LMFDB - Embedded newform 867.6.a.m.1.1

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			1.1
Root			$-10.4725$ 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)

$f(q)$	$=$	$q-10.4725 q^{2} +9.00000 q^{3} +77.6731 q^{4} -93.2583 q^{5} -94.2524 q^{6} +150.382 q^{7} -478.312 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.4725 q^{2} +9.00000 q^{3} +77.6731 q^{4} -93.2583 q^{5} -94.2524 q^{6} +150.382 q^{7} -478.312 q^{8} +81.0000 q^{9} +976.647 q^{10} -253.617 q^{11} +699.058 q^{12} +912.644 q^{13} -1574.88 q^{14} -839.325 q^{15} +2523.57 q^{16} -848.272 q^{18} -767.738 q^{19} -7243.66 q^{20} +1353.44 q^{21} +2656.00 q^{22} +3644.78 q^{23} -4304.80 q^{24} +5572.11 q^{25} -9557.66 q^{26} +729.000 q^{27} +11680.7 q^{28} +3695.02 q^{29} +8789.82 q^{30} +7722.71 q^{31} -11122.2 q^{32} -2282.55 q^{33} -14024.4 q^{35} +6291.52 q^{36} -16436.2 q^{37} +8040.13 q^{38} +8213.80 q^{39} +44606.5 q^{40} -2824.85 q^{41} -14173.9 q^{42} +5982.85 q^{43} -19699.2 q^{44} -7553.92 q^{45} -38169.9 q^{46} +3780.24 q^{47} +22712.2 q^{48} +5807.84 q^{49} -58353.9 q^{50} +70887.9 q^{52} -9717.51 q^{53} -7634.45 q^{54} +23651.9 q^{55} -71929.6 q^{56} -6909.64 q^{57} -38696.1 q^{58} +26246.6 q^{59} -65193.0 q^{60} +40220.5 q^{61} -80876.1 q^{62} +12181.0 q^{63} +35722.3 q^{64} -85111.6 q^{65} +23904.0 q^{66} +20484.7 q^{67} +32803.0 q^{69} +146870. q^{70} -26823.2 q^{71} -38743.2 q^{72} -59383.0 q^{73} +172128. q^{74} +50149.0 q^{75} -59632.6 q^{76} -38139.5 q^{77} -86018.9 q^{78} -2230.75 q^{79} -235344. q^{80} +6561.00 q^{81} +29583.2 q^{82} +112050. q^{83} +105126. q^{84} -62655.3 q^{86} +33255.2 q^{87} +121308. q^{88} +10335.3 q^{89} +79108.4 q^{90} +137246. q^{91} +283101. q^{92} +69504.4 q^{93} -39588.6 q^{94} +71597.9 q^{95} -100099. q^{96} +137302. q^{97} -60822.5 q^{98} -20542.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.4725	−1.85129	−0.925646	−	0.378390i	$-0.876478\pi$
$2$	−10.4725	−1.85129	−0.925646	+	0.378390i	$0.876478\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	77.6731	2.42729
$5$	−93.2583	−1.66825	−0.834127	−	0.551572i	$-0.814028\pi$
$5$	−93.2583	−1.66825	−0.834127	+	0.551572i	$0.814028\pi$
$6$	−94.2524	−1.06884
$7$	150.382	1.15998	0.579991	−	0.814623i	$-0.303056\pi$
$7$	150.382	1.15998	0.579991	+	0.814623i	$0.303056\pi$
$8$	−478.312	−2.64232
$9$	81.0000	0.333333
$10$	976.647	3.08843
$11$	−253.617	−0.631969	−0.315985	−	0.948764i	$-0.602335\pi$
$11$	−253.617	−0.631969	−0.315985	+	0.948764i	$0.602335\pi$
$12$	699.058	1.40139
$13$	912.644	1.49776	0.748881	−	0.662704i	$-0.230591\pi$
$13$	912.644	1.49776	0.748881	+	0.662704i	$0.230591\pi$
$14$	−1574.88	−2.14747
$15$	−839.325	−0.963167
$16$	2523.57	2.46443
$17$	0	0
$17$	0	0
$18$	−848.272	−0.617098
$19$	−767.738	−0.487898	−0.243949	−	0.969788i	$-0.578443\pi$
$19$	−767.738	−0.487898	−0.243949	+	0.969788i	$0.578443\pi$
$20$	−7243.66	−4.04933
$21$	1353.44	0.669716
$22$	2656.00	1.16996
$23$	3644.78	1.43665	0.718326	−	0.695707i	$-0.244909\pi$
$23$	3644.78	1.43665	0.718326	+	0.695707i	$0.244909\pi$
$24$	−4304.80	−1.52555
$25$	5572.11	1.78307
$26$	−9557.66	−2.77280
$27$	729.000	0.192450
$28$	11680.7	2.81561
$29$	3695.02	0.815872	0.407936	−	0.913010i	$-0.366249\pi$
$29$	3695.02	0.815872	0.407936	+	0.913010i	$0.366249\pi$
$30$	8789.82	1.78310
$31$	7722.71	1.44333	0.721665	−	0.692242i	$-0.243377\pi$
$31$	7722.71	1.44333	0.721665	+	0.692242i	$0.243377\pi$
$32$	−11122.2	−1.92006
$33$	−2282.55	−0.364868
$34$	0	0
$35$	−14024.4	−1.93515
$36$	6291.52	0.809095
$37$	−16436.2	−1.97377	−0.986885	−	0.161423i	$-0.948392\pi$
$37$	−16436.2	−1.97377	−0.986885	+	0.161423i	$0.948392\pi$
$38$	8040.13	0.903242
$39$	8213.80	0.864734
$40$	44606.5	4.40807
$41$	−2824.85	−0.262443	−0.131222	−	0.991353i	$-0.541890\pi$
$41$	−2824.85	−0.262443	−0.131222	+	0.991353i	$0.541890\pi$
$42$	−14173.9	−1.23984
$43$	5982.85	0.493443	0.246721	−	0.969086i	$-0.420647\pi$
$43$	5982.85	0.493443	0.246721	+	0.969086i	$0.420647\pi$
