045e6	−2.44242
$357$	98175.3	0.0407692
$358$	−5.63063e6	−2.32193
$359$	−1.39681e6	−0.572007	−0.286003	−	0.958229i	$-0.592327\pi$
$359$	−1.39681e6	−0.572007	−0.286003	+	0.958229i	$0.592327\pi$
$360$	−690443.	−0.280783
$361$	−1.78484e6	−0.720826
$362$	−3.58174e6	−1.43656
$363$	−131769.	−0.0524864
$364$	4.92112e6	1.94675
$365$	1.35581e6	0.532681
$366$	−3.02704e6	−1.18118
$367$	−5.05674e6	−1.95977	−0.979885	−	0.199561i	$-0.936049\pi$
$367$	−5.05674e6	−1.95977	−0.979885	+	0.199561i	$0.936049\pi$
$368$	3.71320e6	1.42932
$369$	777536.	0.297273
$370$	2.53828e6	0.963909
$371$	−898987.	−0.339093
$372$	36906.6	0.0138276
$373$	−4.68117e6	−1.74214	−0.871069	−	0.491161i	$-0.836573\pi$
$373$	−4.68117e6	−1.74214	−0.871069	+	0.491161i	$0.836573\pi$
$374$	−141307.	−0.0522377
$375$	140625.	0.0516398
$376$	6.39241e6	2.33182
$377$	4.61413e6	1.67200
$378$	−669884.	−0.241140
$379$	−3.76641e6	−1.34688	−0.673442	−	0.739240i	$-0.735185\pi$
$379$	−3.76641e6	−1.34688	−0.673442	+	0.739240i	$0.735185\pi$
$380$	−1.37966e6	−0.490134
$381$	1.91591e6	0.676181
$382$	3.32141e6	1.16457
$383$	4.17276e6	1.45354	0.726770	−	0.686881i	$-0.241021\pi$
$383$	4.17276e6	1.45354	0.726770	+	0.686881i	$0.241021\pi$
$384$	2.65829e6	0.919972
$385$	−280254.	−0.0963608
$386$	−2.84308e6	−0.971228
$387$	−1.41533e6	−0.480376
$388$	−2.97484e6	−1.00319
$389$	−3.73222e6	−1.25053	−0.625265	−	0.780413i	$-0.715009\pi$
$389$	−3.73222e6	−1.25053	−0.625265	+	0.780413i	$0.715009\pi$
$390$	1.78588e6	0.594553
$391$	−347603.	−0.114985
$392$	−2.80395e6	−0.921627
$393$	1.31933e6	0.430896
$394$	3.99272e6	1.29577
$395$	1.42491e6	0.459510
$396$	650553.	0.208471
$397$	5.71418e6	1.81961	0.909804	−	0.415038i	$-0.136232\pi$
$397$	5.71418e6	1.81961	0.909804	+	0.415038i	$0.136232\pi$
$398$	5.02725e6	1.59083
$399$	−693251.	−0.218001
$400$	786100.	0.245656
$401$	3.60785e6	1.12044	0.560219	−	0.828345i	$-0.310717\pi$
$401$	3.60785e6	1.12044	0.560219	+	0.828345i	$0.310717\pi$
$402$	445371.	0.137454
$403$	−49439.6	−0.0151639
$404$	5.50070e6	1.67674
$405$	−164025.	−0.0496904
$406$	5.29830e6	1.59522
$407$	−1.23863e6	−0.370642
$408$	361308.	0.107455
$409$	−4.59452e6	−1.35810	−0.679050	−	0.734092i	$-0.737608\pi$
$409$	−4.59452e6	−1.35810	−0.679050	+	0.734092i	$0.737608\pi$
$410$	−2.38024e6	−0.699296
$411$	−3.01567e6	−0.880601
$412$	1.02018e7	2.96098
$413$	−2.26069e6	−0.652179
$414$	2.37181e6	0.680111
$415$	−1.24215e6	−0.354041
$416$	1.25188e6	0.354673
$417$	−270482.	−0.0761725
$418$	997819.	0.279326
$419$	1.92383e6	0.535343	0.267671	−	0.963510i	$-0.413746\pi$
$419$	1.92383e6	0.535343	0.267671	+	0.963510i	$0.413746\pi$
$420$	1.38364e6	0.382735
$421$	−4.28936e6	−1.17947	−0.589736	−	0.807596i	$-0.700768\pi$
$421$	−4.28936e6	−1.17947	−0.589736	+	0.807596i	$0.700768\pi$
$422$	1.65404e6	0.452133
$423$	1.51861e6	0.412663
$424$	−3.30848e6	−0.893746
$425$	−73589.0	−0.0197624
$426$	5.62035e6	1.50051
$427$	3.14165e6	0.833851
$428$	2.76538e6	0.729703
$429$	−871471.	−0.228618
$430$	4.33270e6	1.13002
$431$	477444.	0.123802	0.0619012	−	0.998082i	$-0.480284\pi$
$431$	477444.	0.123802	0.0619012	+	0.998082i	$0.480284\pi$
$432$	−916907.	−0.236383
$433$	−6.24919e6	−1.60178	−0.800892	−	0.598808i	$-0.795641\pi$
$433$	−6.24919e6	−1.60178	−0.800892	+	0.598808i	$0.795641\pi$
$434$	−56770.4	−0.0144676
$435$	1.29732e6	0.328718
$436$	2.63812e6	0.664627
$437$	2.45455e6	0.614849
$438$	4.84113e6	1.20576
$439$	5.45632e6	1.35126	0.675629	−	0.737241i	$-0.263872\pi$
$439$	5.45632e6	1.35126	0.675629	+	0.737241i	$0.263872\pi$
$440$	−1.03140e6	−0.253978
$441$	−666120.	−0.163101
$442$	−934551.	−0.227534
$443$	−3.75783e6	−0.909762	−0.454881	−	0.890552i	$-0.650318\pi$
$443$	−3.75783e6	−0.909762	−0.454881	+	0.890552i	$0.650318\pi$
$444$	6.11519e6	1.47215
$445$	2.19975e6	0.526591
$446$	5.51520e6	1.31288
$447$	−2.16230e6	−0.511855
$448$	−2.29134e6	−0.539380
$449$	−7.17310e6	−1.67916	−0.839578	−	0.543239i	$-0.817198\pi$
