LMFDB - Embedded newform 867.6.a.l.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,6,Mod(1,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("867.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	867.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:	$139.052771778$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 217x^{6} + 561x^{5} + 14182x^{4} - 33552x^{3} - 289744x^{2} + 634992x + 110880 $ x^8 - 3x^7 - 217x^6 + 561x^5 + 14182x^4 - 33552x^3 - 289744x^2 + 634992*x + 110880
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$11.3034$ of defining polynomial
Character	$\chi$	$=$	867.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.3034 q^{2} -9.00000 q^{3} +95.7674 q^{4} -15.2351 q^{5} -101.731 q^{6} +158.615 q^{7} +720.790 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+11.3034 q^{2} -9.00000 q^{3} +95.7674 q^{4} -15.2351 q^{5} -101.731 q^{6} +158.615 q^{7} +720.790 q^{8} +81.0000 q^{9} -172.209 q^{10} +347.978 q^{11} -861.907 q^{12} +351.540 q^{13} +1792.89 q^{14} +137.116 q^{15} +5082.84 q^{16} +915.577 q^{18} +2533.59 q^{19} -1459.02 q^{20} -1427.53 q^{21} +3933.34 q^{22} -1530.29 q^{23} -6487.11 q^{24} -2892.89 q^{25} +3973.60 q^{26} -729.000 q^{27} +15190.1 q^{28} -6623.22 q^{29} +1549.88 q^{30} -2392.32 q^{31} +34388.2 q^{32} -3131.80 q^{33} -2416.51 q^{35} +7757.16 q^{36} -6303.79 q^{37} +28638.3 q^{38} -3163.86 q^{39} -10981.3 q^{40} +2579.35 q^{41} -16136.0 q^{42} -5929.08 q^{43} +33325.0 q^{44} -1234.04 q^{45} -17297.5 q^{46} -17166.4 q^{47} -45745.5 q^{48} +8351.59 q^{49} -32699.6 q^{50} +33666.0 q^{52} +21855.1 q^{53} -8240.20 q^{54} -5301.47 q^{55} +114328. q^{56} -22802.3 q^{57} -74865.1 q^{58} +19769.2 q^{59} +13131.2 q^{60} -37149.6 q^{61} -27041.5 q^{62} +12847.8 q^{63} +226054. q^{64} -5355.73 q^{65} -35400.1 q^{66} +19636.4 q^{67} +13772.6 q^{69} -27314.8 q^{70} +75915.8 q^{71} +58384.0 q^{72} +21259.0 q^{73} -71254.5 q^{74} +26036.0 q^{75} +242636. q^{76} +55194.4 q^{77} -35762.4 q^{78} +63136.7 q^{79} -77437.4 q^{80} +6561.00 q^{81} +29155.5 q^{82} -18767.4 q^{83} -136711. q^{84} -67018.9 q^{86} +59609.0 q^{87} +250819. q^{88} +18972.6 q^{89} -13948.9 q^{90} +55759.3 q^{91} -146552. q^{92} +21530.9 q^{93} -194039. q^{94} -38599.5 q^{95} -309494. q^{96} -50306.4 q^{97} +94401.6 q^{98} +28186.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - 72 q^{3} + 187 q^{4} - 27 q^{6} + 18 q^{7} + 105 q^{8} + 648 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - 72 * q^3 + 187 * q^4 - 27 * q^6 + 18 * q^7 + 105 * q^8 + 648 * q^9	\( 8 q + 3 q^{2} - 72 q^{3} + 187 q^{4} - 27 q^{6} + 18 q^{7} + 105 q^{8} + 648 q^{9} - 373 q^{10} + 966 q^{11} - 1683 q^{12} + 382 q^{13} + 2046 q^{14} + 4275 q^{16} + 243 q^{18} + 4526 q^{19} + 6315 q^{20} - 162 q^{21} + 1577 q^{22} - 240 q^{23} - 945 q^{24} + 14418 q^{25} - 13632 q^{26} - 5832 q^{27} - 2494 q^{28} - 6072 q^{29} + 3357 q^{30} - 17278 q^{31} + 28173 q^{32} - 8694 q^{33} - 7788 q^{35} + 15147 q^{36} + 4682 q^{37} + 11934 q^{38} - 3438 q^{39} - 68063 q^{40} - 15204 q^{41} - 18414 q^{42} + 7278 q^{43} + 51789 q^{44} + 18878 q^{46} + 39768 q^{47} - 38475 q^{48} + 48134 q^{49} - 44262 q^{50} + 65476 q^{52} + 18756 q^{53} - 2187 q^{54} + 15332 q^{55} + 155406 q^{56} - 40734 q^{57} - 111895 q^{58} + 80826 q^{59} - 56835 q^{60} - 9386 q^{61} - 40473 q^{62} + 1458 q^{63} + 221271 q^{64} - 53544 q^{65} - 14193 q^{66} - 21254 q^{67} + 2160 q^{69} + 34060 q^{70} + 75072 q^{71} + 8505 q^{72} + 44910 q^{73} - 394122 q^{74} - 129762 q^{75} + 297954 q^{76} + 67980 q^{77} + 122688 q^{78} + 13300 q^{79} + 178167 q^{80} + 52488 q^{81} - 52594 q^{82} + 254064 q^{83} + 22446 q^{84} - 160422 q^{86} + 54648 q^{87} + 64927 q^{88} - 56796 q^{89} - 30213 q^{90} - 406358 q^{91} - 583602 q^{92} + 155502 q^{93} - 169338 q^{94} + 98496 q^{95} - 253557 q^{96} + 25828 q^{97} - 178635 q^{98} + 78246 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 72 * q^3 + 187 * q^4 - 27 * q^6 + 18 * q^7 + 105 * q^8 + 648 * q^9 - 373 * q^10 + 966 * q^11 - 1683 * q^12 + 382 * q^13 + 2046 * q^14 + 4275 * q^16 + 243 * q^18 + 4526 * q^19 + 6315 * q^20 - 162 * q^21 + 1577 * q^22 - 240 * q^23 - 945 * q^24 + 14418 * q^25 - 13632 * q^26 - 5832 * q^27 - 2494 * q^28 - 6072 * q^29 + 3357 * q^30 - 17278 * q^31 + 28173 * q^32 - 8694 * q^33 - 7788 * q^35 + 15147 * q^36 + 4682 * q^37 + 11934 * q^38 - 3438 * q^39 - 68063 * q^40 - 15204 * q^41 - 18414 * q^42 + 7278 * q^43 + 51789 * q^44 + 18878 * q^46 + 39768 * q^47 - 38475 * q^48 + 48134 * q^49 - 44262 * q^50 + 65476 * q^52 + 18756 * q^53 - 2187 * q^54 + 15332 * q^55 + 155406 * q^56 - 40734 * q^57 - 111895 * q^58 + 80826 * q^59 - 56835 * q^60 - 9386 * q^61 - 40473 * q^62 + 1458 * q^63 + 221271 * q^64 - 53544 * q^65 - 14193 * q^66 - 21254 * q^67 + 2160 * q^69 + 34060 * q^70 + 75072 * q^71 + 8505 * q^72 + 44910 * q^73 - 394122 * q^74 - 129762 * q^75 + 297954 * q^76 + 67980 * q^77 + 122688 * q^78 + 13300 * q^79 + 178167 * q^80 + 52488 * q^81 - 52594 * q^82 + 254064 * q^83 + 22446 * q^84 - 160422 * q^86 + 54648 * q^87 + 64927 * q^88 - 56796 * q^89 - 30213 * q^90 - 406358 * q^91 - 583602 * q^92 + 155502 * q^93 - 169338 * q^94 + 98496 * q^95 - 253557 * q^96 + 25828 * q^97 - 178635 * q^98 + 78246 * 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 $

$2$	11.3034	1.99818	0.999091	−	0.0426287i	$-0.0135732\pi$
$2$	11.3034	1.99818	0.999091	+	0.0426287i	$0.0135732\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	95.7674	2.99273
$5$	−15.2351	−0.272533	−0.136267	−	0.990672i	$-0.543510\pi$
$5$	−15.2351	−0.272533	−0.136267	+	0.990672i	$0.543510\pi$
$6$	−101.731	−1.15365
$7$	158.615	1.22348	0.611742	−	0.791058i	$-0.290469\pi$
$7$	158.615	1.22348	0.611742	+	0.791058i	$0.290469\pi$
$8$	720.790	3.98184
$9$	81.0000	0.333333
$10$	−172.209	−0.544571
$11$	347.978	0.867102	0.433551	−	0.901129i	$-0.357260\pi$
$11$	347.978	0.867102	0.433551	+	0.901129i	$0.357260\pi$
$12$	−861.907	−1.72785
$13$	351.540	0.576920	0.288460	−	0.957492i	$-0.406857\pi$
$13$	351.540	0.576920	0.288460	+	0.957492i	$0.406857\pi$
$14$	1792.89	2.44474
$15$	137.116	0.157347
$16$	5082.84	4.96371
$17$	0	0
$17$	0	0
$18$	915.577	0.666061
$19$	2533.59	1.61010	0.805050	−	0.593207i	$-0.202138\pi$
$19$	2533.59	1.61010	0.805050	+	0.593207i	$0.202138\pi$
$20$	−1459.02	−0.815619
$21$	−1427.53	−0.706378
$22$	3933.34	1.73263