$44$	−19699.2	−1.53397
$45$	−7553.92	−0.556085
$46$	−38169.9	−2.65966
$47$	3780.24	0.249618	0.124809	−	0.992181i	$-0.460168\pi$
$47$	3780.24	0.249618	0.124809	+	0.992181i	$0.460168\pi$
$48$	22712.2	1.42284
$49$	5807.84	0.345561
$50$	−58353.9	−3.30099
$51$	0	0
$52$	70887.9	3.63550
$53$	−9717.51	−0.475188	−0.237594	−	0.971365i	$-0.576359\pi$
$53$	−9717.51	−0.475188	−0.237594	+	0.971365i	$0.576359\pi$
$54$	−7634.45	−0.356281
$55$	23651.9	1.05429
$56$	−71929.6	−3.06505
$57$	−6909.64	−0.281688
$58$	−38696.1	−1.51042
$59$	26246.6	0.981621	0.490810	−	0.871266i	$-0.336701\pi$
$59$	26246.6	0.981621	0.490810	+	0.871266i	$0.336701\pi$
$60$	−65193.0	−2.33788
$61$	40220.5	1.38396	0.691978	−	0.721918i	$-0.256739\pi$
$61$	40220.5	1.38396	0.691978	+	0.721918i	$0.256739\pi$
$62$	−80876.1	−2.67203
$63$	12181.0	0.386661
$64$	35722.3	1.09016
$65$	−85111.6	−2.49865
$66$	23904.0	0.675477
$67$	20484.7	0.557498	0.278749	−	0.960364i	$-0.410080\pi$
$67$	20484.7	0.557498	0.278749	+	0.960364i	$0.410080\pi$
$68$	0	0
$69$	32803.0	0.829451
$70$	146870.	3.58252
$71$	−26823.2	−0.631487	−0.315744	−	0.948845i	$-0.602254\pi$
$71$	−26823.2	−0.631487	−0.315744	+	0.948845i	$0.602254\pi$
$72$	−38743.2	−0.880774
$73$	−59383.0	−1.30423	−0.652116	−	0.758119i	$-0.726119\pi$
$73$	−59383.0	−1.30423	−0.652116	+	0.758119i	$0.726119\pi$
$74$	172128.	3.65403
$75$	50149.0	1.02946
$76$	−59632.6	−1.18427
$77$	−38139.5	−0.733074
$78$	−86018.9	−1.60088
$79$	−2230.75	−0.0402145	−0.0201073	−	0.999798i	$-0.506401\pi$
$79$	−2230.75	−0.0402145	−0.0201073	+	0.999798i	$0.506401\pi$
$80$	−235344.	−4.11129
$81$	6561.00	0.111111
$82$	29583.2	0.485859
$83$	112050.	1.78533	0.892663	−	0.450724i	$-0.148834\pi$
$83$	112050.	1.78533	0.892663	+	0.450724i	$0.148834\pi$
$84$	105126.	1.62559
$85$	0	0
$86$	−62655.3	−0.913507
$87$	33255.2	0.471044
$88$	121308.	1.66987
$89$	10335.3	0.138308	0.0691539	−	0.997606i	$-0.477970\pi$
$89$	10335.3	0.138308	0.0691539	+	0.997606i	$0.477970\pi$
$90$	79108.4	1.02948
$91$	137246.	1.73738
$92$	283101.	3.48716
$93$	69504.4	0.833307
$94$	−39588.6	−0.462115
$95$	71597.9	0.813938
$96$	−100099.	−1.10854
$97$	137302.	1.48165	0.740826	−	0.671697i	$-0.234434\pi$
$97$	137302.	1.48165	0.740826	+	0.671697i	$0.234434\pi$
$98$	−60822.5	−0.639734
$99$	−20542.9	−0.210656
$100$	432803.	4.32803
$101$	105837.	1.03237	0.516184	−	0.856478i	$-0.327352\pi$
$101$	105837.	1.03237	0.516184	+	0.856478i	$0.327352\pi$
$102$	0	0
$103$	−110831.	−1.02936	−0.514680	−	0.857383i	$-0.672089\pi$
$103$	−110831.	−1.02936	−0.514680	+	0.857383i	$0.672089\pi$
$104$	−436528.	−3.95757
$105$	−126220.	−1.11726
$106$	101767.	0.879712
$107$	−85632.8	−0.723071	−0.361535	−	0.932358i	$-0.617747\pi$
$107$	−85632.8	−0.723071	−0.361535	+	0.932358i	$0.617747\pi$
$108$	56623.7	0.467131
$109$	−175968.	−1.41863	−0.709314	−	0.704893i	$-0.750995\pi$
$109$	−175968.	−1.41863	−0.709314	+	0.704893i	$0.750995\pi$
$110$	−247694.	−1.95179
$111$	−147926.	−1.13956
$112$	379501.	2.85870
$113$	−53689.9	−0.395546	−0.197773	−	0.980248i	$-0.563371\pi$
$113$	−53689.9	−0.395546	−0.197773	+	0.980248i	$0.563371\pi$
$114$	72361.2	0.521487
$115$	−339906.	−2.39670
$116$	287004.	1.98035
$117$	73924.2	0.499254
$118$	−274868.	−1.81727
$119$	0	0
$120$	401459.	2.54500
$121$	−96729.6	−0.600615
$122$	−421208.	−2.56211
$123$	−25423.6	−0.151522
$124$	599847.	3.50337
$125$	−228213.	−1.30637
$126$	−127565.	−0.715823
$127$	−109323.	−0.601452	−0.300726	−	0.953711i	$-0.597229\pi$
$127$	−109323.	−0.601452	−0.300726	+	0.953711i	$0.597229\pi$
$128$	−18192.4	−0.0981443
$129$	53845.6	0.284889
$130$	891331.	4.62573
$131$	−69127.1	−0.351941	−0.175971	−	0.984395i	$-0.556306\pi$
$131$	−69127.1	−0.351941	−0.175971	+	0.984395i	$0.556306\pi$
$132$	−177293.	−0.885638
$133$	−115454.	−0.565953
$134$	−214526.	−1.03209
$135$	−67985.3	−0.321056
$136$	0	0
$137$	−81966.3	−0.373107	−0.186554	−	0.982445i	$-0.559732\pi$
$137$	−81966.3	−0.373107	−0.186554	+	0.982445i	$0.559732\pi$