$449$	−7.17310e6	−1.67916	−0.839578	+	0.543239i	$0.817198\pi$
$450$	502123.	0.116890
$451$	1.16150e6	0.268893
$452$	−1.26883e7	−2.92116
$453$	−341980.	−0.0782988
$454$	5.03709e6	1.14694
$455$	−1.85350e6	−0.419724
$456$	−2.55133e6	−0.574585
$457$	−3.21240e6	−0.719513	−0.359757	−	0.933046i	$-0.617140\pi$
$457$	−3.21240e6	−0.719513	−0.359757	+	0.933046i	$0.617140\pi$
$458$	−6.22080e6	−1.38574
$459$	85834.2	0.0190164
$460$	−4.89895e6	−1.07946
$461$	−5.17808e6	−1.13479	−0.567396	−	0.823445i	$-0.692049\pi$
$461$	−5.17808e6	−1.13479	−0.567396	+	0.823445i	$0.692049\pi$
$462$	−1.00069e6	−0.218120
$463$	2.95142e6	0.639851	0.319926	−	0.947443i	$-0.396342\pi$
$463$	2.95142e6	0.639851	0.319926	+	0.947443i	$0.396342\pi$
$464$	7.25208e6	1.56375
$465$	−13900.6	−0.00298126
$466$	9.48077e6	2.02245
$467$	7.26608e6	1.54173	0.770865	−	0.636999i	$-0.219825\pi$
$467$	7.26608e6	1.54173	0.770865	+	0.636999i	$0.219825\pi$
$468$	4.30251e6	0.908045
$469$	−462234.	−0.0970352
$470$	−4.64886e6	−0.970738
$471$	2.34460e6	0.486985
$472$	−8.31989e6	−1.71895
$473$	−2.11426e6	−0.434516
$474$	5.08786e6	1.04013
$475$	519639.	0.105674
$476$	−724056.	−0.146472
$477$	−785980.	−0.158167
$478$	−5.05103e6	−1.01114
$479$	−4.09584e6	−0.815651	−0.407826	−	0.913060i	$-0.633713\pi$
$479$	−4.09584e6	−0.815651	−0.407826	+	0.913060i	$0.633713\pi$
$480$	351981.	0.0697295
$481$	−8.19181e6	−1.61442
$482$	−6.60694e6	−1.29534
$483$	−2.46162e6	−0.480123
$484$	971814.	0.188569
$485$	1.12045e6	0.216290
$486$	−585676.	−0.112478
$487$	218477.	0.0417429	0.0208715	−	0.999782i	$-0.493356\pi$
$487$	218477.	0.0417429	0.0208715	+	0.999782i	$0.493356\pi$
$488$	1.15620e7	2.19778
$489$	3.28267e6	0.620805
$490$	2.03917e6	0.383674
$491$	−3.49848e6	−0.654901	−0.327451	−	0.944868i	$-0.606190\pi$
$491$	−3.49848e6	−0.654901	−0.327451	+	0.944868i	$0.606190\pi$
$492$	−5.73443e6	−1.06802
$493$	−678887.	−0.125800
$494$	6.59920e6	1.21667
$495$	−245025.	−0.0449467
$496$	−77704.7	−0.0141822
$497$	−5.83315e6	−1.05928
$498$	−4.43528e6	−0.801397
$499$	−3.62715e6	−0.652100	−0.326050	−	0.945353i	$-0.605718\pi$
$499$	−3.62715e6	−0.652100	−0.326050	+	0.945353i	$0.605718\pi$
$500$	−1.03713e6	−0.185527
$501$	−638963.	−0.113732
$502$	5.00893e6	0.887127
$503$	6.00845e6	1.05887	0.529435	−	0.848351i	$-0.322404\pi$
$503$	6.00845e6	1.05887	0.529435	+	0.848351i	$0.322404\pi$
$504$	2.55867e6	0.448682
$505$	−2.07179e6	−0.361508
$506$	3.54308e6	0.615184
$507$	−2.42194e6	−0.418451
$508$	−1.41301e7	−2.42933
$509$	4.28786e6	0.733578	0.366789	−	0.930304i	$-0.380457\pi$
$509$	4.28786e6	0.733578	0.366789	+	0.930304i	$0.380457\pi$
$510$	−262761.	−0.0447337
$511$	−5.02443e6	−0.851205
$512$	−1.17554e7	−1.98182
$513$	−606106.	−0.101685
$514$	−2.01017e7	−3.35602
$515$	−3.84243e6	−0.638392
$516$	1.04383e7	1.72585
$517$	2.26854e6	0.373268
$518$	−9.40648e6	−1.54029
$519$	−2.66139e6	−0.433701
$520$	−6.82131e6	−1.10627
$521$	1.06243e7	1.71477	0.857386	−	0.514673i	$-0.172087\pi$
$521$	1.06243e7	1.71477	0.857386	+	0.514673i	$0.172087\pi$
$522$	4.63228e6	0.744078
$523$	123402.	0.0197273	0.00986367	−	0.999951i	$-0.496860\pi$
$523$	123402.	0.0197273	0.00986367	+	0.999951i	$0.496860\pi$
$524$	−9.73023e6	−1.54809
$525$	−521134.	−0.0825185
$526$	1.56066e7	2.45949
$527$	7274.16	0.00114092
$528$	−1.36970e6	−0.213816
$529$	2.27934e6	0.354136
$530$	2.40609e6	0.372067
$531$	−1.97651e6	−0.304203
$532$	5.11282e6	0.783216
$533$	7.68176e6	1.17123
$534$	7.85455e6	1.19198
$535$	−1.04156e6	−0.157325
$536$	−1.70113e6	−0.255756
$537$	5.10922e6	0.764573
$538$	−1.54686e7	−2.30407
$539$	−995069.	−0.147530
$540$	1.20971e6	0.178524
$541$	−5.60908e6	−0.823946	−0.411973	−	0.911196i	$-0.635160\pi$
$541$	−5.60908e6	−0.823946	−0.411973	+	0.911196i	$0.635160\pi$
$542$	1.34171e7	1.96183
$543$	3.25006e6	0.473034
$544$	−184192.	−0.0266853
$545$	−993624.	−0.143295
$546$	−6.61819e6	−0.950075
$547$	2.72729e6	0.389729	0.194864	−	0.980830i	$-0.437573\pi$