$23$	−1530.29	−0.603190	−0.301595	−	0.953436i	$-0.597519\pi$
$23$	−1530.29	−0.603190	−0.301595	+	0.953436i	$0.597519\pi$
$24$	−6487.11	−2.29892
$25$	−2892.89	−0.925726
$26$	3973.60	1.15279
$27$	−729.000	−0.192450
$28$	15190.1	3.66156
$29$	−6623.22	−1.46243	−0.731213	−	0.682149i	$-0.761046\pi$
$29$	−6623.22	−1.46243	−0.731213	+	0.682149i	$0.761046\pi$
$30$	1549.88	0.314408
$31$	−2392.32	−0.447112	−0.223556	−	0.974691i	$-0.571766\pi$
$31$	−2392.32	−0.447112	−0.223556	+	0.974691i	$0.571766\pi$
$32$	34388.2	5.93655
$33$	−3131.80	−0.500622
$34$	0	0
$35$	−2416.51	−0.333440
$36$	7757.16	0.997577
$37$	−6303.79	−0.757003	−0.378502	−	0.925601i	$-0.623561\pi$
$37$	−6303.79	−0.757003	−0.378502	+	0.925601i	$0.623561\pi$
$38$	28638.3	3.21727
$39$	−3163.86	−0.333085
$40$	−10981.3	−1.08518
$41$	2579.35	0.239635	0.119817	−	0.992796i	$-0.461769\pi$
$41$	2579.35	0.239635	0.119817	+	0.992796i	$0.461769\pi$
$42$	−16136.0	−1.41147
$43$	−5929.08	−0.489008	−0.244504	−	0.969648i	$-0.578625\pi$
$43$	−5929.08	−0.489008	−0.244504	+	0.969648i	$0.578625\pi$
$44$	33325.0	2.59500
$45$	−1234.04	−0.0908445
$46$	−17297.5	−1.20528
$47$	−17166.4	−1.13353	−0.566767	−	0.823878i	$-0.691806\pi$
$47$	−17166.4	−1.13353	−0.566767	+	0.823878i	$0.691806\pi$
$48$	−45745.5	−2.86580
$49$	8351.59	0.496911
$50$	−32699.6	−1.84977
$51$	0	0
$52$	33666.0	1.72657
$53$	21855.1	1.06872	0.534359	−	0.845258i	$-0.320553\pi$
$53$	21855.1	1.06872	0.534359	+	0.845258i	$0.320553\pi$
$54$	−8240.20	−0.384550
$55$	−5301.47	−0.236314
$56$	114328.	4.87171
$57$	−22802.3	−0.929592
$58$	−74865.1	−2.92219
$59$	19769.2	0.739367	0.369683	−	0.929158i	$-0.379466\pi$
$59$	19769.2	0.739367	0.369683	+	0.929158i	$0.379466\pi$
$60$	13131.2	0.470898
$61$	−37149.6	−1.27829	−0.639146	−	0.769085i	$-0.720712\pi$
$61$	−37149.6	−1.27829	−0.639146	+	0.769085i	$0.720712\pi$
$62$	−27041.5	−0.893410
$63$	12847.8	0.407828
$64$	226054.	6.89861
$65$	−5355.73	−0.157230
$66$	−35400.1	−1.00033
$67$	19636.4	0.534410	0.267205	−	0.963640i	$-0.413900\pi$
$67$	19636.4	0.534410	0.267205	+	0.963640i	$0.413900\pi$
$68$	0	0
$69$	13772.6	0.348252
$70$	−27314.8	−0.666274
$71$	75915.8	1.78725	0.893627	−	0.448810i	$-0.148152\pi$
$71$	75915.8	1.78725	0.893627	+	0.448810i	$0.148152\pi$
$72$	58384.0	1.32728
$73$	21259.0	0.466913	0.233456	−	0.972367i	$-0.424996\pi$
$73$	21259.0	0.466913	0.233456	+	0.972367i	$0.424996\pi$
$74$	−71254.5	−1.51263
$75$	26036.0	0.534468
$76$	242636.	4.81860
$77$	55194.4	1.06088
$78$	−35762.4	−0.665565
$79$	63136.7	1.13819	0.569094	−	0.822272i	$-0.307294\pi$
$79$	63136.7	1.13819	0.569094	+	0.822272i	$0.307294\pi$
$80$	−77437.4	−1.35278
$81$	6561.00	0.111111
$82$	29155.5	0.478834
$83$	−18767.4	−0.299026	−0.149513	−	0.988760i	$-0.547771\pi$
$83$	−18767.4	−0.299026	−0.149513	+	0.988760i	$0.547771\pi$
$84$	−136711.	−2.11400
$85$	0	0
$86$	−67018.9	−0.977127
$87$	59609.0	0.844333
$88$	250819.	3.45266
$89$	18972.6	0.253894	0.126947	−	0.991909i	$-0.459482\pi$
$89$	18972.6	0.253894	0.126947	+	0.991909i	$0.459482\pi$
$90$	−13948.9	−0.181524
$91$	55759.3	0.705852
$92$	−146552.	−1.80519
$93$	21530.9	0.258140
$94$	−194039.	−2.26501
$95$	−38599.5	−0.438806
$96$	−309494.	−3.42747
$97$	−50306.4	−0.542868	−0.271434	−	0.962457i	$-0.587498\pi$
$97$	−50306.4	−0.542868	−0.271434	+	0.962457i	$0.587498\pi$
$98$	94401.6	0.992919
$99$	28186.2	0.289034
$100$	−277045.	−2.77045
$101$	−143165.	−1.39648	−0.698240	−	0.715864i	$-0.746033\pi$
$101$	−143165.	−1.39648	−0.698240	+	0.715864i	$0.746033\pi$
$102$	0	0
$103$	−109346.	−1.01557	−0.507784	−	0.861484i	$-0.669535\pi$
$103$	−109346.	−1.01557	−0.507784	+	0.861484i	$0.669535\pi$
$104$	253386.	2.29720
$105$	21748.6	0.192512
$106$	247037.	2.13549
$107$	−25741.2	−0.217355	−0.108678	−	0.994077i	$-0.534662\pi$
$107$	−25741.2	−0.217355	−0.108678	+	0.994077i	$0.534662\pi$
$108$	−69814.4	−0.575951
$109$	−57019.6	−0.459682	−0.229841	−	0.973228i	$-0.573821\pi$
$109$	−57019.6	−0.459682	−0.229841	+	0.973228i	$0.573821\pi$
$110$	−59924.8	−0.472199
$111$	56734.1	0.437056
$112$	806212.	6.07301
$113$	141793.	1.04462	0.522310	−	0.852756i	$-0.325071\pi$
$113$	141793.	1.04462	0.522310	+	0.852756i	$0.325071\pi$
$114$	−257745.	−1.85749
$115$	23314.1	0.164390
$116$	−634288.	−4.37665
$117$	28474.7	0.192307
$118$	223460.	1.47739
$119$	0	0
$120$	98831.6	0.626531
$121$	−39962.3	−0.248134
$122$	−419918.	−2.55426
$123$	−23214.1	−0.138353
$124$	−229107.	−1.33808
$125$	91683.1	0.524825
$126$	145224.	0.814914
$127$	75210.7	0.413781	0.206891	−	0.978364i	$-0.433666\pi$
$127$	75210.7	0.413781	0.206891	+	0.978364i	$0.433666\pi$
$128$	1.45476e6	7.84812
$129$	53361.7	0.282329
$130$	−60538.1	−0.314174
$131$	214172.	1.09040	0.545199	−	0.838307i	$-0.316454\pi$
$131$	214172.	1.09040	0.545199	+	0.838307i	$0.316454\pi$
$132$	−299925.	−1.49823
$133$	401865.	1.96993
$134$	221959.	1.06785
$135$	11106.4	0.0524491
$136$	0	0
$137$	−145593.	−0.662732	−0.331366	−	0.943502i	$-0.607509\pi$
$137$	−145593.	−0.662732	−0.331366	+	0.943502i	$0.607509\pi$
$138$	155678.	0.695871
$139$	−333317.	−1.46326	−0.731629	−	0.681703i	$-0.761240\pi$
$139$	−333317.	−1.46326	−0.731629	+	0.681703i	$0.761240\pi$
$140$	−231422.	−0.997896
$141$	154498.	0.654447
$142$	858109.	3.57126
$143$	122328.	0.500249
$144$	411710.	1.65457
$145$	100905.	0.398560
$146$	240299.	0.932977
$147$	−75164.3	−0.286892
$148$	−603698.	−2.26551
$149$	−68155.5	−0.251498	−0.125749	−	0.992062i	$-0.540133\pi$
$149$	−68155.5	−0.251498	−0.125749	+	0.992062i	$0.540133\pi$
$150$	294296.	1.06796
$151$	−66390.7	−0.236954	−0.118477	−	0.992957i	$-0.537801\pi$
$151$	−66390.7	−0.236954	−0.118477	+	0.992957i	$0.537801\pi$
$152$	1.82619e6	6.41116
$153$	0	0
$154$	623886.	2.11984
$155$	36447.3	0.121853
$156$	−302994.	−0.996834
$157$	−507369.	−1.64276	−0.821382	−	0.570378i	$-0.806797\pi$
$157$	−507369.	−1.64276	−0.821382	+	0.570378i	$0.806797\pi$
$158$	713661.	2.27431
$159$	−196696.	−0.617024
$160$	−523907.	−1.61791
$161$	−242726.	−0.737993
$162$	74161.8	0.222020
$163$	387413.	1.14210	0.571051	−	0.820915i	$-0.306536\pi$
$163$	387413.	1.14210	0.571051	+	0.820915i	$0.306536\pi$
$164$	247017.	0.717163
$165$	47713.3	0.136436
$166$	−212136.	−0.597508
$167$	82664.3	0.229365	0.114682	−	0.993402i	$-0.463415\pi$
$167$	82664.3	0.229365	0.114682	+	0.993402i	$0.463415\pi$
$168$	−1.02895e6	−2.81269
$169$	−247713.	−0.667163
$170$	0	0
$171$	205221.	0.536700
$172$	−567812.	−1.46347