$138$	−343529.	−1.53556
$139$	167072.	0.733442	0.366721	−	0.930331i	$-0.380480\pi$
$139$	167072.	0.733442	0.366721	+	0.930331i	$0.380480\pi$
$140$	−1.08932e6	−4.69715
$141$	34022.2	0.144117
$142$	280906.	1.16907
$143$	−231462.	−0.946540
$144$	204410.	0.821476
$145$	−344592.	−1.36108
$146$	621888.	2.41452
$147$	52270.5	0.199509
$148$	−1.27665e6	−4.79090
$149$	90875.4	0.335336	0.167668	−	0.985843i	$-0.446376\pi$
$149$	90875.4	0.335336	0.167668	+	0.985843i	$0.446376\pi$
$150$	−525185.	−1.90583
$151$	−341778.	−1.21984	−0.609919	−	0.792464i	$-0.708798\pi$
$151$	−341778.	−1.21984	−0.609919	+	0.792464i	$0.708798\pi$
$152$	367218.	1.28918
$153$	0	0
$154$	399415.	1.35713
$155$	−720207.	−2.40784
$156$	637991.	2.09896
$157$	75628.8	0.244871	0.122436	−	0.992476i	$-0.460929\pi$
$157$	75628.8	0.244871	0.122436	+	0.992476i	$0.460929\pi$
$158$	23361.5	0.0744489
$159$	−87457.6	−0.274350
$160$	1.03723e6	3.20314
$161$	548110.	1.66649
$162$	−68710.0	−0.205699
$163$	−319378.	−0.941533	−0.470767	−	0.882258i	$-0.656023\pi$
$163$	−319378.	−0.941533	−0.470767	+	0.882258i	$0.656023\pi$
$164$	−219415.	−0.637024
$165$	212867.	0.608692
$166$	−1.17345e6	−3.30516
$167$	225222.	0.624913	0.312457	−	0.949932i	$-0.398848\pi$
$167$	225222.	0.624913	0.312457	+	0.949932i	$0.398848\pi$
$168$	−647366.	−1.76961
$169$	461626.	1.24329
$170$	0	0
$171$	−62186.8	−0.162633
$172$	464707.	1.19773
$173$	−160296.	−0.407199	−0.203599	−	0.979054i	$-0.565264\pi$
$173$	−160296.	−0.407199	−0.203599	+	0.979054i	$0.565264\pi$
$174$	−348265.	−0.872041
$175$	837946.	2.06834
$176$	−640021.	−1.55744
$177$	236220.	0.566739
$178$	−108236.	−0.256048
$179$	−109228.	−0.254800	−0.127400	−	0.991851i	$-0.540663\pi$
$179$	−109228.	−0.254800	−0.127400	+	0.991851i	$0.540663\pi$
$180$	−586737.	−1.34978
$181$	−186068.	−0.422159	−0.211080	−	0.977469i	$-0.567698\pi$
$181$	−186068.	−0.422159	−0.211080	+	0.977469i	$0.567698\pi$
$182$	−1.43730e6	−3.21640
$183$	361984.	0.799028
$184$	−1.74334e6	−3.79610
$185$	1.53281e6	3.29275
$186$	−727885.	−1.54270
$187$	0	0
$188$	293623.	0.605893
$189$	109629.	0.223239
$190$	−749809.	−1.50684
$191$	−146849.	−0.291265	−0.145633	−	0.989339i	$-0.546522\pi$
$191$	−146849.	−0.291265	−0.145633	+	0.989339i	$0.546522\pi$
$192$	321500.	0.629402
$193$	−841804.	−1.62674	−0.813370	−	0.581747i	$-0.802369\pi$
$193$	−841804.	−1.62674	−0.813370	+	0.581747i	$0.802369\pi$
$194$	−1.43789e6	−2.74297
$195$	−766005.	−1.44260
$196$	451113.	0.838774
$197$	−318712.	−0.585103	−0.292552	−	0.956250i	$-0.594504\pi$
$197$	−318712.	−0.585103	−0.292552	+	0.956250i	$0.594504\pi$
$198$	215136.	0.389987
$199$	128511.	0.230043	0.115021	−	0.993363i	$-0.463306\pi$
$199$	128511.	0.230043	0.115021	+	0.993363i	$0.463306\pi$
$200$	−2.66520e6	−4.71146
$201$	184363.	0.321872
$202$	−1.10838e6	−1.91122
$203$	555666.	0.946398
$204$	0	0
$205$	263440.	0.437822
$206$	1.16067e6	1.90565
$207$	295227.	0.478884
$208$	2.30313e6	3.69113
$209$	194711.	0.308337
$210$	1.32183e6	2.06837
$211$	960079.	1.48457	0.742285	−	0.670084i	$-0.233742\pi$
$211$	960079.	1.48457	0.742285	+	0.670084i	$0.233742\pi$
$212$	−754789.	−1.15342
$213$	−241409.	−0.364589
$214$	896789.	1.33862
$215$	−557950.	−0.823189
$216$	−348689.	−0.508515
$217$	1.16136e6	1.67424
$218$	1.84283e6	2.62630
$219$	−534447.	−0.752999
$220$	1.83711e6	2.55905
$221$	0	0
$222$	1.54915e6	2.10965
$223$	−101009.	−0.136018	−0.0680091	−	0.997685i	$-0.521665\pi$
$223$	−101009.	−0.136018	−0.0680091	+	0.997685i	$0.521665\pi$
$224$	−1.67257e6	−2.22723
$225$	451341.	0.594358
$226$	562267.	0.732271
$227$	230560.	0.296975	0.148488	−	0.988914i	$-0.452559\pi$
$227$	230560.	0.296975	0.148488	+	0.988914i	$0.452559\pi$
$228$	−536693.	−0.683737
$229$	−607415.	−0.765415	−0.382708	−	0.923870i	$-0.625008\pi$
$229$	−607415.	−0.765415	−0.382708	+	0.923870i	$0.625008\pi$
$230$	3.55966e6	4.43700
$231$	−343255.	−0.423240
$232$	−1.76737e6	−2.15580
$233$	102906.	0.124179	0.0620897	−	0.998071i	$-0.480224\pi$