$547$	2.72729e6	0.389729	0.194864	+	0.980830i	$0.437573\pi$
$548$	2.22410e7	3.16375
$549$	2.74673e6	0.388942
$550$	750085.	0.105731
$551$	4.79387e6	0.672678
$552$	−9.05933e6	−1.26546
$553$	−5.28050e6	−0.734280
$554$	2.45190e7	3.39413
$555$	−2.30323e6	−0.317399
$556$	1.99484e6	0.273666
$557$	3.50042e6	0.478059	0.239030	−	0.971012i	$-0.423171\pi$
$557$	3.50042e6	0.478059	0.239030	+	0.971012i	$0.423171\pi$
$558$	−49634.1	−0.00674830
$559$	−1.39829e7	−1.89264
$560$	−2.91316e6	−0.392550
$561$	128221.	0.0172010
$562$	7.63337e6	1.01947
$563$	1.03320e7	1.37377	0.686886	−	0.726766i	$-0.258977\pi$
$563$	1.03320e7	1.37377	0.686886	+	0.726766i	$0.258977\pi$
$564$	−1.12000e7	−1.48258
$565$	4.77892e6	0.629809
$566$	2.50825e7	3.29101
$567$	607851.	0.0794034
$568$	−2.14674e7	−2.79195
$569$	−1.31943e7	−1.70846	−0.854229	−	0.519897i	$-0.825970\pi$
$569$	−1.31943e7	−1.70846	−0.854229	+	0.519897i	$0.825970\pi$
$570$	1.85545e6	0.239200
$571$	−5.98575e6	−0.768295	−0.384148	−	0.923272i	$-0.625505\pi$
$571$	−5.98575e6	−0.768295	−0.384148	+	0.923272i	$0.625505\pi$
$572$	6.42721e6	0.821358
$573$	−3.01384e6	−0.383472
$574$	8.82079e6	1.11745
$575$	1.84515e6	0.232735
$576$	−2.00331e6	−0.251589
$577$	7.74177e6	0.968056	0.484028	−	0.875052i	$-0.339173\pi$
$577$	7.74177e6	0.968056	0.484028	+	0.875052i	$0.339173\pi$
$578$	−1.39453e7	−1.73624
$579$	2.57981e6	0.319809
$580$	−9.56791e6	−1.18099
$581$	4.60321e6	0.565744
$582$	4.00072e6	0.489589
$583$	−1.17412e6	−0.143067
$584$	−1.84911e7	−2.24352
$585$	−1.62050e6	−0.195776
$586$	2.04858e7	2.46439
$587$	1.19577e7	1.43236	0.716181	−	0.697915i	$-0.245889\pi$
$587$	1.19577e7	1.43236	0.716181	+	0.697915i	$0.245889\pi$
$588$	4.91273e6	0.585975
$589$	−51365.5	−0.00610075
$590$	6.05062e6	0.715599
$591$	−3.62298e6	−0.426676
$592$	−1.28752e7	−1.50990
$593$	−1.08502e7	−1.26707	−0.633536	−	0.773713i	$-0.718397\pi$
$593$	−1.08502e7	−1.26707	−0.633536	+	0.773713i	$0.718397\pi$
$594$	−874899.	−0.101740
$595$	272709.	0.0315797
$596$	1.59472e7	1.83895
$597$	−4.56171e6	−0.523832
$598$	2.34326e7	2.67959
$599$	−1.23306e7	−1.40416	−0.702082	−	0.712096i	$-0.747746\pi$
$599$	−1.23306e7	−1.40416	−0.702082	+	0.712096i	$0.747746\pi$
$600$	−1.91790e6	−0.217494
$601$	1.17382e7	1.32561	0.662807	−	0.748790i	$-0.269365\pi$
$601$	1.17382e7	1.32561	0.662807	+	0.748790i	$0.269365\pi$
$602$	−1.60563e7	−1.80574
$603$	−404129.	−0.0452612
$604$	2.52215e6	0.281305
$605$	−366025.	−0.0406558
$606$	−7.39765e6	−0.818299
$607$	9.20559e6	1.01410	0.507049	−	0.861917i	$-0.330736\pi$
$607$	9.20559e6	1.01410	0.507049	+	0.861917i	$0.330736\pi$
$608$	1.30064e6	0.142692
$609$	−4.80766e6	−0.525280
$610$	−8.40845e6	−0.914938
$611$	1.50033e7	1.62586
$612$	−633039.	−0.0683206
$613$	5.83164e6	0.626815	0.313408	−	0.949619i	$-0.398529\pi$
$613$	5.83164e6	0.626815	0.313408	+	0.949619i	$0.398529\pi$
$614$	−2.15316e7	−2.30491
$615$	2.15982e6	0.230266
$616$	3.82221e6	0.405848
$617$	−9.28462e6	−0.981863	−0.490932	−	0.871198i	$-0.663344\pi$
$617$	−9.28462e6	−0.981863	−0.490932	+	0.871198i	$0.663344\pi$
$618$	−1.37200e7	−1.44505
$619$	2.47650e6	0.259784	0.129892	−	0.991528i	$-0.458537\pi$
$619$	2.47650e6	0.259784	0.129892	+	0.991528i	$0.458537\pi$
$620$	102518.	0.0107108
$621$	−2.15218e6	−0.223949
$622$	−1.96957e6	−0.204125
$623$	−8.15193e6	−0.841474
$624$	−9.05869e6	−0.931330
$625$	390625.	0.0400000
$626$	−4.79819e6	−0.489374
$627$	−905418.	−0.0919772
$628$	−1.72917e7	−1.74960
$629$	1.20528e6	0.121468
$630$	−1.86079e6	−0.186787
$631$	8.58315e6	0.858170	0.429085	−	0.903264i	$-0.358836\pi$
$631$	8.58315e6	0.858170	0.429085	+	0.903264i	$0.358836\pi$
$632$	−1.94335e7	−1.93534
$633$	−1.50087e6	−0.148880
$634$	−1.66728e7	−1.64735
$635$	5.32197e6	0.523767
$636$	5.79670e6	0.568248
$637$	−6.58101e6	−0.642605
$638$	6.91982e6	0.673044
$639$	−5.09989e6	−0.494093
$640$	7.38414e6	0.712607