$173$	120594.	0.306345	0.153172	−	0.988200i	$-0.451051\pi$
$173$	120594.	0.306345	0.153172	+	0.988200i	$0.451051\pi$
$174$	673786.	1.68713
$175$	−458855.	−1.13261
$176$	1.76872e6	4.30404
$177$	−177923.	−0.426874
$178$	214456.	0.507326
$179$	89575.3	0.208956	0.104478	−	0.994527i	$-0.466683\pi$
$179$	89575.3	0.208956	0.104478	+	0.994527i	$0.466683\pi$
$180$	−118181.	−0.271873
$181$	−552636.	−1.25384	−0.626920	−	0.779083i	$-0.715685\pi$
$181$	−552636.	−1.25384	−0.626920	+	0.779083i	$0.715685\pi$
$182$	630271.	1.41042
$183$	334347.	0.738022
$184$	−1.10302e6	−2.40181
$185$	96038.8	0.206309
$186$	243373.	0.515811
$187$	0	0
$188$	−1.64398e6	−3.39236
$189$	−115630.	−0.235459
$190$	−436307.	−0.876815
$191$	318622.	0.631964	0.315982	−	0.948765i	$-0.397666\pi$
$191$	318622.	0.631964	0.315982	+	0.948765i	$0.397666\pi$
$192$	−2.03448e6	−3.98291
$193$	14075.5	0.0272001	0.0136000	−	0.999908i	$-0.495671\pi$
$193$	14075.5	0.0272001	0.0136000	+	0.999908i	$0.495671\pi$
$194$	−568635.	−1.08475
$195$	48201.6	0.0907768
$196$	799810.	1.48712
$197$	94120.1	0.172789	0.0863946	−	0.996261i	$-0.472465\pi$
$197$	94120.1	0.172789	0.0863946	+	0.996261i	$0.472465\pi$
$198$	318601.	0.577543
$199$	731840.	1.31004	0.655018	−	0.755613i	$-0.272661\pi$
$199$	731840.	1.31004	0.655018	+	0.755613i	$0.272661\pi$
$200$	−2.08517e6	−3.68609
$201$	−176728.	−0.308542
$202$	−1.61826e6	−2.79042
$203$	−1.05054e6	−1.78925
$204$	0	0
$205$	−39296.6	−0.0653085
$206$	−1.23598e6	−2.02929
$207$	−123954.	−0.201063
$208$	1.78682e6	2.86366
$209$	881635.	1.39612
$210$	245833.	0.384673
$211$	730671.	1.12984	0.564918	−	0.825147i	$-0.308908\pi$
$211$	730671.	1.12984	0.564918	+	0.825147i	$0.308908\pi$
$212$	2.09301e6	3.19838
$213$	−683242.	−1.03187
$214$	−290964.	−0.434315
$215$	90330.0	0.133271
$216$	−525456.	−0.766305
$217$	−379458.	−0.547034
$218$	−644516.	−0.918529
$219$	−191331.	−0.269572
$220$	−507708.	−0.707225
$221$	0	0
$222$	641290.	0.873317
$223$	217281.	0.292590	0.146295	−	0.989241i	$-0.453265\pi$
$223$	217281.	0.292590	0.146295	+	0.989241i	$0.453265\pi$
$224$	5.45447e6	7.26327
$225$	−234324.	−0.308575
$226$	1.60274e6	2.08734
$227$	590842.	0.761039	0.380520	−	0.924773i	$-0.375745\pi$
$227$	590842.	0.761039	0.380520	+	0.924773i	$0.375745\pi$
$228$	−2.18372e6	−2.78202
$229$	−874166.	−1.10155	−0.550776	−	0.834653i	$-0.685668\pi$
$229$	−874166.	−1.10155	−0.550776	+	0.834653i	$0.685668\pi$
$230$	263529.	0.328480
$231$	−496750.	−0.612502
$232$	−4.77395e6	−5.82315
$233$	−1.09350e6	−1.31956	−0.659781	−	0.751458i	$-0.729351\pi$
$233$	−1.09350e6	−1.31956	−0.659781	+	0.751458i	$0.729351\pi$
$234$	321862.	0.384264
$235$	261532.	0.308926
$236$	1.89325e6	2.21273
$237$	−568230.	−0.657133
$238$	0	0
$239$	−465995.	−0.527699	−0.263849	−	0.964564i	$-0.584992\pi$
$239$	−465995.	−0.527699	−0.263849	+	0.964564i	$0.584992\pi$
$240$	696937.	0.781026
$241$	−1.13812e6	−1.26225	−0.631126	−	0.775680i	$-0.717407\pi$
$241$	−1.13812e6	−1.26225	−0.631126	+	0.775680i	$0.717407\pi$
$242$	−451710.	−0.495817
$243$	−59049.0	−0.0641500
$244$	−3.55772e6	−3.82558
$245$	−127237.	−0.135425
$246$	−262399.	−0.276455
$247$	890658.	0.928900
$248$	−1.72436e6	−1.78033
$249$	168906.	0.172642
$250$	1.03633e6	1.04869
$251$	1.50267e6	1.50550	0.752748	−	0.658309i	$-0.228728\pi$
$251$	1.50267e6	1.50550	0.752748	+	0.658309i	$0.228728\pi$
$252$	1.23040e6	1.22052
$253$	−532508.	−0.523028
$254$	850139.	0.826810
$255$	0	0
$256$	9.21002e6	8.78336
$257$	−171490.	−0.161959	−0.0809796	−	0.996716i	$-0.525805\pi$
$257$	−171490.	−0.161959	−0.0809796	+	0.996716i	$0.525805\pi$
$258$	603170.	0.564145
$259$	−999874.	−0.926181
$260$	−512905.	−0.470547
$261$	−536481.	−0.487476
$262$	2.42088e6	2.17881
$263$	758588.	0.676265	0.338132	−	0.941099i	$-0.390205\pi$
$263$	758588.	0.676265	0.338132	+	0.941099i	$0.390205\pi$
$264$	−2.25737e6	−1.99339
$265$	−332964.	−0.291261
$266$	4.54245e6	3.93628
$267$	−170754.	−0.146586
$268$	1.88053e6	1.59935
$269$	622791.	0.524761	0.262380	−	0.964964i	$-0.415492\pi$
$269$	622791.	0.524761	0.262380	+	0.964964i	$0.415492\pi$
$270$	125540.	0.104803
$271$	−469858.	−0.388636	−0.194318	−	0.980939i	$-0.562249\pi$
$271$	−469858.	−0.388636	−0.194318	+	0.980939i	$0.562249\pi$
$272$	0	0
$273$	−501834.	−0.407524
$274$	−1.64569e6	−1.32426
$275$	−1.00666e6	−0.802698
$276$	1.31897e6	1.04223
$277$	−313497.	−0.245490	−0.122745	−	0.992438i	$-0.539170\pi$
$277$	−313497.	−0.245490	−0.122745	+	0.992438i	$0.539170\pi$
$278$	−3.76763e6	−2.92385
$279$	−193778.	−0.149037
$280$	−1.74179e6	−1.32770
$281$	261054.	0.197226	0.0986129	−	0.995126i	$-0.468559\pi$
$281$	261054.	0.197226	0.0986129	+	0.995126i	$0.468559\pi$
$282$	1.74635e6	1.30770
$283$	854832.	0.634476	0.317238	−	0.948346i	$-0.397245\pi$
$283$	854832.	0.634476	0.317238	+	0.948346i	$0.397245\pi$
$284$	7.27026e6	5.34877
$285$	347396.	0.253345
$286$	1.38273e6	0.999588
$287$	409122.	0.293189
$288$	2.78544e6	1.97885
$289$	0	0
$290$	1.14058e6	0.796396
$291$	452758.	0.313425
$292$	2.03592e6	1.39734
$293$	805056.	0.547844	0.273922	−	0.961752i	$-0.411679\pi$
$293$	805056.	0.547844	0.273922	+	0.961752i	$0.411679\pi$
$294$	−849614.	−0.573262
$295$	−301186.	−0.201502
$296$	−4.54371e6	−3.01427
$297$	−253676.	−0.166874
$298$	−770391.	−0.502540
$299$	−537958.	−0.347993
$300$	2.49340e6	1.59952
$301$	−940438.	−0.598293
$302$	−750442.	−0.473478
$303$	1.28849e6	0.806258
$304$	1.28778e7	7.99207
$305$	565978.	0.348377
$306$	0	0
$307$	−1.40671e6	−0.851839	−0.425920	−	0.904761i	$-0.640049\pi$
$307$	−1.40671e6	−0.851839	−0.425920	+	0.904761i	$0.640049\pi$
$308$	5.28582e6	3.17494
$309$	984113.	0.586339
$310$	411979.	0.243484
$311$	111668.	0.0654678	0.0327339	−	0.999464i	$-0.489579\pi$
$311$	111668.	0.0654678	0.0327339	+	0.999464i	$0.489579\pi$
$312$	−2.28048e6	−1.32629
$313$	−3.22392e6	−1.86004	−0.930022	−	0.367504i	$-0.880212\pi$
$313$	−3.22392e6	−1.86004	−0.930022	+	0.367504i	$0.880212\pi$
$314$	−5.73501e6	−3.28254
$315$	−195737.	−0.111147
$316$	6.04644e6	3.40629
$317$	1.20718e6	0.674723	0.337362	−	0.941375i	$-0.390466\pi$
$317$	1.20718e6	0.674723	0.337362	+	0.941375i	$0.390466\pi$
$318$	−2.22334e6	−1.23293
$319$	−2.30474e6	−1.26807
$320$	−3.44394e6	−1.88010
$321$	231671.	0.125490
$322$	−2.74364e6	−1.47465
$323$	0	0
$324$	628330.	0.332526
$325$	−1.01697e6	−0.534070
$326$	4.37909e6	2.28213
$327$	513176.	0.265398
$328$	1.85917e6	0.954188
$329$	−2.72284e6	−1.38686