$233$	102906.	0.124179	0.0620897	+	0.998071i	$0.480224\pi$
$234$	−774170.	−0.924266
$235$	−352539.	−0.416426
$236$	2.03866e6	2.38267
$237$	−20076.7	−0.0232179
$238$	0	0
$239$	−85845.1	−0.0972122	−0.0486061	−	0.998818i	$-0.515478\pi$
$239$	−85845.1	−0.0972122	−0.0486061	+	0.998818i	$0.515478\pi$
$240$	−2.11810e6	−2.37366
$241$	496635.	0.550801	0.275401	−	0.961330i	$-0.411190\pi$
$241$	496635.	0.550801	0.275401	+	0.961330i	$0.411190\pi$
$242$	1.01300e6	1.11191
$243$	59049.0	0.0641500
$244$	3.12405e6	3.35926
$245$	−541629.	−0.576483
$246$	266249.	0.280511
$247$	−700671.	−0.730755
$248$	−3.69386e6	−3.81374
$249$	1.00845e6	1.03076
$250$	2.38996e6	2.41847
$251$	1.33966e6	1.34218	0.671089	−	0.741377i	$-0.265827\pi$
$251$	1.33966e6	1.34218	0.671089	+	0.741377i	$0.265827\pi$
$252$	946134.	0.938537
$253$	−924377.	−0.907920
$254$	1.14488e6	1.11346
$255$	0	0
$256$	−952593.	−0.908463
$257$	263614.	0.248964	0.124482	−	0.992222i	$-0.460273\pi$
$257$	263614.	0.248964	0.124482	+	0.992222i	$0.460273\pi$
$258$	−563898.	−0.527414
$259$	−2.47171e6	−2.28954
$260$	−6.61089e6	−6.06494
$261$	299297.	0.271957
$262$	723933.	0.651546
$263$	−128838.	−0.114856	−0.0574280	−	0.998350i	$-0.518290\pi$
$263$	−128838.	−0.114856	−0.0574280	+	0.998350i	$0.518290\pi$
$264$	1.09177e6	0.964098
$265$	906238.	0.792734
$266$	1.20909e6	1.04775
$267$	93017.4	0.0798521
$268$	1.59111e6	1.35321
$269$	1.41408e6	1.19150	0.595750	−	0.803170i	$-0.296855\pi$
$269$	1.41408e6	1.19150	0.595750	+	0.803170i	$0.296855\pi$
$270$	711976.	0.594368
$271$	1.78727e6	1.47831	0.739156	−	0.673534i	$-0.235224\pi$
$271$	1.78727e6	1.47831	0.739156	+	0.673534i	$0.235224\pi$
$272$	0	0
$273$	1.23521e6	1.00308
$274$	858392.	0.690731
$275$	−1.41318e6	−1.12685
$276$	2.54791e6	2.01331
$277$	−200453.	−0.156969	−0.0784843	−	0.996915i	$-0.525008\pi$
$277$	−200453.	−0.156969	−0.0784843	+	0.996915i	$0.525008\pi$
$278$	−1.74966e6	−1.35782
$279$	625540.	0.481110
$280$	6.70803e6	5.11328
$281$	−1.43244e6	−1.08220	−0.541102	−	0.840957i	$-0.681993\pi$
$281$	−1.43244e6	−1.08220	−0.541102	+	0.840957i	$0.681993\pi$
$282$	−356297.	−0.266802
$283$	180366.	0.133872	0.0669358	−	0.997757i	$-0.478678\pi$
$283$	180366.	0.133872	0.0669358	+	0.997757i	$0.478678\pi$
$284$	−2.08344e6	−1.53280
$285$	644381.	0.469927
$286$	2.42398e6	1.75232
$287$	−424807.	−0.304430
$288$	−900894.	−0.640019
$289$	0	0
$290$	3.60873e6	2.51976
$291$	1.23571e6	0.855432
$292$	−4.61246e6	−3.16574
$293$	1.98770e6	1.35264	0.676321	−	0.736607i	$-0.263573\pi$
$293$	1.98770e6	1.35264	0.676321	+	0.736607i	$0.263573\pi$
$294$	−547403.	−0.369350
$295$	−2.44772e6	−1.63759
$296$	7.86162e6	5.21534
$297$	−184887.	−0.121623
$298$	−951692.	−0.620806
$299$	3.32639e6	2.15176
$300$	3.89523e6	2.49879
$301$	899715.	0.572385
$302$	3.57927e6	2.25828
$303$	952534.	0.596038
$304$	−1.93744e6	−1.20239
$305$	−3.75089e6	−2.30879
$306$	0	0
$307$	77377.9	0.0468566	0.0234283	−	0.999726i	$-0.492542\pi$
$307$	77377.9	0.0468566	0.0234283	+	0.999726i	$0.492542\pi$
$308$	−2.96241e6	−1.77938
$309$	−997476.	−0.594301
$310$	7.54236e6	4.45762
$311$	2.37721e6	1.39369	0.696846	−	0.717221i	$-0.254586\pi$
$311$	2.37721e6	1.39369	0.696846	+	0.717221i	$0.254586\pi$
$312$	−3.92875e6	−2.28491
$313$	2.78643e6	1.60764	0.803818	−	0.594876i	$-0.202799\pi$
$313$	2.78643e6	1.60764	0.803818	+	0.594876i	$0.202799\pi$
$314$	−792022.	−0.453329
$315$	−1.13598e6	−0.645049
$316$	−173269.	−0.0976121
$317$	−2.91813e6	−1.63101	−0.815504	−	0.578752i	$-0.803540\pi$
$317$	−2.91813e6	−1.63101	−0.815504	+	0.578752i	$0.803540\pi$
$318$	915899.	0.507902
$319$	−937120.	−0.515606
$320$	−3.33140e6	−1.81866
$321$	−770696.	−0.417465
$322$	−5.74008e6	−3.08516
$323$	0	0
$324$	509613.	0.269698
$325$	5.08535e6	2.67062
$326$	3.34468e6	1.74305
$327$	−1.58372e6	−0.819045
$328$	1.35116e6	0.693459
$329$	568482.	0.289552
$330$	−2.22925e6	−1.12687
$331$	2.29970e6	1.15372	0.576862	−	0.816842i	$-0.304277\pi$
$331$	2.29970e6	1.15372	0.576862	+	0.816842i	$0.304277\pi$