$641$	4.59033e6	0.441264	0.220632	−	0.975357i	$-0.429188\pi$
$641$	4.59033e6	0.441264	0.220632	+	0.975357i	$0.429188\pi$
$642$	−3.71904e6	−0.356117
$643$	9.70391e6	0.925592	0.462796	−	0.886465i	$-0.346846\pi$
$643$	9.70391e6	0.925592	0.462796	+	0.886465i	$0.346846\pi$
$644$	1.81547e7	1.72494
$645$	−3.93148e6	−0.372097
$646$	−970955.	−0.0915415
$647$	−9.01887e6	−0.847015	−0.423508	−	0.905892i	$-0.639201\pi$
$647$	−9.01887e6	−0.847015	−0.423508	+	0.905892i	$0.639201\pi$
$648$	2.23703e6	0.209284
$649$	−2.95257e6	−0.275162
$650$	4.96078e6	0.460539
$651$	51513.3	0.00476395
$652$	−2.42101e7	−2.23038
$653$	1.94337e6	0.178349	0.0891747	−	0.996016i	$-0.471577\pi$
$653$	1.94337e6	0.178349	0.0891747	+	0.996016i	$0.471577\pi$
$654$	−3.54789e6	−0.324358
$655$	3.66481e6	0.333770
$656$	1.20735e7	1.09540
$657$	−4.39283e6	−0.397037
$658$	1.72279e7	1.55120
$659$	−6.36990e6	−0.571372	−0.285686	−	0.958323i	$-0.592221\pi$
$659$	−6.36990e6	−0.571372	−0.285686	+	0.958323i	$0.592221\pi$
$660$	1.80709e6	0.161481
$661$	−7.88417e6	−0.701863	−0.350931	−	0.936401i	$-0.614135\pi$
$661$	−7.88417e6	−0.701863	−0.350931	+	0.936401i	$0.614135\pi$
$662$	−1.17912e7	−1.04571
$663$	848009.	0.0749232
$664$	1.69409e7	1.49113
$665$	−1.92570e6	−0.168863
$666$	−8.22404e6	−0.718455
$667$	1.70222e7	1.48150
$668$	4.71244e6	0.408606
$669$	−5.00448e6	−0.432308
$670$	1.23714e6	0.106471
$671$	4.10314e6	0.351812
$672$	−1.30439e6	−0.111425
$673$	−4.51895e6	−0.384592	−0.192296	−	0.981337i	$-0.561593\pi$
$673$	−4.51895e6	−0.384592	−0.192296	+	0.981337i	$0.561593\pi$
$674$	1.77106e7	1.50170
$675$	−455625.	−0.0384900
$676$	1.78622e7	1.50337
$677$	1.17659e7	0.986624	0.493312	−	0.869852i	$-0.335786\pi$
$677$	1.17659e7	0.986624	0.493312	+	0.869852i	$0.335786\pi$
$678$	1.70639e7	1.42562
$679$	−4.15220e6	−0.345624
$680$	1.00363e6	0.0832345
$681$	−4.57064e6	−0.377667
$682$	−74144.7	−0.00610407
$683$	−1.27636e7	−1.04694	−0.523470	−	0.852044i	$-0.675363\pi$
$683$	−1.27636e7	−1.04694	−0.523470	+	0.852044i	$0.675363\pi$
$684$	4.47011e6	0.365324
$685$	−8.37686e6	−0.682111
$686$	−2.30009e7	−1.86610
$687$	5.64474e6	0.456302
$688$	−2.19771e7	−1.77011
$689$	−7.76518e6	−0.623165
$690$	6.58837e6	0.526812
$691$	1.94008e7	1.54570	0.772849	−	0.634590i	$-0.218831\pi$
$691$	1.94008e7	1.54570	0.772849	+	0.634590i	$0.218831\pi$
$692$	1.96281e7	1.55816
$693$	908024.	0.0718231
$694$	2.69474e7	2.12382
$695$	−751339.	−0.0590030
$696$	−1.76933e7	−1.38448
$697$	−1.13023e6	−0.0881225
$698$	−1.85525e7	−1.44133
$699$	−8.60283e6	−0.665960
$700$	3.84343e6	0.296465
$701$	1.81026e7	1.39138	0.695690	−	0.718342i	$-0.255099\pi$
$701$	1.81026e7	1.39138	0.695690	+	0.718342i	$0.255099\pi$
$702$	−5.78625e6	−0.443154
$703$	−8.51092e6	−0.649514
$704$	−2.99260e6	−0.227571
$705$	4.21837e6	0.319648
$706$	−4.24463e7	−3.20500
$707$	7.67773e6	0.577676
$708$	1.45771e7	1.09292
$709$	1.55411e7	1.16109	0.580547	−	0.814227i	$-0.302839\pi$
$709$	1.55411e7	1.16109	0.580547	+	0.814227i	$0.302839\pi$
$710$	1.56121e7	1.16229
$711$	−4.61671e6	−0.342499
$712$	−3.00010e7	−2.21787
$713$	−182390.	−0.0134362
$714$	973750.	0.0714828
$715$	−2.42075e6	−0.177086
$716$	−3.76812e7	−2.74689
$717$	4.58329e6	0.332951
$718$	−1.38542e7	−1.00293
$719$	8.88792e6	0.641177	0.320589	−	0.947219i	$-0.396119\pi$
$719$	8.88792e6	0.641177	0.320589	+	0.947219i	$0.396119\pi$
$720$	−2.54696e6	−0.183101
$721$	1.42394e7	1.02013
$722$	−1.77029e7	−1.26386
$723$	5.99512e6	0.426533
$724$	−2.39697e7	−1.69948
$725$	3.60367e6	0.254624
$726$	−1.30695e6	−0.0920273
$727$	−5.73697e6	−0.402575	−0.201287	−	0.979532i	$-0.564513\pi$
$727$	−5.73697e6	−0.402575	−0.201287	+	0.979532i	$0.564513\pi$
$728$	2.52787e7	1.76777
$729$	531441.	0.0370370
$730$	1.34476e7	0.933980
$731$	2.05734e6	0.142401
$732$	−2.02575e7	−1.39736
$733$	1.77002e6	0.121680	0.0608399	−	0.998148i	$-0.480622\pi$
$733$	1.77002e6	0.121680	0.0608399	+	0.998148i	$0.480622\pi$
$734$	−5.01551e7	−3.43618