$330$	539323.	0.272624
$331$	−911316.	−0.457192	−0.228596	−	0.973521i	$-0.573414\pi$
$331$	−911316.	−0.457192	−0.228596	+	0.973521i	$0.573414\pi$
$332$	−1.79730e6	−0.894903
$333$	−510607.	−0.252334
$334$	934389.	0.458313
$335$	−299162.	−0.145645
$336$	−7.25591e6	−3.50626
$337$	580007.	0.278201	0.139100	−	0.990278i	$-0.455579\pi$
$337$	580007.	0.278201	0.139100	+	0.990278i	$0.455579\pi$
$338$	−2.80000e6	−1.33311
$339$	−1.27613e6	−0.603111
$340$	0	0
$341$	−832477.	−0.387691
$342$	2.31970e6	1.07242
$343$	−1.34115e6	−0.615521
$344$	−4.27362e6	−1.94715
$345$	−209827.	−0.0949103
$346$	1.36312e6	0.612132
$347$	−3.42654e6	−1.52768	−0.763840	−	0.645406i	$-0.776688\pi$
$347$	−3.42654e6	−1.52768	−0.763840	+	0.645406i	$0.776688\pi$
$348$	5.70860e6	2.52686
$349$	−1.81948e6	−0.799620	−0.399810	−	0.916598i	$-0.630924\pi$
$349$	−1.81948e6	−0.799620	−0.399810	+	0.916598i	$0.630924\pi$
$350$	−5.18663e6	−2.26316
$351$	−256272.	−0.111028
$352$	1.19663e7	5.14760
$353$	780591.	0.333416	0.166708	−	0.986006i	$-0.446686\pi$
$353$	780591.	0.333416	0.166708	+	0.986006i	$0.446686\pi$
$354$	−2.01114e6	−0.852971
$355$	−1.15658e6	−0.487087
$356$	1.81696e6	0.759837
$357$	0	0
$358$	1.01251e6	0.417533
$359$	−2.75888e6	−1.12979	−0.564893	−	0.825164i	$-0.691082\pi$
$359$	−2.75888e6	−1.12979	−0.564893	+	0.825164i	$0.691082\pi$
$360$	−889485.	−0.361728
$361$	3.94300e6	1.59242
$362$	−6.24667e6	−2.50540
$363$	359660.	0.143260
$364$	5.33992e6	2.11243
$365$	−323883.	−0.127249
$366$	3.77926e6	1.47470
$367$	−1.51066e6	−0.585467	−0.292734	−	0.956194i	$-0.594565\pi$
$367$	−1.51066e6	−0.585467	−0.292734	+	0.956194i	$0.594565\pi$
$368$	−7.77822e6	−2.99406
$369$	208927.	0.0798783
$370$	1.08557e6	0.412242
$371$	3.46654e6	1.30756
$372$	2.06196e6	0.772544
$373$	2.49116e6	0.927107	0.463554	−	0.886069i	$-0.346574\pi$
$373$	2.49116e6	0.927107	0.463554	+	0.886069i	$0.346574\pi$
$374$	0	0
$375$	−825148.	−0.303008
$376$	−1.23734e7	−4.51355
$377$	−2.32832e6	−0.843704
$378$	−1.30702e6	−0.470491
$379$	1.38911e6	0.496750	0.248375	−	0.968664i	$-0.420103\pi$
$379$	1.38911e6	0.496750	0.248375	+	0.968664i	$0.420103\pi$
$380$	−3.69657e6	−1.31323
$381$	−676897.	−0.238897
$382$	3.60152e6	1.26278
$383$	4.49032e6	1.56416	0.782079	−	0.623180i	$-0.214160\pi$
$383$	4.49032e6	1.56416	0.782079	+	0.623180i	$0.214160\pi$
$384$	−1.30928e7	−4.53111
$385$	−840891.	−0.289127
$386$	159101.	0.0543507
$387$	−480255.	−0.163003
$388$	−4.81772e6	−1.62466
$389$	−2.23604e6	−0.749215	−0.374607	−	0.927184i	$-0.622223\pi$
$389$	−2.23604e6	−0.749215	−0.374607	+	0.927184i	$0.622223\pi$
$390$	544843.	0.181389
$391$	0	0
$392$	6.01974e6	1.97862
$393$	−1.92755e6	−0.629542
$394$	1.06388e6	0.345264
$395$	−961892.	−0.310194
$396$	2.69932e6	0.865001
$397$	−1.08050e6	−0.344070	−0.172035	−	0.985091i	$-0.555034\pi$
$397$	−1.08050e6	−0.344070	−0.172035	+	0.985091i	$0.555034\pi$
$398$	8.27230e6	2.61769
$399$	−3.61678e6	−1.13734
$400$	−1.47041e7	−4.59503
$401$	−3.36895e6	−1.04625	−0.523123	−	0.852257i	$-0.675233\pi$
$401$	−3.36895e6	−1.04625	−0.523123	+	0.852257i	$0.675233\pi$
$402$	−1.99763e6	−0.616523
$403$	−840997.	−0.257948
$404$	−1.37106e7	−4.17929
$405$	−99957.4	−0.0302815
$406$	−1.18747e7	−3.57526
$407$	−2.19358e6	−0.656399
$408$	0	0
$409$	−4.75530e6	−1.40562	−0.702812	−	0.711375i	$-0.748073\pi$
$409$	−4.75530e6	−1.40562	−0.702812	+	0.711375i	$0.748073\pi$
$410$	−444186.	−0.130498
$411$	1.31033e6	0.382628
$412$	−1.04718e7	−3.03932
$413$	3.13569e6	0.904603
$414$	−1.40110e6	−0.401761
$415$	285922.	0.0814945
$416$	1.20888e7	3.42492
$417$	2.99986e6	0.844812
$418$	9.96550e6	2.78970
$419$	−5.14241e6	−1.43097	−0.715487	−	0.698626i	$-0.753795\pi$
$419$	−5.14241e6	−1.43097	−0.715487	+	0.698626i	$0.753795\pi$
$420$	2.08280e6	0.576136
$421$	4.29400e6	1.18075	0.590374	−	0.807130i	$-0.298980\pi$
$421$	4.29400e6	1.18075	0.590374	+	0.807130i	$0.298980\pi$
$422$	8.25908e6	2.25762
$423$	−1.39048e6	−0.377845
$424$	1.57529e7	4.25546
$425$	0	0
$426$	−7.72298e6	−2.06187
$427$	−5.89248e6	−1.56397
$428$	−2.46517e6	−0.650485
$429$	−1.10095e6	−0.288819
$430$	1.02104e6	0.266300
$431$	1.77484e6	0.460222	0.230111	−	0.973164i	$-0.426091\pi$
$431$	1.77484e6	0.460222	0.230111	+	0.973164i	$0.426091\pi$
$432$	−3.70539e6	−0.955266
$433$	−5.00346e6	−1.28248	−0.641240	−	0.767341i	$-0.721580\pi$
$433$	−5.00346e6	−1.28248	−0.641240	+	0.767341i	$0.721580\pi$
$434$	−4.28917e6	−1.09307
$435$	−908148.	−0.230109
$436$	−5.46062e6	−1.37571
$437$	−3.87714e6	−0.971197
$438$	−2.16270e6	−0.538654
$439$	5.15051e6	1.27552	0.637762	−	0.770234i	$-0.279860\pi$
$439$	5.15051e6	1.27552	0.637762	+	0.770234i	$0.279860\pi$
$440$	−3.82125e6	−0.940965
$441$	676479.	0.165637
$442$	0	0
$443$	−6.36634e6	−1.54128	−0.770639	−	0.637273i	$-0.780063\pi$
$443$	−6.36634e6	−1.54128	−0.770639	+	0.637273i	$0.780063\pi$
$444$	5.43328e6	1.30799
$445$	−289050.	−0.0691946
$446$	2.45602e6	0.584648
$447$	613400.	0.145203
$448$	3.58554e7	8.44033
$449$	3.62690e6	0.849023	0.424511	−	0.905423i	$-0.360446\pi$
$449$	3.62690e6	0.849023	0.424511	+	0.905423i	$0.360446\pi$
$450$	−2.64867e6	−0.616589
$451$	897556.	0.207788
$452$	1.35791e7	3.12626
$453$	597516.	0.136806
$454$	6.67854e6	1.52069
$455$	−849497.	−0.192368
$456$	−1.64357e7	−3.70149
$457$	8.19649e6	1.83585	0.917925	−	0.396754i	$-0.129863\pi$
$457$	8.19649e6	1.83585	0.917925	+	0.396754i	$0.129863\pi$
$458$	−9.88107e6	−2.20110
$459$	0	0
$460$	2.23273e6	0.491974
$461$	−7.34263e6	−1.60916	−0.804581	−	0.593844i	$-0.797610\pi$
$461$	−7.34263e6	−1.60916	−0.804581	+	0.593844i	$0.797610\pi$
$462$	−5.61497e6	−1.22389
$463$	−2.47465e6	−0.536490	−0.268245	−	0.963351i	$-0.586444\pi$
$463$	−2.47465e6	−0.536490	−0.268245	+	0.963351i	$0.586444\pi$
$464$	−3.36648e7	−7.25906
$465$	−328025.	−0.0703518
$466$	−1.23603e7	−2.63672
$467$	2.06157e6	0.437426	0.218713	−	0.975789i	$-0.429814\pi$
$467$	2.06157e6	0.437426	0.218713	+	0.975789i	$0.429814\pi$
$468$	2.72695e6	0.575522
$469$	3.11462e6	0.653842
$470$	2.95620e6	0.617291
$471$	4.56633e6	0.948450
$472$	1.42495e7	2.94404
$473$	−2.06319e6	−0.424020
$474$	−6.42295e6	−1.31307
$475$	−7.32941e6	−1.49051
$476$	0	0
$477$	1.77026e6	0.356239
$478$	−5.26734e6	−1.05444
$479$	−4.48457e6	−0.893064	−0.446532	−	0.894768i	$-0.647341\pi$
$479$	−4.48457e6	−0.893064	−0.446532	+	0.894768i	$0.647341\pi$
$480$	4.71516e6	0.934100
$481$	−2.21603e6	−0.436731
$482$	−1.28647e7	−2.52221