$332$	8.70330e6	4.33350
$333$	−1.33133e6	−0.657924
$334$	−2.35864e6	−1.15690
$335$	−1.91037e6	−0.930049
$336$	3.41551e6	1.65047
$337$	1.07589e6	0.516049	0.258025	−	0.966138i	$-0.416928\pi$
$337$	1.07589e6	0.516049	0.258025	+	0.966138i	$0.416928\pi$
$338$	−4.83438e6	−2.30170
$339$	−483209.	−0.228368
$340$	0	0
$341$	−1.95861e6	−0.912141
$342$	651251.	0.301081
$343$	−1.65408e6	−0.759139
$344$	−2.86167e6	−1.30384
$345$	−3.05915e6	−1.38374
$346$	1.67869e6	0.753844
$347$	−2.83423e6	−1.26361	−0.631803	−	0.775129i	$-0.717685\pi$
$347$	−2.83423e6	−1.26361	−0.631803	+	0.775129i	$0.717685\pi$
$348$	2.58304e6	1.14336
$349$	2.59840e6	1.14194	0.570970	−	0.820971i	$-0.306567\pi$
$349$	2.59840e6	1.14194	0.570970	+	0.820971i	$0.306567\pi$
$350$	−8.77539e6	−3.82910
$351$	665318.	0.288245
$352$	2.82076e6	1.21342
$353$	2.28314e6	0.975203	0.487601	−	0.873066i	$-0.337872\pi$
$353$	2.28314e6	0.975203	0.487601	+	0.873066i	$0.337872\pi$
$354$	−2.47381e6	−1.04920
$355$	2.50149e6	1.05348
$356$	802773.	0.335713
$357$	0	0
$358$	1.14389e6	0.471710
$359$	1.26290e6	0.517170	0.258585	−	0.965989i	$-0.416744\pi$
$359$	1.26290e6	0.517170	0.258585	+	0.965989i	$0.416744\pi$
$360$	3.61313e6	1.46936
$361$	−1.88668e6	−0.761956
$362$	1.94860e6	0.781540
$363$	−870566.	−0.346765
$364$	1.06603e7	4.21712
$365$	5.53796e6	2.17579
$366$	−3.79088e6	−1.47923
$367$	2.93897e6	1.13901	0.569507	−	0.821986i	$-0.307134\pi$
$367$	2.93897e6	1.13901	0.569507	+	0.821986i	$0.307134\pi$
$368$	9.19787e6	3.54053
$369$	−228813.	−0.0874810
$370$	−1.60523e7	−6.09585
$371$	−1.46134e6	−0.551210
$372$	5.39863e6	2.02267
$373$	3.02229e6	1.12477	0.562385	−	0.826875i	$-0.309884\pi$
$373$	3.02229e6	1.12477	0.562385	+	0.826875i	$0.309884\pi$
$374$	0	0
$375$	−2.05392e6	−0.754232
$376$	−1.80813e6	−0.659570
$377$	3.37224e6	1.22198
$378$	−1.14809e6	−0.413280
$379$	2.79840e6	1.00072	0.500360	−	0.865818i	$-0.333201\pi$
$379$	2.79840e6	1.00072	0.500360	+	0.865818i	$0.333201\pi$
$380$	5.56123e6	1.97566
$381$	−983904.	−0.347249
$382$	1.53788e6	0.539217
$383$	3.29574e6	1.14804	0.574019	−	0.818842i	$-0.305384\pi$
$383$	3.29574e6	1.14804	0.574019	+	0.818842i	$0.305384\pi$
$384$	−163732.	−0.0566636
$385$	3.55682e6	1.22295
$386$	8.81579e6	3.01157
$387$	484611.	0.164481
$388$	1.06646e7	3.59639
$389$	4.44413e6	1.48906	0.744531	−	0.667588i	$-0.232673\pi$
$389$	4.44413e6	1.48906	0.744531	+	0.667588i	$0.232673\pi$
$390$	8.02198e6	2.67067
$391$	0	0
$392$	−2.77795e6	−0.913082
$393$	−622144.	−0.203193
$394$	3.33771e6	1.08320
$395$	208036.	0.0670881
$396$	−1.59564e6	−0.511323
$397$	−2.36455e6	−0.752960	−0.376480	−	0.926425i	$-0.622866\pi$
$397$	−2.36455e6	−0.752960	−0.376480	+	0.926425i	$0.622866\pi$
$398$	−1.34583e6	−0.425877
$399$	−1.03909e6	−0.326753
$400$	1.40616e7	4.39426
$401$	−4.91512e6	−1.52642	−0.763208	−	0.646153i	$-0.776377\pi$
$401$	−4.91512e6	−1.52642	−0.763208	+	0.646153i	$0.776377\pi$
$402$	−1.93074e6	−0.595879
$403$	7.04809e6	2.16177
$404$	8.22070e6	2.50585
$405$	−611868.	−0.185362
$406$	−5.81921e6	−1.75206
$407$	4.16849e6	1.24736
$408$	0	0
$409$	5.33098e6	1.57579	0.787896	−	0.615808i	$-0.211170\pi$
$409$	5.33098e6	1.57579	0.787896	+	0.615808i	$0.211170\pi$
$410$	−2.75888e6	−0.810537
$411$	−737697.	−0.215414
$412$	−8.60857e6	−2.49855
$413$	3.94703e6	1.13866
$414$	−3.09176e6	−0.886554
$415$	−1.04496e7	−2.97838
$416$	−1.01506e7	−2.87579
$417$	1.50364e6	0.423453
$418$	−2.03911e6	−0.570821
$419$	3.69753e6	1.02891	0.514455	−	0.857518i	$-0.327994\pi$
$419$	3.69753e6	1.02891	0.514455	+	0.857518i	$0.327994\pi$
$420$	−9.80387e6	−2.71190
$421$	662209.	0.182091	0.0910457	−	0.995847i	$-0.470979\pi$
$421$	662209.	0.182091	0.0910457	+	0.995847i	$0.470979\pi$
$422$	−1.00544e7	−2.74837
$423$	306200.	0.0832058
$424$	4.64800e6	1.25560
$425$	0	0
$426$	2.52815e6	0.674962
$427$	6.04844e6	1.60537
$428$	−6.65137e6	−1.75510
$429$	−2.08316e6	−0.546485
$430$	5.84313e6	1.52396
$431$	−7.63799e6	−1.98055	−0.990275	−	0.139122i	$-0.955572\pi$