$735$	−1.85033e6	−0.126337
$736$	4.61836e6	0.314263
$737$	−603698.	−0.0409403
$738$	7.71198e6	0.521224
$739$	1.53957e7	1.03702	0.518512	−	0.855070i	$-0.326486\pi$
$739$	1.53957e7	1.03702	0.518512	+	0.855070i	$0.326486\pi$
$740$	1.69866e7	1.14032
$741$	−5.98810e6	−0.400630
$742$	−8.91658e6	−0.594550
$743$	1.65861e7	1.10223	0.551115	−	0.834429i	$-0.314202\pi$
$743$	1.65861e7	1.10223	0.551115	+	0.834429i	$0.314202\pi$
$744$	189581.	0.0125563
$745$	−6.00639e6	−0.396481
$746$	−4.64301e7	−3.05459
$747$	4.02456e6	0.263886
$748$	−945650.	−0.0617983
$749$	3.85985e6	0.251400
$750$	1.39479e6	0.0905429
$751$	9.40157e6	0.608276	0.304138	−	0.952628i	$-0.401632\pi$
$751$	9.40157e6	0.608276	0.304138	+	0.952628i	$0.401632\pi$
$752$	2.35808e7	1.52060
$753$	−4.54509e6	−0.292116
$754$	4.57651e7	2.93161
$755$	−949944.	−0.0606500
$756$	−4.48298e6	−0.285274
$757$	1.22686e7	0.778134	0.389067	−	0.921209i	$-0.372797\pi$
$757$	1.22686e7	0.778134	0.389067	+	0.921209i	$0.372797\pi$
$758$	−3.73571e7	−2.36157
$759$	−3.21498e6	−0.202570
$760$	−7.08703e6	−0.445072
$761$	−2.14104e7	−1.34018	−0.670090	−	0.742280i	$-0.733744\pi$
$761$	−2.14104e7	−1.34018	−0.670090	+	0.742280i	$0.733744\pi$
$762$	1.90029e7	1.18559
$763$	3.68221e6	0.228980
$764$	2.22275e7	1.37771
$765$	238428.	0.0147301
$766$	4.13875e7	2.54857
$767$	−1.95272e7	−1.19854
$768$	1.92433e7	1.17727
$769$	8.34064e6	0.508609	0.254304	−	0.967124i	$-0.418154\pi$
$769$	8.34064e6	0.508609	0.254304	+	0.967124i	$0.418154\pi$
$770$	−2.77970e6	−0.168955
$771$	1.82402e7	1.10508
$772$	−1.90264e7	−1.14898
$773$	3.00417e7	1.80832	0.904162	−	0.427191i	$-0.140497\pi$
$773$	3.00417e7	1.80832	0.904162	+	0.427191i	$0.140497\pi$
$774$	−1.40379e7	−0.842269
$775$	−38612.7	−0.00230927
$776$	−1.52811e7	−0.910960
$777$	8.53541e6	0.507192
$778$	−3.70180e7	−2.19262
$779$	7.98099e6	0.471209
$780$	1.19514e7	0.703369
$781$	−7.61836e6	−0.446924
$782$	−3.44769e6	−0.201610
$783$	−4.20332e6	−0.245012
$784$	−1.03434e7	−0.601001
$785$	6.51277e6	0.377217
$786$	1.30857e7	0.755513
$787$	−1.55411e7	−0.894427	−0.447213	−	0.894427i	$-0.647584\pi$
$787$	−1.55411e7	−0.894427	−0.447213	+	0.894427i	$0.647584\pi$
$788$	2.67200e7	1.53292
$789$	−1.41614e7	−0.809868
$790$	1.41329e7	0.805684
$791$	−1.77099e7	−1.00641
$792$	3.34174e6	0.189304
$793$	2.71366e7	1.53240
$794$	5.66760e7	3.19042
$795$	−2.18328e6	−0.122515
$796$	3.36432e7	1.88198
$797$	−2.13571e7	−1.19096	−0.595478	−	0.803371i	$-0.703037\pi$
$797$	−2.13571e7	−1.19096	−0.595478	+	0.803371i	$0.703037\pi$
$798$	−6.87600e6	−0.382233
$799$	−2.20747e6	−0.122328
$800$	977726.	0.0540122
$801$	−7.12720e6	−0.392498
$802$	3.57844e7	1.96453
$803$	−6.56213e6	−0.359134
$804$	2.98050e6	0.162611
$805$	−6.83782e6	−0.371902
$806$	−490365.	−0.0265878
$807$	1.40362e7	0.758692
$808$	2.82559e7	1.52258
$809$	9.58699e6	0.515004	0.257502	−	0.966278i	$-0.417101\pi$
$809$	9.58699e6	0.515004	0.257502	+	0.966278i	$0.417101\pi$
$810$	−1.62688e6	−0.0871249
$811$	2.27762e6	0.121599	0.0607995	−	0.998150i	$-0.480635\pi$
$811$	2.27762e6	0.121599	0.0607995	+	0.998150i	$0.480635\pi$
$812$	3.54572e7	1.88718
$813$	−1.21747e7	−0.645998
$814$	−1.22853e7	−0.649867
$815$	9.11853e6	0.480874
$816$	1.33282e6	0.0700725
$817$	−1.45276e7	−0.761447
$818$	−4.55706e7	−2.38123
$819$	6.00533e6	0.312844
$820$	−1.59290e7	−0.827282
$821$	2.31851e7	1.20047	0.600234	−	0.799824i	$-0.295074\pi$
$821$	2.31851e7	1.20047	0.600234	+	0.799824i	$0.295074\pi$
$822$	−2.99109e7	−1.54401
$823$	3.30629e7	1.70153	0.850767	−	0.525542i	$-0.176138\pi$
$823$	3.30629e7	1.70153	0.850767	+	0.525542i	$0.176138\pi$
$824$	5.24045e7	2.68875
$825$	−680625.	−0.0348155
$826$	−2.24226e7	−1.14350
$827$	2.84571e7	1.44686	0.723431	−	0.690396i	$-0.242564\pi$
$827$	2.84571e7	1.44686	0.723431	+	0.690396i	$0.242564\pi$
$828$	1.58726e7	0.804585
$829$	−3.34334e7	−1.68964	−0.844821	−	0.535050i	$-0.820293\pi$
$829$	−3.34334e7	−1.68964	−0.844821	+	0.535050i	$0.820293\pi$