$483$	2.18454e6	0.426081
$484$	−3.82708e6	−0.742599
$485$	766422.	0.147950
$486$	−667456.	−0.128183
$487$	4.15417e6	0.793709	0.396855	−	0.917881i	$-0.370102\pi$
$487$	4.15417e6	0.793709	0.396855	+	0.917881i	$0.370102\pi$
$488$	−2.67771e7	−5.08995
$489$	−3.48671e6	−0.659393
$490$	−1.43822e6	−0.270604
$491$	−3.67245e6	−0.687467	−0.343733	−	0.939067i	$-0.611692\pi$
$491$	−3.67245e6	−0.687467	−0.343733	+	0.939067i	$0.611692\pi$
$492$	−2.22316e6	−0.414054
$493$	0	0
$494$	1.00675e7	1.85611
$495$	−429419.	−0.0787714
$496$	−1.21598e7	−2.21933
$497$	1.20414e7	2.18668
$498$	1.90922e6	0.344971
$499$	−5.83718e6	−1.04943	−0.524713	−	0.851279i	$-0.675827\pi$
$499$	−5.83718e6	−1.04943	−0.524713	+	0.851279i	$0.675827\pi$
$500$	8.78025e6	1.57066
$501$	−743979.	−0.132424
$502$	1.69853e7	3.00825
$503$	8.87979e6	1.56489	0.782443	−	0.622723i	$-0.213973\pi$
$503$	8.87979e6	1.56489	0.782443	+	0.622723i	$0.213973\pi$
$504$	9.26055e6	1.62390
$505$	2.18114e6	0.380587
$506$	−6.01916e6	−1.04510
$507$	2.22942e6	0.385187
$508$	7.20274e6	1.23834
$509$	6.05604e6	1.03608	0.518041	−	0.855356i	$-0.326661\pi$
$509$	6.05604e6	1.03608	0.518041	+	0.855356i	$0.326661\pi$
$510$	0	0
$511$	3.37199e6	0.571260
$512$	5.75525e7	9.70263
$513$	−1.84699e6	−0.309864
$514$	−1.93842e6	−0.323624
$515$	1.66589e6	0.276776
$516$	5.11031e6	0.844935
$517$	−5.97353e6	−0.982890
$518$	−1.13020e7	−1.85068
$519$	−1.08535e6	−0.176868
$520$	−3.86036e6	−0.626065
$521$	−2.31171e6	−0.373111	−0.186556	−	0.982444i	$-0.559732\pi$
$521$	−2.31171e6	−0.373111	−0.186556	+	0.982444i	$0.559732\pi$
$522$	−6.06407e6	−0.974065
$523$	4.08804e6	0.653522	0.326761	−	0.945107i	$-0.394043\pi$
$523$	4.08804e6	0.653522	0.326761	+	0.945107i	$0.394043\pi$
$524$	2.05107e7	3.26327
$525$	4.12969e6	0.653913
$526$	8.57465e6	1.35130
$527$	0	0
$528$	−1.59184e7	−2.48494
$529$	−4.09455e6	−0.636161
$530$	−3.76363e6	−0.581993
$531$	1.60131e6	0.246456
$532$	3.84856e7	5.89547
$533$	906743.	0.138250
$534$	−1.93010e6	−0.292905
$535$	392170.	0.0592365
$536$	1.41537e7	2.12794
$537$	−806178.	−0.120641
$538$	7.03967e6	1.04857
$539$	2.90617e6	0.430873
$540$	1.06363e6	0.156966
$541$	6.49749e6	0.954448	0.477224	−	0.878782i	$-0.341643\pi$
$541$	6.49749e6	0.954448	0.477224	+	0.878782i	$0.341643\pi$
$542$	−5.31100e6	−0.776566
$543$	4.97372e6	0.723905
$544$	0	0
$545$	868698.	0.125279
$546$	−5.67244e6	−0.814307
$547$	7.49312e6	1.07077	0.535383	−	0.844609i	$-0.320167\pi$
$547$	7.49312e6	1.07077	0.535383	+	0.844609i	$0.320167\pi$
$548$	−1.39430e7	−1.98338
$549$	−3.00912e6	−0.426097
$550$	−1.13787e7	−1.60394
$551$	−1.67805e7	−2.35465
$552$	9.92716e6	1.38668
$553$	1.00144e7	1.39255
$554$	−3.54359e6	−0.490533
$555$	−864349.	−0.119112
$556$	−3.19209e7	−4.37914
$557$	5.12263e6	0.699608	0.349804	−	0.936823i	$-0.386248\pi$
$557$	5.12263e6	0.699608	0.349804	+	0.936823i	$0.386248\pi$
$558$	−2.19036e6	−0.297803
$559$	−2.08431e6	−0.282119
$560$	−1.22827e7	−1.65510
$561$	0	0
$562$	2.95080e6	0.394093
$563$	1.23766e6	0.164563	0.0822813	−	0.996609i	$-0.473779\pi$
$563$	1.23766e6	0.164563	0.0822813	+	0.996609i	$0.473779\pi$
$564$	1.47958e7	1.95858
$565$	−2.16022e6	−0.284694
$566$	9.66253e6	1.26780
$567$	1.04067e6	0.135943
$568$	5.47194e7	7.11656
$569$	−2.04863e6	−0.265267	−0.132633	−	0.991165i	$-0.542343\pi$
$569$	−2.04863e6	−0.265267	−0.132633	+	0.991165i	$0.542343\pi$
$570$	3.92676e6	0.506229
$571$	5.95884e6	0.764842	0.382421	−	0.923988i	$-0.375090\pi$
$571$	5.95884e6	0.764842	0.382421	+	0.923988i	$0.375090\pi$
$572$	1.17150e7	1.49711
$573$	−2.86760e6	−0.364865
$574$	4.62448e6	0.585846
$575$	4.42697e6	0.558389
$576$	1.83103e7	2.29954
$577$	−4.64374e6	−0.580669	−0.290334	−	0.956925i	$-0.593767\pi$
$577$	−4.64374e6	−0.580669	−0.290334	+	0.956925i	$0.593767\pi$
$578$	0	0
$579$	−126679.	−0.0157040
$580$	9.66344e6	1.19278
$581$	−2.97678e6	−0.365853
$582$	5.11771e6	0.626280
$583$	7.60509e6	0.926687
$584$	1.53233e7	1.85917
$585$	−433814.	−0.0524100
$586$	9.09989e6	1.09469
$587$	1.76851e6	0.211842	0.105921	−	0.994375i	$-0.466221\pi$
$587$	1.76851e6	0.211842	0.105921	+	0.994375i	$0.466221\pi$
$588$	−7.19829e6	−0.858590
$589$	−6.06118e6	−0.719895
$590$	−3.40443e6	−0.402638
$591$	−847081.	−0.0997599
$592$	−3.20412e7	−3.75754
$593$	−1.12250e7	−1.31084	−0.655419	−	0.755265i	$-0.727508\pi$
$593$	−1.12250e7	−1.31084	−0.655419	+	0.755265i	$0.727508\pi$
$594$	−2.86741e6	−0.333444
$595$	0	0
$596$	−6.52708e6	−0.752667
$597$	−6.58656e6	−0.756350
$598$	−6.08076e6	−0.695353
$599$	4.11139e6	0.468189	0.234095	−	0.972214i	$-0.424787\pi$
$599$	4.11139e6	0.468189	0.234095	+	0.972214i	$0.424787\pi$
$600$	1.87665e7	2.12817
$601$	−1.70735e7	−1.92813	−0.964064	−	0.265672i	$-0.914406\pi$
$601$	−1.70735e7	−1.92813	−0.964064	+	0.265672i	$0.914406\pi$
$602$	−1.06302e7	−1.19550
$603$	1.59055e6	0.178137
$604$	−6.35806e6	−0.709141
$605$	608828.	0.0676248
$606$	1.45643e7	1.61105
$607$	1.61915e7	1.78367	0.891835	−	0.452360i	$-0.149418\pi$
$607$	1.61915e7	1.78367	0.891835	+	0.452360i	$0.149418\pi$
$608$	8.71257e7	9.55845
$609$	9.45485e6	1.03303
$610$	6.39749e6	0.696121
$611$	−6.03467e6	−0.653959
$612$	0	0
$613$	−1.55108e7	−1.66718	−0.833591	−	0.552382i	$-0.813719\pi$
$613$	−1.55108e7	−1.66718	−0.833591	+	0.552382i	$0.813719\pi$
$614$	−1.59006e7	−1.70213
$615$	353669.	0.0377059
$616$	3.97836e7	4.22427
$617$	−1.72641e7	−1.82571	−0.912854	−	0.408287i	$-0.866126\pi$
$617$	−1.72641e7	−1.82571	−0.912854	+	0.408287i	$0.866126\pi$
$618$	1.11238e7	1.17161
$619$	−8.01052e6	−0.840300	−0.420150	−	0.907455i	$-0.638023\pi$
$619$	−8.01052e6	−0.840300	−0.420150	+	0.907455i	$0.638023\pi$
$620$	3.49046e6	0.364673
$621$	1.11558e6	0.116084
$622$	1.26223e6	0.130817
$623$	3.00934e6	0.310635
$624$	−1.60814e7	−1.65334
$625$	7.64349e6	0.782693
$626$	−3.64413e7	−3.71671
$627$	−7.93472e6	−0.806051
$628$	−4.85895e7	−4.91635
$629$	0	0
$630$	−2.21250e6	−0.222091
$631$	9.44326e6	0.944166	0.472083	−	0.881554i	$-0.343502\pi$
$631$	9.44326e6	0.944166	0.472083	+	0.881554i	$0.343502\pi$
$632$	4.55083e7	4.53208
$633$	−6.57604e6	−0.652311
$634$	1.36453e7	1.34822
$635$	−1.14584e6	−0.112769
$636$	−1.88370e7	−1.84659
$637$	2.93591e6	0.286678
$638$	−2.60514e7	−2.53384
$639$	6.14918e6	0.595751
$640$	−2.21633e7	−2.13887
$641$	3.43129e6	0.329847	0.164924	−	0.986306i	$-0.447262\pi$
$641$	3.43129e6	0.329847	0.164924	+	0.986306i	$0.447262\pi$
$642$	2.61868e6	0.250752