$431$	−7.63799e6	−1.98055	−0.990275	+	0.139122i	$0.955572\pi$
$432$	1.83969e6	0.474279
$433$	−1.61173e6	−0.413117	−0.206558	−	0.978434i	$-0.566226\pi$
$433$	−1.61173e6	−0.413117	−0.206558	+	0.978434i	$0.566226\pi$
$434$	−1.21623e7	−3.09951
$435$	−3.10132e6	−0.785822
$436$	−1.36680e7	−3.44342
$437$	−2.79823e6	−0.700939
$438$	5.59699e6	1.39402
$439$	−653485.	−0.161836	−0.0809179	−	0.996721i	$-0.525785\pi$
$439$	−653485.	−0.161836	−0.0809179	+	0.996721i	$0.525785\pi$
$440$	−1.13130e7	−2.78576
$441$	470435.	0.115187
$442$	0	0
$443$	5.59496e6	1.35453	0.677264	−	0.735740i	$-0.263166\pi$
$443$	5.59496e6	1.35453	0.677264	+	0.735740i	$0.263166\pi$
$444$	−1.14898e7	−2.76603
$445$	−963850.	−0.230733
$446$	1.05781e6	0.251810
$447$	817879.	0.193607
$448$	5.37200e6	1.26456
$449$	−3.23068e6	−0.756273	−0.378137	−	0.925750i	$-0.623435\pi$
$449$	−3.23068e6	−0.756273	−0.378137	+	0.925750i	$0.623435\pi$
$450$	−4.72666e6	−1.10033
$451$	716428.	0.165856
$452$	−4.17026e6	−0.960102
$453$	−3.07600e6	−0.704273
$454$	−2.41454e6	−0.549788
$455$	−1.27993e7	−2.89839
$456$	3.30496e6	0.744311
$457$	1.23055e6	0.275618	0.137809	−	0.990459i	$-0.455994\pi$
$457$	1.23055e6	0.275618	0.137809	+	0.990459i	$0.455994\pi$
$458$	6.36115e6	1.41701
$459$	0	0
$460$	−2.64015e7	−5.81748
$461$	−3.45295e6	−0.756725	−0.378362	−	0.925658i	$-0.623513\pi$
$461$	−3.45295e6	−0.756725	−0.378362	+	0.925658i	$0.623513\pi$
$462$	3.59474e6	0.783542
$463$	2.31824e6	0.502582	0.251291	−	0.967912i	$-0.419145\pi$
$463$	2.31824e6	0.502582	0.251291	+	0.967912i	$0.419145\pi$
$464$	9.32467e6	2.01066
$465$	−6.48186e6	−1.39017
$466$	−1.07768e6	−0.229893
$467$	−131014.	−0.0277987	−0.0138994	−	0.999903i	$-0.504424\pi$
$467$	−131014.	−0.0277987	−0.0138994	+	0.999903i	$0.504424\pi$
$468$	5.74192e6	1.21183
$469$	3.08054e6	0.646689
$470$	3.69196e6	0.770926
$471$	680659.	0.141377
$472$	−1.25541e7	−2.59376
$473$	−1.51735e6	−0.311841
$474$	210254.	0.0429831
$475$	−4.27792e6	−0.869958
$476$	0	0
$477$	−787118.	−0.158396
$478$	899012.	0.179968
$479$	−4.52186e6	−0.900489	−0.450244	−	0.892905i	$-0.648663\pi$
$479$	−4.52186e6	−0.900489	−0.450244	+	0.892905i	$0.648663\pi$
$480$	9.33509e6	1.84934
$481$	−1.50004e7	−2.95624
$482$	−5.20101e6	−1.01969
$483$	4.93299e6	0.962149
$484$	−7.51329e6	−1.45786
$485$	−1.28045e7	−2.47177
$486$	−618390.	−0.118760
$487$	3.28266e6	0.627197	0.313598	−	0.949556i	$-0.398465\pi$
$487$	3.28266e6	0.627197	0.313598	+	0.949556i	$0.398465\pi$
$488$	−1.92379e7	−3.65686
$489$	−2.87440e6	−0.543595
$490$	5.67220e6	1.06724
$491$	8.99826e6	1.68444	0.842219	−	0.539136i	$-0.181249\pi$
$491$	8.99826e6	1.68444	0.842219	+	0.539136i	$0.181249\pi$
$492$	−1.97473e6	−0.367786
$493$	0	0
$494$	7.33778e6	1.35284
$495$	1.91580e6	0.351429
$496$	1.94888e7	3.55698
$497$	−4.03373e6	−0.732515
$498$	−1.05610e7	−1.90824
$499$	8.09709e6	1.45572	0.727860	−	0.685726i	$-0.240515\pi$
$499$	8.09709e6	1.45572	0.727860	+	0.685726i	$0.240515\pi$
$500$	−1.77260e7	−3.17093
$501$	2.02700e6	0.360794
$502$	−1.40296e7	−2.48476
$503$	932454.	0.164326	0.0821632	−	0.996619i	$-0.473817\pi$
$503$	932454.	0.164326	0.0821632	+	0.996619i	$0.473817\pi$
$504$	−5.82630e6	−1.02168
$505$	−9.87019e6	−1.72225
$506$	9.68053e6	1.68083
$507$	4.15464e6	0.717816
$508$	−8.49144e6	−1.45990
$509$	−9.42784e6	−1.61294	−0.806469	−	0.591276i	$-0.798624\pi$
$509$	−9.42784e6	−1.61294	−0.806469	+	0.591276i	$0.798624\pi$
$510$	0	0
$511$	−8.93015e6	−1.51289
$512$	1.05582e7	1.77998
$513$	−559681.	−0.0938960
$514$	−2.76070e6	−0.460905
$515$	1.03359e7	1.71723
$516$	4.18236e6	0.691508
$517$	−958733.	−0.157751
$518$	2.58850e7	4.23861
$519$	−1.44266e6	−0.235096
$520$	4.07099e7	6.60224
$521$	1.19440e7	1.92776	0.963882	−	0.266331i	$-0.0858114\pi$
$521$	1.19440e7	1.92776	0.963882	+	0.266331i	$0.0858114\pi$
$522$	−3.13439e6	−0.503473
$523$	−1.80911e6	−0.289208	−0.144604	−	0.989490i	$-0.546191\pi$
$523$	−1.80911e6	−0.289208	−0.144604	+	0.989490i	$0.546191\pi$
$524$	−5.36932e6	−0.854261
$525$	7.54152e6	1.19415