$830$	−1.23202e7	−0.620759
$831$	−2.22485e7	−1.11763
$832$	−1.97919e7	−0.991243
$833$	968279.	0.0483491
$834$	−2.68277e6	−0.133558
$835$	−1.77490e6	−0.0880962
$836$	6.67758e6	0.330448
$837$	45037.8	0.00222210
$838$	1.90815e7	0.938646
$839$	−1.79019e7	−0.877999	−0.438999	−	0.898487i	$-0.644667\pi$
$839$	−1.79019e7	−0.877999	−0.438999	+	0.898487i	$0.644667\pi$
$840$	7.10742e6	0.347547
$841$	1.27341e7	0.620837
$842$	−4.25440e7	−2.06803
$843$	−6.92650e6	−0.335695
$844$	1.10691e7	0.534882
$845$	−6.72762e6	−0.324130
$846$	1.50623e7	0.723545
$847$	1.35643e6	0.0649665
$848$	−1.22046e7	−0.582820
$849$	−2.27598e7	−1.08368
$850$	−729891.	−0.0346506
$851$	−3.02208e7	−1.43048
$852$	3.76124e7	1.77514
$853$	−2.79631e7	−1.31587	−0.657934	−	0.753076i	$-0.728569\pi$
$853$	−2.79631e7	−1.31587	−0.657934	+	0.753076i	$0.728569\pi$
$854$	3.11604e7	1.46204
$855$	−1.68363e6	−0.0787646
$856$	1.42052e7	0.662615
$857$	9.24668e6	0.430065	0.215032	−	0.976607i	$-0.431014\pi$
$857$	9.24668e6	0.430065	0.215032	+	0.976607i	$0.431014\pi$
$858$	−8.64366e6	−0.400848
$859$	1.46860e7	0.679081	0.339540	−	0.940591i	$-0.389728\pi$
$859$	1.46860e7	0.679081	0.339540	+	0.940591i	$0.389728\pi$
$860$	2.89952e7	1.33684
$861$	−8.00396e6	−0.367957
$862$	4.73551e6	0.217070
$863$	1.14915e7	0.525231	0.262615	−	0.964901i	$-0.415415\pi$
$863$	1.14915e7	0.525231	0.262615	+	0.964901i	$0.415415\pi$
$864$	−1.14042e6	−0.0519733
$865$	−7.39275e6	−0.335943
$866$	−6.19825e7	−2.80850
$867$	1.26539e7	0.571713
$868$	−379917.	−0.0171155
$869$	−6.89657e6	−0.309802
$870$	1.28674e7	0.576360
$871$	−3.99263e6	−0.178326
$872$	1.35514e7	0.603523
$873$	−3.63025e6	−0.161213
$874$	2.43454e7	1.07805
$875$	−1.44759e6	−0.0639185
$876$	3.23977e7	1.42644
$877$	2.92652e7	1.28485	0.642426	−	0.766348i	$-0.277928\pi$
$877$	2.92652e7	1.28485	0.642426	+	0.766348i	$0.277928\pi$
$878$	5.41184e7	2.36924
$879$	−1.85888e7	−0.811481
$880$	−3.80472e6	−0.165621
$881$	−6.92950e6	−0.300789	−0.150395	−	0.988626i	$-0.548054\pi$
$881$	−6.92950e6	−0.300789	−0.150395	+	0.988626i	$0.548054\pi$
$882$	−6.60690e6	−0.285974
$883$	4.40887e7	1.90294	0.951470	−	0.307740i	$-0.0995727\pi$
$883$	4.40887e7	1.90294	0.951470	+	0.307740i	$0.0995727\pi$
$884$	−6.25418e6	−0.269178
$885$	−5.49032e6	−0.235635
$886$	−3.72719e7	−1.59514
$887$	4.26047e7	1.81823	0.909115	−	0.416545i	$-0.136759\pi$
$887$	4.26047e7	1.81823	0.909115	+	0.416545i	$0.136759\pi$
$888$	3.14123e7	1.33680
$889$	−1.97224e7	−0.836961
$890$	2.18182e7	0.923302
$891$	793881.	0.0335013
$892$	3.69087e7	1.55316
$893$	1.55877e7	0.654115
$894$	−2.14467e7	−0.897464
$895$	1.41923e7	0.592236
$896$	−2.73645e7	−1.13872
$897$	−2.12627e7	−0.882342
$898$	−7.11462e7	−2.94416
$899$	−356217.	−0.0146999
$900$	3.36029e6	0.138284
$901$	1.14251e6	0.0468864
$902$	1.15204e7	0.471465
$903$	1.45694e7	0.594598
$904$	−6.51767e7	−2.65260
$905$	9.02796e6	0.366411
$906$	−3.39192e6	−0.137286
$907$	2.03750e7	0.822392	0.411196	−	0.911547i	$-0.365111\pi$
$907$	2.03750e7	0.822392	0.411196	+	0.911547i	$0.365111\pi$
$908$	3.37091e7	1.35685
$909$	6.71260e6	0.269452
$910$	−1.83839e7	−0.735925
$911$	1.25015e7	0.499077	0.249538	−	0.968365i	$-0.419721\pi$
$911$	1.25015e7	0.499077	0.249538	+	0.968365i	$0.419721\pi$
$912$	−9.41156e6	−0.374692
$913$	6.01200e6	0.238694
$914$	−3.18621e7	−1.26156
$915$	7.62981e6	0.301273
$916$	−4.16307e7	−1.63936
$917$	−1.35812e7	−0.533353
$918$	851345.	0.0333425
$919$	2.12364e7	0.829455	0.414728	−	0.909946i	$-0.363877\pi$
$919$	2.12364e7	0.829455	0.414728	+	0.909946i	$0.363877\pi$
$920$	−2.51648e7	−0.980221
$921$	1.95377e7	0.758969
$922$	−5.13586e7	−1.98969
$923$	−5.03850e7	−1.94669
$924$	−6.69680e6	−0.258040
$925$	−6.39787e6	−0.245856
$926$	2.92736e7	1.12189
$927$	1.24495e7	0.475829
$928$	9.01990e6	0.343821
$929$	2.38747e7	0.907608	0.453804	−	0.891102i	$-0.350067\pi$
$929$	2.38747e7	0.907608	0.453804	+	0.891102i	$0.350067\pi$