$643$	6.79041e6	0.647693	0.323846	−	0.946110i	$-0.395024\pi$
$643$	6.79041e6	0.647693	0.323846	+	0.946110i	$0.395024\pi$
$644$	−2.32453e7	−2.20862
$645$	−812970.	−0.0769441
$646$	0	0
$647$	1.32178e6	0.124136	0.0620682	−	0.998072i	$-0.480230\pi$
$647$	1.32178e6	0.124136	0.0620682	+	0.998072i	$0.480230\pi$
$648$	4.72910e6	0.442427
$649$	6.87926e6	0.641106
$650$	−1.14952e7	−1.06717
$651$	3.41512e6	0.315830
$652$	3.71015e7	3.41800
$653$	−1.06627e7	−0.978549	−0.489274	−	0.872130i	$-0.662738\pi$
$653$	−1.06627e7	−0.978549	−0.489274	+	0.872130i	$0.662738\pi$
$654$	5.80065e6	0.530313
$655$	−3.26293e6	−0.297170
$656$	1.31104e7	1.18948
$657$	1.72198e6	0.155638
$658$	−3.07775e7	−2.77120
$659$	−7.77801e6	−0.697678	−0.348839	−	0.937183i	$-0.613424\pi$
$659$	−7.77801e6	−0.697678	−0.348839	+	0.937183i	$0.613424\pi$
$660$	4.56938e6	0.408317
$661$	−5.94891e6	−0.529583	−0.264791	−	0.964306i	$-0.585303\pi$
$661$	−5.94891e6	−0.529583	−0.264791	+	0.964306i	$0.585303\pi$
$662$	−1.03010e7	−0.913554
$663$	0	0
$664$	−1.35273e7	−1.19067
$665$	−6.12245e6	−0.536872
$666$	−5.77161e6	−0.504210
$667$	1.01355e7	0.882122
$668$	7.91654e6	0.686427
$669$	−1.95553e6	−0.168927
$670$	−3.38156e6	−0.291025
$671$	−1.29273e7	−1.10841
$672$	−4.90902e7	−4.19345
$673$	−7.25131e6	−0.617133	−0.308566	−	0.951203i	$-0.599849\pi$
$673$	−7.25131e6	−0.617133	−0.308566	+	0.951203i	$0.599849\pi$
$674$	6.55607e6	0.555896
$675$	2.10892e6	0.178156
$676$	−2.37228e7	−1.99664
$677$	1.93480e7	1.62242	0.811212	−	0.584752i	$-0.198808\pi$
$677$	1.93480e7	1.62242	0.811212	+	0.584752i	$0.198808\pi$
$678$	−1.44247e7	−1.20513
$679$	−7.97933e6	−0.664190
$680$	0	0
$681$	−5.31758e6	−0.439386
$682$	−9.40984e6	−0.774678
$683$	−3.77545e6	−0.309683	−0.154841	−	0.987939i	$-0.549487\pi$
$683$	−3.77545e6	−0.309683	−0.154841	+	0.987939i	$0.549487\pi$
$684$	1.96535e7	1.60620
$685$	2.21811e6	0.180617
$686$	−1.51596e7	−1.22992
$687$	7.86750e6	0.635982
$688$	−3.01365e7	−2.42729
$689$	7.68293e6	0.616565
$690$	−2.37176e6	−0.189648
$691$	−1.53309e7	−1.22144	−0.610719	−	0.791847i	$-0.709120\pi$
$691$	−1.53309e7	−1.22144	−0.610719	+	0.791847i	$0.709120\pi$
$692$	1.15490e7	0.916807
$693$	4.47075e6	0.353628
$694$	−3.87317e7	−3.05258
$695$	5.07811e6	0.398787
$696$	4.29656e7	3.36200
$697$	0	0
$698$	−2.05664e7	−1.59779
$699$	9.84152e6	0.761849
$700$	−4.39433e7	−3.38960
$701$	1.51247e7	1.16250	0.581249	−	0.813725i	$-0.302564\pi$
$701$	1.51247e7	1.16250	0.581249	+	0.813725i	$0.302564\pi$
$702$	−2.89675e6	−0.221855
$703$	−1.59713e7	−1.21885
$704$	7.86617e7	5.98179
$705$	−2.35378e6	−0.178359
$706$	8.82335e6	0.666226
$707$	−2.27081e7	−1.70857
$708$	−1.70392e7	−1.27752
$709$	2.67901e6	0.200151	0.100076	−	0.994980i	$-0.468091\pi$
$709$	2.67901e6	0.200151	0.100076	+	0.994980i	$0.468091\pi$
$710$	−1.30734e7	−0.973287
$711$	5.11407e6	0.379396
$712$	1.36753e7	1.01097
$713$	3.66095e6	0.269693
$714$	0	0
$715$	−1.86368e6	−0.136334
$716$	8.57839e6	0.625350
$717$	4.19395e6	0.304667
$718$	−3.11847e7	−2.25752
$719$	2.49457e7	1.79959	0.899795	−	0.436313i	$-0.143716\pi$
$719$	2.49457e7	1.79959	0.899795	+	0.436313i	$0.143716\pi$
$720$	−6.27243e6	−0.450925
$721$	−1.73439e7	−1.24253
$722$	4.45694e7	3.18195
$723$	1.02431e7	0.728762
$724$	−5.29245e7	−3.75241
$725$	1.91603e7	1.35381
$726$	4.06539e6	0.286260
$727$	−9.52558e6	−0.668429	−0.334215	−	0.942497i	$-0.608471\pi$
$727$	−9.52558e6	−0.668429	−0.334215	+	0.942497i	$0.608471\pi$
$728$	4.01907e7	2.81059
$729$	531441.	0.0370370
$730$	−3.66098e6	−0.254267
$731$	0	0
$732$	3.20195e7	2.20870
$733$	−52854.8	−0.00363349	−0.00181675	−	0.999998i	$-0.500578\pi$
$733$	−52854.8	−0.00363349	−0.00181675	+	0.999998i	$0.500578\pi$
$734$	−1.70757e7	−1.16987
$735$	1.14513e6	0.0781876
$736$	−5.26239e7	−3.58087
$737$	6.83304e6	0.463388
$738$	2.36159e6	0.159611
$739$	6.71590e6	0.452369	0.226185	−	0.974084i	$-0.427375\pi$
$739$	6.71590e6	0.452369	0.226185	+	0.974084i	$0.427375\pi$
$740$	9.19739e6	0.617426
$741$	−8.01593e6	−0.536301
$742$	3.91837e7	2.61274
$743$	9.82147e6	0.652687	0.326343	−	0.945251i	$-0.394183\pi$
$743$	9.82147e6	0.652687	0.326343	+	0.945251i	$0.394183\pi$
$744$	1.55193e7	1.02787
$745$	1.03835e6	0.0685417
$746$	2.81587e7	1.85253
$747$	−1.52016e6	−0.0996752
$748$	0	0
$749$	−4.08294e6	−0.265930
$750$	−9.32699e6	−0.605464
$751$	−2.36298e7	−1.52883	−0.764416	−	0.644723i	$-0.776973\pi$
$751$	−2.36298e7	−1.52883	−0.764416	+	0.644723i	$0.776973\pi$
$752$	−8.72541e7	−5.62654
$753$	−1.35240e7	−0.869198
$754$	−2.63180e7	−1.68587
$755$	1.01147e6	0.0645780
$756$	−1.10736e7	−0.704667
$757$	1.52671e7	0.968319	0.484159	−	0.874980i	$-0.339126\pi$
$757$	1.52671e7	0.968319	0.484159	+	0.874980i	$0.339126\pi$
$758$	1.57017e7	0.992597
$759$	4.79257e6	0.301970
$760$	−2.78221e7	−1.74726
$761$	−1.38655e7	−0.867909	−0.433954	−	0.900935i	$-0.642882\pi$
$761$	−1.38655e7	−0.867909	−0.433954	+	0.900935i	$0.642882\pi$
$762$	−7.65125e6	−0.477359
$763$	−9.04414e6	−0.562413
$764$	3.05136e7	1.89130
$765$	0	0
$766$	5.07560e7	3.12547
$767$	6.94967e6	0.426556
$768$	−8.28902e7	−5.07107
$769$	9.06887e6	0.553016	0.276508	−	0.961012i	$-0.410823\pi$
$769$	9.06887e6	0.553016	0.276508	+	0.961012i	$0.410823\pi$
$770$	−9.50495e6	−0.577727
$771$	1.54341e6	0.0935071
$772$	1.34797e6	0.0814025
$773$	−1.98248e7	−1.19333	−0.596664	−	0.802491i	$-0.703507\pi$
$773$	−1.98248e7	−1.19333	−0.596664	+	0.802491i	$0.703507\pi$
$774$	−5.42853e6	−0.325709
$775$	6.92074e6	0.413903
$776$	−3.62604e7	−2.16161
$777$	8.99886e6	0.534731
$778$	−2.52750e7	−1.49707
$779$	6.53502e6	0.385836
$780$	4.61614e6	0.271671
$781$	2.64170e7	1.54973
$782$	0	0
$783$	4.82833e6	0.281444
$784$	4.24498e7	2.46652
$785$	7.72981e6	0.447708
$786$	−2.17879e7	−1.25794
$787$	−2.20057e7	−1.26648	−0.633241	−	0.773955i	$-0.718276\pi$
$787$	−2.20057e7	−1.26648	−0.633241	+	0.773955i	$0.718276\pi$
$788$	9.01364e6	0.517112
$789$	−6.82729e6	−0.390442
$790$	−1.08727e7	−0.619825
$791$	2.24904e7	1.27807
$792$	2.03163e7	1.15089
$793$	−1.30596e7	−0.737473
$794$	−1.22133e7	−0.687515
$795$	2.99668e6	0.168160
$796$	7.00864e7	3.92059
$797$	−4.58884e6	−0.255892	−0.127946	−	0.991781i	$-0.540838\pi$
$797$	−4.58884e6	−0.255892	−0.127946	+	0.991781i	$0.540838\pi$
$798$	−4.08821e7	−2.27261
$799$	0	0
$800$	−9.94813e7	−5.49562
$801$	1.53678e6	0.0846313
$802$	−3.80807e7	−2.09059
$803$	7.39767e6	0.404861
$804$	−1.69247e7	−0.923383
$805$	3.69796e6	0.201128