$526$	1.34925e6	0.212632
$527$	0	0
$528$	−5.76019e6	−0.899190
$529$	6.84807e6	1.06397
$530$	−9.49057e6	−1.46758
$531$	2.12598e6	0.327207
$532$	−8.96769e6	−1.37373
$533$	−2.57808e6	−0.393078
$534$	−974125.	−0.147830
$535$	7.98597e6	1.20627
$536$	−9.79809e6	−1.47309
$537$	−983049.	−0.147109
$538$	−1.48090e7	−2.20581
$539$	−1.47296e6	−0.218384
$540$	−5.28063e6	−0.779294
$541$	−2.48165e6	−0.364542	−0.182271	−	0.983248i	$-0.558345\pi$
$541$	−2.48165e6	−0.364542	−0.182271	+	0.983248i	$0.558345\pi$
$542$	−1.87172e7	−2.73679
$543$	−1.67462e6	−0.243734
$544$	0	0
$545$	1.64105e7	2.36663
$546$	−1.29357e7	−1.85699
$547$	−5.24279e6	−0.749194	−0.374597	−	0.927188i	$-0.622219\pi$
$547$	−5.24279e6	−0.749194	−0.374597	+	0.927188i	$0.622219\pi$
$548$	−6.36658e6	−0.905638
$549$	3.25786e6	0.461319
$550$	1.47995e7	2.08613
$551$	−2.83681e6	−0.398062
$552$	−1.56901e7	−2.19168
$553$	−335465.	−0.0466482
$554$	2.09924e6	0.290595
$555$	1.37953e7	1.90107
$556$	1.29770e7	1.78027
$557$	7.59512e6	1.03728	0.518641	−	0.854992i	$-0.326438\pi$
$557$	7.59512e6	1.03728	0.518641	+	0.854992i	$0.326438\pi$
$558$	−6.55096e6	−0.890676
$559$	5.46021e6	0.739060
$560$	−3.53916e7	−4.76903
$561$	0	0
$562$	1.50012e7	2.00348
$563$	9.64741e6	1.28274	0.641371	−	0.767231i	$-0.278366\pi$
$563$	9.64741e6	1.28274	0.641371	+	0.767231i	$0.278366\pi$
$564$	2.64261e6	0.349812
$565$	5.00703e6	0.659871
$566$	−1.88888e6	−0.247835
$567$	986658.	0.128887
$568$	1.28298e7	1.66859
$569$	−9.36617e6	−1.21278	−0.606389	−	0.795168i	$-0.707383\pi$
$569$	−9.36617e6	−1.21278	−0.606389	+	0.795168i	$0.707383\pi$
$570$	−6.74828e6	−0.869973
$571$	1.02880e7	1.32051	0.660256	−	0.751040i	$-0.270448\pi$
$571$	1.02880e7	1.32051	0.660256	+	0.751040i	$0.270448\pi$
$572$	−1.79784e7	−2.29752
$573$	−1.32164e6	−0.168162
$574$	4.44879e6	0.563588
$575$	2.03091e7	2.56166
$576$	2.89350e6	0.363386
$577$	5.81882e6	0.727605	0.363802	−	0.931476i	$-0.381478\pi$
$577$	5.81882e6	0.727605	0.363802	+	0.931476i	$0.381478\pi$
$578$	0	0
$579$	−7.57624e6	−0.939198
$580$	−2.67655e7	−3.30374
$581$	1.68504e7	2.07095
$582$	−1.29410e7	−1.58365
$583$	2.46452e6	0.300304
$584$	2.84036e7	3.44620
$585$	−6.89404e6	−0.832883
$586$	−2.08162e7	−2.50414
$587$	−5.23001e6	−0.626480	−0.313240	−	0.949674i	$-0.601414\pi$
$587$	−5.23001e6	−0.626480	−0.313240	+	0.949674i	$0.601414\pi$
$588$	4.06001e6	0.484266
$589$	−5.92902e6	−0.704198
$590$	2.56337e7	3.03167
$591$	−2.86840e6	−0.337809
$592$	−4.14779e7	−4.86422
$593$	2.07154e6	0.241911	0.120956	−	0.992658i	$-0.461404\pi$
$593$	2.07154e6	0.241911	0.120956	+	0.992658i	$0.461404\pi$
$594$	1.93622e6	0.225159
$595$	0	0
$596$	7.05858e6	0.813957
$597$	1.15660e6	0.132815
$598$	−3.48355e7	−3.98354
$599$	7.34545e6	0.836472	0.418236	−	0.908338i	$-0.362649\pi$
$599$	7.34545e6	0.836472	0.418236	+	0.908338i	$0.362649\pi$
$600$	−2.39868e7	−2.72016
$601$	−1.30755e7	−1.47663	−0.738314	−	0.674458i	$-0.764378\pi$
$601$	−1.30755e7	−1.47663	−0.738314	+	0.674458i	$0.764378\pi$
$602$	−9.42226e6	−1.05965
$603$	1.65926e6	0.185833
$604$	−2.65470e7	−2.96089
$605$	9.02084e6	1.00198
$606$	−9.97541e6	−1.10344
$607$	−877223.	−0.0966359	−0.0483180	−	0.998832i	$-0.515386\pi$
$607$	−877223.	−0.0966359	−0.0483180	+	0.998832i	$0.515386\pi$
$608$	8.53890e6	0.936791
$609$	5.00100e6	0.546403
$610$	3.92812e7	4.27425
$611$	3.45002e6	0.373868
$612$	0	0
$613$	1.65349e7	1.77725	0.888627	−	0.458631i	$-0.151660\pi$
$613$	1.65349e7	1.77725	0.888627	+	0.458631i	$0.151660\pi$
$614$	−810339.	−0.0867453
$615$	2.37096e6	0.252777
$616$	1.82425e7	1.93702
$617$	−437456.	−0.0462616	−0.0231308	−	0.999732i	$-0.507363\pi$
$617$	−437456.	−0.0462616	−0.0231308	+	0.999732i	$0.507363\pi$
$618$	1.04461e7	1.10023
$619$	2.29678e6	0.240931	0.120466	−	0.992717i	$-0.461561\pi$
$619$	2.29678e6	0.240931	0.120466	+	0.992717i	$0.461561\pi$
$620$	−5.59407e7	−5.84452
$621$	2.65704e6	0.276484
$622$	−2.48953e7	−2.58013
$623$	1.55424e6	0.160435
$624$	2.07281e7	2.13107
$625$	3.86992e6	0.396280