$930$	−137872.	−0.00522721
$931$	−6.83737e6	−0.258532
$932$	6.34470e7	2.39261
$933$	1.78719e6	0.0672149
$934$	7.20685e7	2.70320
$935$	356171.	0.0133238
$936$	2.21010e7	0.824561
$937$	−1.33814e7	−0.497914	−0.248957	−	0.968515i	$-0.580088\pi$
$937$	−1.33814e7	−0.497914	−0.248957	+	0.968515i	$0.580088\pi$
$938$	−4.58465e6	−0.170137
$939$	4.35386e6	0.161143
$940$	−3.11110e7	−1.14840
$941$	5.91644e6	0.217814	0.108907	−	0.994052i	$-0.465265\pi$
$941$	5.91644e6	0.217814	0.108907	+	0.994052i	$0.465265\pi$
$942$	2.32548e7	0.853858
$943$	2.83391e7	1.03778
$944$	−3.06911e7	−1.12094
$945$	1.68847e6	0.0615056
$946$	−2.09703e7	−0.761861
$947$	−4.78035e7	−1.73215	−0.866074	−	0.499916i	$-0.833364\pi$
$947$	−4.78035e7	−1.73215	−0.866074	+	0.499916i	$0.833364\pi$
$948$	3.40489e7	1.23050
$949$	−4.33995e7	−1.56430
$950$	5.15402e6	0.185284
$951$	1.51289e7	0.542445
$952$	−3.71931e6	−0.133006
$953$	−3.75680e7	−1.33994	−0.669971	−	0.742387i	$-0.733694\pi$
$953$	−3.75680e7	−1.33994	−0.669971	+	0.742387i	$0.733694\pi$
$954$	−7.79572e6	−0.277323
$955$	−8.37177e6	−0.297036
$956$	−3.38024e7	−1.19620
$957$	−6.27903e6	−0.221622
$958$	−4.06245e7	−1.43013
$959$	3.10433e7	1.08999
$960$	−5.56475e6	−0.194880
$961$	−2.86253e7	−0.999867
$962$	−8.12503e7	−2.83066
$963$	3.37465e6	0.117263
$964$	−4.42148e7	−1.53241
$965$	7.16613e6	0.247723
$966$	−2.44155e7	−0.841826
$967$	−2.07684e7	−0.714228	−0.357114	−	0.934061i	$-0.616239\pi$
$967$	−2.07684e7	−0.714228	−0.357114	+	0.934061i	$0.616239\pi$
$968$	4.99199e6	0.171232
$969$	881042.	0.0301431
$970$	1.11131e7	0.379234
$971$	1.39451e7	0.474650	0.237325	−	0.971430i	$-0.423729\pi$
$971$	1.39451e7	0.474650	0.237325	+	0.971430i	$0.423729\pi$
$972$	−3.91945e6	−0.133064
$973$	2.78434e6	0.0942846
$974$	2.16696e6	0.0731902
$975$	−4.50140e6	−0.151648
$976$	4.26510e7	1.43319
$977$	2.07797e7	0.696471	0.348236	−	0.937407i	$-0.386781\pi$
$977$	2.07797e7	0.696471	0.348236	+	0.937407i	$0.386781\pi$
$978$	3.25591e7	1.08849
$979$	−1.06468e7	−0.355028
$980$	1.36465e7	0.453894
$981$	3.21934e6	0.106806
$982$	−3.46996e7	−1.14828
$983$	1.16598e7	0.384864	0.192432	−	0.981310i	$-0.438363\pi$
$983$	1.16598e7	0.384864	0.192432	+	0.981310i	$0.438363\pi$
$984$	−2.94565e7	−0.969824
$985$	−1.00638e7	−0.330501
$986$	−6.73353e6	−0.220572
$987$	−1.56326e7	−0.510785
$988$	4.41630e7	1.43935
$989$	−5.15851e7	−1.67700
$990$	−2.43027e6	−0.0788075
$991$	−2.35287e7	−0.761050	−0.380525	−	0.924771i	$-0.624257\pi$
$991$	−2.35287e7	−0.761050	−0.380525	+	0.924771i	$0.624257\pi$
$992$	−96646.7	−0.00311823
$993$	1.06993e7	0.344336
$994$	−5.78559e7	−1.85730
$995$	−1.26714e7	−0.405759
$996$	−2.96817e7	−0.948069
$997$	−4.85989e7	−1.54842	−0.774210	−	0.632929i	$-0.781853\pi$
$997$	−4.85989e7	−1.54842	−0.774210	+	0.632929i	$0.781853\pi$
$998$	−3.59758e7	−1.14336
$999$	7.46247e6	0.236575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.e.1.3	✓	3
3.2	odd	2		495.6.a.a.1.1		3
5.4	even	2		825.6.a.f.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.e.1.3	✓	3	1.1	even	1	trivial
495.6.a.a.1.1		3	3.2	odd	2
825.6.a.f.1.1		3	5.4	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q+9.91848 q^{2} -9.00000 q^{3} +66.3762 q^{4} -25.0000 q^{5} -89.2663 q^{6} +92.6461 q^{7} +340.959 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.91848 q^{2} -9.00000 q^{3} +66.3762 q^{4} -25.0000 q^{5} -89.2663 q^{6} +92.6461 q^{7} +340.959 q^{8} +81.0000 q^{9} -247.962 q^{10} +121.000 q^{11} -597.386 q^{12} +800.249 q^{13} +918.908 q^{14} +225.000 q^{15} +1257.76 q^{16} -117.742 q^{17} +803.397 q^{18} +831.422 q^{19} -1659.40 q^{20} -833.814 q^{21} +1200.14 q^{22} +2952.23 q^{23} -3068.63 q^{24} +625.000 q^{25} +7937.25 q^{26} -729.000 q^{27} +6149.49 q^{28} +5765.87 q^{29} +2231.66 q^{30} -61.7803 q^{31} +1564.36 q^{32} -1089.00 q^{33} -1167.83 q^{34} -2316.15 q^{35} +5376.47 q^{36} -10236.6 q^{37} +8246.44 q^{38} -7202.24 q^{39} -8523.98 