$806$	−9.50614e6	−0.515427
$807$	−5.60512e6	−0.302971
$808$	−1.03192e8	−5.56056
$809$	2.20765e7	1.18593	0.592964	−	0.805229i	$-0.297958\pi$
$809$	2.20765e7	1.18593	0.592964	+	0.805229i	$0.297958\pi$
$810$	−1.12986e6	−0.0605079
$811$	3.34783e7	1.78736	0.893678	−	0.448708i	$-0.148116\pi$
$811$	3.34783e7	1.78736	0.893678	+	0.448708i	$0.148116\pi$
$812$	−1.00607e8	−5.35476
$813$	4.22872e6	0.224379
$814$	−2.47950e7	−1.31160
$815$	−5.90226e6	−0.311261
$816$	0	0
$817$	−1.50219e7	−0.787352
$818$	−5.37511e7	−2.80869
$819$	4.51650e6	0.235284
$820$	−3.76333e6	−0.195451
$821$	2.29971e7	1.19074	0.595369	−	0.803453i	$-0.297006\pi$
$821$	2.29971e7	1.19074	0.595369	+	0.803453i	$0.297006\pi$
$822$	1.48113e7	0.764561
$823$	9.86002e6	0.507432	0.253716	−	0.967279i	$-0.418347\pi$
$823$	9.86002e6	0.507432	0.253716	+	0.967279i	$0.418347\pi$
$824$	−7.88154e7	−4.04383
$825$	9.05997e6	0.463438
$826$	3.54440e7	1.80756
$827$	−1.80635e7	−0.918414	−0.459207	−	0.888329i	$-0.651866\pi$
$827$	−1.80635e7	−0.918414	−0.459207	+	0.888329i	$0.651866\pi$
$828$	−1.18707e7	−0.601729
$829$	−3.76375e6	−0.190210	−0.0951052	−	0.995467i	$-0.530319\pi$
$829$	−3.76375e6	−0.190210	−0.0951052	+	0.995467i	$0.530319\pi$
$830$	3.23190e6	0.162841
$831$	2.82147e6	0.141734
$832$	7.94668e7	3.97995
$833$	0	0
$834$	3.39086e7	1.68809
$835$	−1.25940e6	−0.0625096
$836$	8.44319e7	4.17822
$837$	1.74400e6	0.0860467
$838$	−5.81269e7	−2.85935
$839$	3.11062e7	1.52560	0.762801	−	0.646633i	$-0.223823\pi$
$839$	3.11062e7	1.52560	0.762801	+	0.646633i	$0.223823\pi$
$840$	1.56761e7	0.766551
$841$	2.33559e7	1.13869
$842$	4.85369e7	2.35935
$843$	−2.34948e6	−0.113868
$844$	6.99744e7	3.38130
$845$	3.77393e6	0.181824
$846$	−1.57172e7	−0.755003
$847$	−6.33860e6	−0.303588
$848$	1.11086e8	5.30480
$849$	−7.69349e6	−0.366315
$850$	0	0
$851$	9.64664e6	0.456617
$852$	−6.54323e7	−3.08811
$853$	−2.09421e6	−0.0985480	−0.0492740	−	0.998785i	$-0.515691\pi$
$853$	−2.09421e6	−0.0985480	−0.0492740	+	0.998785i	$0.515691\pi$
$854$	−6.66051e7	−3.12509
$855$	−3.12656e6	−0.146269
$856$	−1.85540e7	−0.865473
$857$	2.46110e7	1.14466	0.572331	−	0.820022i	$-0.306039\pi$
$857$	2.46110e7	1.14466	0.572331	+	0.820022i	$0.306039\pi$
$858$	−1.24445e7	−0.577112
$859$	−2.98042e7	−1.37814	−0.689072	−	0.724693i	$-0.741982\pi$
$859$	−2.98042e7	−1.37814	−0.689072	+	0.724693i	$0.741982\pi$
$860$	8.65067e6	0.398844
$861$	−3.68210e6	−0.169273
$862$	2.00618e7	0.919607
$863$	2.23270e7	1.02048	0.510238	−	0.860033i	$-0.329557\pi$
$863$	2.23270e7	1.02048	0.510238	+	0.860033i	$0.329557\pi$
$864$	−2.50690e7	−1.14249
$865$	−1.83726e6	−0.0834891
$866$	−5.65562e7	−2.56263
$867$	0	0
$868$	−3.63397e7	−1.63712
$869$	2.19702e7	0.986925
$870$	−1.02652e7	−0.459799
$871$	6.90297e6	0.308312
$872$	−4.10991e7	−1.83038
$873$	−4.07482e6	−0.180956
$874$	−4.38249e7	−1.94063
$875$	1.45423e7	0.642114
$876$	−1.83233e7	−0.806757
$877$	2.85426e7	1.25313	0.626563	−	0.779371i	$-0.284461\pi$
$877$	2.85426e7	1.25313	0.626563	+	0.779371i	$0.284461\pi$
$878$	5.82184e7	2.54873
$879$	−7.24551e6	−0.316298
$880$	−2.69465e7	−1.17300
$881$	−1.05803e7	−0.459260	−0.229630	−	0.973278i	$-0.573752\pi$
$881$	−1.05803e7	−0.459260	−0.229630	+	0.973278i	$0.573752\pi$
$882$	7.64653e6	0.330973
$883$	−574552.	−0.0247986	−0.0123993	−	0.999923i	$-0.503947\pi$
$883$	−574552.	−0.0247986	−0.0123993	+	0.999923i	$0.503947\pi$
$884$	0	0
$885$	2.71067e6	0.116337
$886$	−7.19615e7	−3.07975
$887$	−3.45290e7	−1.47358	−0.736792	−	0.676120i	$-0.763660\pi$
$887$	−3.45290e7	−1.47358	−0.736792	+	0.676120i	$0.763660\pi$
$888$	4.08934e7	1.74029
$889$	1.19295e7	0.506254
$890$	−3.26725e6	−0.138263
$891$	2.28308e6	0.0963447
$892$	2.08084e7	0.875643
$893$	−4.34927e7	−1.82511
$894$	6.93352e6	0.290141
$895$	−1.36469e6	−0.0569476
$896$	2.30746e8	9.60204
$897$	4.84162e6	0.200914
$898$	4.09964e7	1.69650
$899$	1.58449e7	0.653868
$900$	−2.24406e7	−0.923483
$901$	0	0
$902$	1.01455e7	0.415198
$903$	8.46395e6	0.345425
$904$	1.02203e8	4.15951
$905$	8.41945e6	0.341713
$906$	6.75398e6	0.273363
$907$	1.68995e7	0.682111	0.341055	−	0.940043i	$-0.389216\pi$
$907$	1.68995e7	0.682111	0.341055	+	0.940043i	$0.389216\pi$
$908$	5.65834e7	2.27759
$909$	−1.15964e7	−0.465493
$910$	−9.60223e6	−0.384387
$911$	−3.60555e7	−1.43938	−0.719690	−	0.694295i	$-0.755716\pi$
$911$	−3.60555e7	−1.43938	−0.719690	+	0.694295i	$0.755716\pi$
$912$	−1.15901e8	−4.61422
$913$	−6.53064e6	−0.259286
$914$	9.26484e7	3.66836
$915$	−5.09380e6	−0.201136
$916$	−8.37166e7	−3.29665
$917$	3.39709e7	1.33408
$918$	0	0
$919$	−2.90149e7	−1.13327	−0.566633	−	0.823970i	$-0.691754\pi$
$919$	−2.90149e7	−1.13327	−0.566633	+	0.823970i	$0.691754\pi$
$920$	1.68046e7	0.654573
$921$	1.26604e7	0.491810
$922$	−8.29969e7	−3.21540
$923$	2.66874e7	1.03110
$924$	−4.75724e7	−1.83305
$925$	1.82362e7	0.700777
$926$	−2.79721e7	−1.07201
$927$	−8.85702e6	−0.338523
$928$	−2.27761e8	−8.68178
$929$	−2.48349e7	−0.944111	−0.472056	−	0.881569i	$-0.656488\pi$
$929$	−2.48349e7	−0.944111	−0.472056	+	0.881569i	$0.656488\pi$
$930$	−3.70781e6	−0.140576
$931$	2.11595e7	0.800077
$932$	−1.04722e8	−3.94909
$933$	−1.00501e6	−0.0377978
$934$	2.33027e7	0.874057
$935$	0	0
$936$	2.05243e7	0.765735
$937$	1.49094e6	0.0554767	0.0277383	−	0.999615i	$-0.491169\pi$
$937$	1.49094e6	0.0554767	0.0277383	+	0.999615i	$0.491169\pi$
$938$	3.52059e7	1.30650
$939$	2.90153e7	1.07390
$940$	2.50462e7	0.924533
$941$	−1.31967e7	−0.485839	−0.242920	−	0.970046i	$-0.578105\pi$
$941$	−1.31967e7	−0.485839	−0.242920	+	0.970046i	$0.578105\pi$
$942$	5.16151e7	1.89518
$943$	−3.94715e6	−0.144545
$944$	1.00484e8	3.67000
$945$	1.76163e6	0.0641706
$946$	−2.33211e7	−0.847269
$947$	5.36816e6	0.194514	0.0972568	−	0.995259i	$-0.468993\pi$
$947$	5.36816e6	0.194514	0.0972568	+	0.995259i	$0.468993\pi$
$948$	−5.44179e7	−1.96662
$949$	7.47338e6	0.269371
$950$	−8.28475e7	−2.97831
$951$	−1.08647e7	−0.389552
$952$	0	0
$953$	1.22546e7	0.437085	0.218542	−	0.975827i	$-0.429870\pi$
$953$	1.22546e7	0.437085	0.218542	+	0.975827i	$0.429870\pi$
$954$	2.00100e7	0.711831
$955$	−4.85423e6	−0.172231
$956$	−4.46271e7	−1.57926
$957$	2.07426e7	0.732122
$958$	−5.06910e7	−1.78450
$959$	−2.30931e7	−0.810841
$960$	3.09955e7	1.08548
$961$	−2.29059e7	−0.800091
$962$	−2.50488e7	−0.872667
$963$	−2.08504e6	−0.0724517
$964$	−1.08995e8	−3.77758
$965$	−214441.	−0.00741293
$966$	2.46928e7	0.851387
$967$	4.19528e7	1.44276	0.721381	−	0.692538i	$-0.243508\pi$