q^{40} +9599.21 q^{41} -8270.17 q^{42} -17473.2 q^{43} +8031.52 q^{44} -2025.00 q^{45} +29281.7 q^{46} +18748.3 q^{47} -11319.8 q^{48} -8223.71 q^{49} +6199.05 q^{50} +1059.68 q^{51} +53117.5 q^{52} -9703.45 q^{53} -7230.57 q^{54} -3025.00 q^{55} +31588.5 q^{56} -7482.79 q^{57} +57188.6 q^{58} -24401.4 q^{59} +14934.6 q^{60} +33910.3 q^{61} -612.766 q^{62} +7504.33 q^{63} -24732.2 q^{64} -20006.2 q^{65} -10801.2 q^{66} -4989.24 q^{67} -7815.29 q^{68} -26570.1 q^{69} -22972.7 q^{70} -62961.6 q^{71} +27617.7 q^{72} -54232.5 q^{73} -101531. q^{74} -5625.00 q^{75} +55186.6 q^{76} +11210.2 q^{77} -71435.2 q^{78} -56996.4 q^{79} -31444.0 q^{80} +6561.00 q^{81} +95209.6 q^{82} +49685.9 q^{83} -55345.4 q^{84} +2943.56 q^{85} -173308. q^{86} -51892.8 q^{87} +41256.1 q^{88} -87990.1 q^{89} -20084.9 q^{90} +74139.9 q^{91} +195958. q^{92} +556.022 q^{93} +185954. q^{94} -20785.5 q^{95} -14079.3 q^{96} -44817.9 q^{97} -81566.7 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9	\( 3 q + 7 q^{2} - 27 q^{3} + 73 q^{4} - 75 q^{5} - 63 q^{6} + 92 q^{7} + 231 q^{8} + 243 q^{9} - 175 q^{10} + 363 q^{11} - 657 q^{12} - 90 q^{13} - 784 q^{14} + 675 q^{15} - 415 q^{16} + 1934 q^{17} + 567 q^{18} + 2084 q^{19} - 1825 q^{20} - 828 q^{21} + 847 q^{22} + 1220 q^{23} - 2079 q^{24} + 1875 q^{25} + 17062 q^{26} - 2187 q^{27} + 11120 q^{28} + 4402 q^{29} + 1575 q^{30} - 10688 q^{31} + 12439 q^{32} - 3267 q^{33} - 4094 q^{34} - 2300 q^{35} + 5913 q^{36} - 8190 q^{37} + 13792 q^{38} + 810 q^{39} - 5775 q^{40} + 5974 q^{41} + 7056 q^{42} + 18868 q^{43} + 8833 q^{44} - 6075 q^{45} + 46220 q^{46} + 55500 q^{47} + 3735 q^{48} + 1907 q^{49} + 4375 q^{50} - 17406 q^{51} + 27330 q^{52} + 9206 q^{53} - 5103 q^{54} - 9075 q^{55} + 73248 q^{56} - 18756 q^{57} + 15366 q^{58} - 59196 q^{59} + 16425 q^{60} + 79902 q^{61} + 64616 q^{62} + 7452 q^{63} + 2129 q^{64} + 2250 q^{65} - 7623 q^{66} + 4468 q^{67} - 1218 q^{68} - 10980 q^{69} + 19600 q^{70} - 75164 q^{71} + 18711 q^{72} - 61290 q^{73} - 56766 q^{74} - 16875 q^{75} + 37816 q^{76} + 11132 q^{77} - 153558 q^{78} - 83564 q^{79} + 10375 q^{80} + 19683 q^{81} + 147410 q^{82} + 74764 q^{83} - 100080 q^{84} - 48350 q^{85} - 253432 q^{86} - 39618 q^{87} + 27951 q^{88} + 37342 q^{89} - 14175 q^{90} - 126488 q^{91} + 148164 q^{92} + 96192 q^{93} + 59252 q^{94} - 52100 q^{95} - 111951 q^{96} + 33486 q^{97} - 95249 q^{98} + 29403 q^{99}+O(q^{100}) \) 3 * q + 7 * q^2 - 27 * q^3 + 73 * q^4 - 75 * q^5 - 63 * q^6 + 92 * q^7 + 231 * q^8 + 243 * q^9 - 175 * q^10 + 363 * q^11 - 657 * q^12 - 90 * q^13 - 784 * q^14 + 675 * q^15 - 415 * q^16 + 1934 * q^17 + 567 * q^18 + 2084 * q^19 - 1825 * q^20 - 828 * q^21 + 847 * q^22 + 1220 * q^23 - 2079 * q^24 + 1875 * q^25 + 17062 * q^26 - 2187 * q^27 + 11120 * q^28 + 4402 * q^29 + 1575 * q^30 - 10688 * q^31 + 12439 * q^32 - 3267 * q^33 - 4094 * q^34 - 2300 * q^35 + 5913 * q^36 - 8190 * q^37 + 13792 * q^38 + 810 * q^39 - 5775 * q^40 + 5974 * q^41 + 7056 * q^42 + 18868 * q^43 + 8833 * q^44 - 6075 * q^45 + 46220 * q^46 + 55500 * q^47 + 3735 * q^48 + 1907 * q^49 + 4375 * q^50 - 17406 * q^51 + 27330 * q^52 + 9206 * q^53 - 5103 * q^54 - 9075 * q^55 + 73248 * q^56 - 18756 * q^57 + 15366 * q^58 - 59196 * q^59 + 16425 * q^60 + 79902 * q^61 + 64616 * q^62 + 7452 * q^63 + 2129 * q^64 + 2250 * q^65 - 7623 * q^66 + 4468 * q^67 - 1218 * q^68 - 10980 * q^69 + 19600 * q^70 - 75164 * q^71 + 18711 * q^72 - 61290 * q^73 - 56766 * q^74 - 16875 * q^75 + 37816 * q^76 + 11132 * q^77 - 153558 * q^78 - 83564 * q^79 + 10375 * q^80 + 19683 * q^81 + 147410 * q^82 + 74764 * q^83 - 100080 * q^84 - 48350 * q^85 - 253432 * q^86 - 39618 * q^87 + 27951 * q^88 + 37342 * q^89 - 14175 * q^90 - 126488 * q^91 + 148164 * q^92 + 96192 * q^93 + 59252 * q^94 - 52100 * q^95 - 111951 * q^96 + 33486 * q^97 - 95249 * q^98 + 29403 * q^99

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