$967$	4.19528e7	1.44276	0.721381	+	0.692538i	$0.243508\pi$
$968$	−2.88044e7	−0.988030
$969$	0	0
$970$	8.66320e6	0.295630
$971$	−5.65937e7	−1.92628	−0.963141	−	0.268998i	$-0.913307\pi$
$971$	−5.65937e7	−1.92628	−0.963141	+	0.268998i	$0.913307\pi$
$972$	−5.65497e6	−0.191984
$973$	−5.28690e7	−1.79027
$974$	4.69563e7	1.58598
$975$	9.15269e6	0.308345
$976$	−1.88826e8	−6.34507
$977$	−1.25653e7	−0.421149	−0.210575	−	0.977578i	$-0.567534\pi$
$977$	−1.25653e7	−0.421149	−0.210575	+	0.977578i	$0.567534\pi$
$978$	−3.94118e7	−1.31759
$979$	6.60206e6	0.220152
$980$	−1.21852e7	−0.405290
$981$	−4.61858e6	−0.153227
$982$	−4.15112e7	−1.37368
$983$	8.63730e6	0.285098	0.142549	−	0.989788i	$-0.454470\pi$
$983$	8.63730e6	0.285098	0.142549	+	0.989788i	$0.454470\pi$
$984$	−1.67325e7	−0.550901
$985$	−1.43393e6	−0.0470909
$986$	0	0
$987$	2.45056e7	0.800705
$988$	8.52960e7	2.77995
$989$	9.07322e6	0.294965
$990$	−4.85391e6	−0.157400
$991$	−2.00417e7	−0.648262	−0.324131	−	0.946012i	$-0.605072\pi$
$991$	−2.00417e7	−0.648262	−0.324131	+	0.946012i	$0.605072\pi$
$992$	−8.22677e7	−2.65430
$993$	8.20184e6	0.263960
$994$	1.36109e8	4.36938
$995$	−1.11496e7	−0.357029
$996$	1.61757e7	0.516673
$997$	−1.14644e7	−0.365269	−0.182635	−	0.983181i	$-0.558463\pi$
$997$	−1.14644e7	−0.365269	−0.182635	+	0.983181i	$0.558463\pi$
$998$	−6.59801e7	−2.09694
$999$	4.59547e6	0.145685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.6.a.l.1.8	✓	8
17.16	even	2		867.6.a.m.1.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.6.a.l.1.8	✓	8	1.1	even	1	trivial
867.6.a.m.1.8	yes	8	17.16	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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	867.a (trivial)

\(f(q)\)	\(=\)	\(q+11.3034 q^{2} -9.00000 q^{3} +95.7674 q^{4} -15.2351 q^{5} -101.731 q^{6} +158.615 q^{7} +720.790 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+11.3034 q^{2} -9.00000 q^{3} +95.7674 q^{4} -15.2351 q^{5} -101.731 q^{6} +158.615 q^{7} +720.790 q^{8} +81.0000 q^{9} -172.209 q^{10} +347.978 q^{11} -861.907 q^{12} +351.540 q^{13} +1792.89 q^{14} +137.116 q^{15} +5082.84 q^{16} +915.577 q^{18} +2533.59 q^{19} -1459.02 q^{20} -1427.53 q^{21} +3933.34 q^{22} -1530.29 q^{23} -6487.11 q^{24} -2892.89 q^{25} +3973.60 q^{26} -729.000 q^{27} +15190.1 q^{28} -6623.22 q^{29} +1549.88 q^{30} -2392.32 q^{31} +34388.2 q^{32} -3131.80 q^{33} -2416.51 q^{35} +7757.16 q^{36} -6303.79 q^{37} +28638.3 q^{38} -3163.86 q^{39} -10981.3 q^{40} +2579.35 q^{41} -16136.0 q^{42} -5929.08 q^{43} +33325.0 q^{44} -1234.04 q^{45} -17297.5 q^{46} -17166.4 q^{47} -45745.5 q^{48} +8351.59 q^{49} -32699.6 q^{50} +33666.0 q^{52} +21855.1 q^{53} -8240.20 q^{54} -5301.47 q^{55} +114328. q^{56} -22802.3 q^{57} -74865.1 q^{58} +19769.2 q^{59} +13131.2 q^{60} -37149.6 q^{61} -27041.5 q^{62} +12847.8 q^{63} +226054. q^{64} -5355.73 q^{65} -35400.1 q^{66} +19636.4 q^{67} +13772.6 q^{69} -27314.8 q^{70} +75915.8 q^{71} +58384.0 q^{72} +21259.0 q^{73} -71254.5 q^{74} +26036.0 q^{75} +242636. q^{76} +55194.4 q^{77} -35762.4 q^{78} +63136.7 q^{79} -77437.4 q^{80} +6561.00 q^{81} +29155.5 q^{82} -18767.4 q^{83} -136711. q^{84} -67018.9 q^{86} +59609.0 q^{87} +250819. q^{88} +18972.6 q^{89} -13948.9 q^{90} +55759.3 q^{91} -146552. q^{92} +21530.9 q^{93} -194039. q^{94} -38599.5 q^{95} -309494. q^{96} -50306.4 q^{97} +94401.6 q^{98} +28186.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 72 q^{3} + 187 q^{4} - 27 q^{6} + 18 q^{7} + 105 q^{8} + 648 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - 72 * q^3 + 187 * q^4 - 27 * q^6 + 18 * q^7 + 105 * q^8 + 648 * q^9	\( 8 q + 3 q^{2} - 72 q^{3} + 187 q^{4} - 27 q^{6} + 18 q^{7} + 105 q^{8} + 648 q^{9} - 373 q^{10} + 966 q^{11} - 1683 q^{12} + 382 q^{13} + 2046 q^{14} + 4275 q^{16} + 243 q^{18} + 4526 q^{19} + 6315 q^{20} - 162 q^{21} + 1577 q^{22} - 240 q^{23} - 945 q^{24} + 14418 q^{25} - 13632 q^{26} - 5832 q^{27} - 2494 q^{28} - 6072 q^{29} + 3357 q^{30} - 17278 q^{31} + 28173 q^{32} - 8694 q^{33} - 7788 q^{35} + 15147 q^{36} + 4682 q^{37} + 11934 q^{38} - 3438 q^{39} - 68063 q^{40} - 15204 q^{41} - 18414 q^{42} + 7278 q^{43} + 51789 q^{44} + 18878 q^{46} + 39768 q^{47} - 38475 q^{48} + 48134 q^{49} - 44262 q^{50} + 65476 q^{52} + 18756 q^{53} - 2187 q^{54} + 15332 q^{55} + 155406 q^{56} - 40734 q^{57} - 111895 q^{58} + 80826 q^{59} - 56835 q^{60} - 9386 q^{61} - 40473 q^{62} + 1458 q^{63} + 221271 q^{64} - 53544 q^{65} - 14193 q^{66} - 21254 q^{67} + 2160 q^{69} + 34060 q^{70} + 75072 q^{71} + 8505 q^{72} + 44910 q^{73} - 394122 q^{74} - 129762 q^{75} + 297954 q^{76} + 67980 q^{77} + 122688 q^{78} + 13300 q^{79} + 178167 q^{80} + 52488 q^{81} - 52594 q^{82} + 254064 q^{83} + 22446 q^{84} - 160422 q^{86} + 54648 q^{87} + 64927 q^{88} - 56796 q^{89} - 30213 q^{90} - 406358 q^{91} - 583602 q^{92} + 155502 q^{93} - 169338 q^{94} + 98496 q^{95} - 253557 q^{96} + 25828 q^{97} - 178635 q^{98} + 78246 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - 72 * q^3 + 187 * q^4 - 27 * q^6 + 18 * q^7 + 105 * q^8 + 648 * q^9 - 373 * q^10 + 966 * q^11 - 1683 * q^12 + 382 * q^13 + 2046 * q^14 + 4275 * q^16 + 243 * q^18 + 4526 * q^19 + 6315 * q^20 - 162 * q^21 + 1577 * q^22 - 240 * q^23 - 945 * q^24 + 14418 * q^25 - 13632 * q^26 - 5832 * q^27 - 2494 * q^28 - 6072 * q^29 + 3357 * q^30 - 17278 * q^31 + 28173 * q^32 - 8694 * q^33 - 7788 * q^35 + 15147 * q^36 + 4682 * q^37 + 11934 * q^38 - 3438 * q^39 - 68063 * q^40 - 15204 * q^41 - 18414 * q^42 + 7278 * q^43 + 51789 * q^44 + 18878 * q^46 + 39768 * q^47 - 38475 * q^48 + 48134 * q^49 - 44262 * q^50 + 65476 * q^52 + 18756 * q^53 - 2187 * q^54 + 15332 * q^55 + 155406 * q^56 - 40734 * q^57 - 111895 * q^58 + 80826 * q^59 - 56835 * q^60 - 9386 * q^61 - 40473 * q^62 + 1458 * q^63 + 221271 * q^64 - 53544 * q^65 - 14193 * q^66 - 21254 * q^67 + 2160 * q^69 + 34060 * q^70 + 75072 * q^71 + 8505 * q^72 + 44910 * q^73 - 394122 * q^74 - 129762 * q^75 + 297954 * q^76 + 67980 * q^77 + 122688 * q^78 + 13300 * q^79 + 178167 * q^80 + 52488 * q^81 - 52594 * q^82 + 254064 * q^83 + 22446 * q^84 - 160422 * q^86 + 54648 * q^87 + 64927 * q^88 - 56796 * q^89 - 30213 * q^90 - 406358 * q^91 - 583602 * q^92 + 155502 * q^93 - 169338 * q^94 + 98496 * q^95 - 253557 * q^96 + 25828 * q^97 - 178635 * q^98 + 78246 * q^99

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