$626$	−2.91809e7	−2.97620
$627$	1.75240e6	0.178018
$628$	5.87433e6	0.594373
$629$	0	0
$630$	1.18965e7	1.19417
$631$	8.14726e6	0.814588	0.407294	−	0.913297i	$-0.366472\pi$
$631$	8.14726e6	0.814588	0.407294	+	0.913297i	$0.366472\pi$
$632$	1.06699e6	0.106260
$633$	8.64071e6	0.857117
$634$	3.05601e7	3.01947
$635$	1.01952e7	1.00338
$636$	−6.79310e6	−0.665925
$637$	5.30049e6	0.517568
$638$	9.81398e6	0.954538
$639$	−2.17268e6	−0.210496
$640$	1.69659e6	0.163730
$641$	−4.61597e6	−0.443729	−0.221864	−	0.975078i	$-0.571214\pi$
$641$	−4.61597e6	−0.443729	−0.221864	+	0.975078i	$0.571214\pi$
$642$	8.07111e6	0.772850
$643$	7.29909e6	0.696212	0.348106	−	0.937455i	$-0.386825\pi$
$643$	7.29909e6	0.696212	0.348106	+	0.937455i	$0.386825\pi$
$644$	4.25734e7	4.04505
$645$	−5.02155e6	−0.475268
$646$	0	0
$647$	−8.68678e6	−0.815827	−0.407913	−	0.913021i	$-0.633743\pi$
$647$	−8.68678e6	−0.815827	−0.407913	+	0.913021i	$0.633743\pi$
$648$	−3.13820e6	−0.293591
$649$	−6.65659e6	−0.620354
$650$	−5.32563e7	−4.94410
$651$	1.04522e7	0.966622
$652$	−2.48071e7	−2.28537
$653$	1.62841e6	0.149445	0.0747226	−	0.997204i	$-0.476193\pi$
$653$	1.62841e6	0.149445	0.0747226	+	0.997204i	$0.476193\pi$
$654$	1.65855e7	1.51629
$655$	6.44667e6	0.587127
$656$	−7.12871e6	−0.646772
$657$	−4.81002e6	−0.434744
$658$	−5.95342e6	−0.536046
$659$	1.60842e7	1.44273	0.721366	−	0.692554i	$-0.243515\pi$
$659$	1.60842e7	1.44273	0.721366	+	0.692554i	$0.243515\pi$
$660$	1.65340e7	1.47747
$661$	3.26756e6	0.290884	0.145442	−	0.989367i	$-0.453540\pi$
$661$	3.26756e6	0.290884	0.145442	+	0.989367i	$0.453540\pi$
$662$	−2.40836e7	−2.13588
$663$	0	0
$664$	−5.35949e7	−4.71741
$665$	1.07671e7	0.944154
$666$	1.39424e7	1.21801
$667$	1.34675e7	1.17212
$668$	1.74937e7	1.51684
$669$	−909079.	−0.0785302
$670$	2.00064e7	1.72179
$671$	−1.02006e7	−0.874618
$672$	−1.50532e7	−1.28589
$673$	4.53424e6	0.385893	0.192946	−	0.981209i	$-0.438196\pi$
$673$	4.53424e6	0.385893	0.192946	+	0.981209i	$0.438196\pi$
$674$	−1.12672e7	−0.955359
$675$	4.06207e6	0.343153
$676$	3.58559e7	3.01783
$677$	1.19188e7	0.999453	0.499727	−	0.866183i	$-0.333434\pi$
$677$	1.19188e7	0.999453	0.499727	+	0.866183i	$0.333434\pi$
$678$	5.06041e6	0.422777
$679$	2.06477e7	1.71869
$680$	0	0
$681$	2.07504e6	0.171459
$682$	2.05115e7	1.68864
$683$	−2.82866e6	−0.232022	−0.116011	−	0.993248i	$-0.537011\pi$
$683$	−2.82866e6	−0.232022	−0.116011	+	0.993248i	$0.537011\pi$
$684$	−4.83024e6	−0.394756
$685$	7.64404e6	0.622438
$686$	1.73223e7	1.40539
$687$	−5.46674e6	−0.441913
$688$	1.50982e7	1.21605
$689$	−8.86862e6	−0.711718
$690$	3.20370e7	2.56170
$691$	−1.04051e7	−0.828991	−0.414496	−	0.910051i	$-0.636042\pi$
$691$	−1.04051e7	−0.828991	−0.414496	+	0.910051i	$0.636042\pi$
$692$	−1.24507e7	−0.988387
$693$	−3.08930e6	−0.244358
$694$	2.96815e7	2.33931
$695$	−1.55808e7	−1.22357
$696$	−1.59064e7	−1.24465
$697$	0	0
$698$	−2.72118e7	−2.11406
$699$	926151.	0.0716950
$700$	6.50859e7	5.02044
$701$	−1.27561e7	−0.980441	−0.490221	−	0.871598i	$-0.663084\pi$
$701$	−1.27561e7	−0.980441	−0.490221	+	0.871598i	$0.663084\pi$
$702$	−6.96753e6	−0.533625
$703$	1.26187e7	0.962999
$704$	−9.05976e6	−0.688946
$705$	−3.17285e6	−0.240423
$706$	−2.39101e7	−1.80539
$707$	1.59160e7	1.19753
$708$	1.83479e7	1.37564
$709$	7.59269e6	0.567257	0.283629	−	0.958934i	$-0.408462\pi$
$709$	7.59269e6	0.567257	0.283629	+	0.958934i	$0.408462\pi$
$710$	−2.61968e7	−1.95030
$711$	−180691.	−0.0134048
$712$	−4.94348e6	−0.365454
$713$	2.81476e7	2.07356
$714$	0	0
$715$	2.15857e7	1.57907
$716$	−8.48405e6	−0.618473
$717$	−772606.	−0.0561255
$718$	−1.32257e7	−0.957433
$719$	−1.90858e7	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$719$	−1.90858e7	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$720$	−1.90629e7	−1.37043
$721$	−1.66670e7	−1.19404
$722$	1.97582e7	1.41060
$723$	4.46972e6	0.318005
$724$	−1.44525e7	−1.02470
$725$	2.05891e7	1.45476
$726$	9.11700e6	0.641964
$727$	2.70782e7	1.90013	0.950066	−	0.312051i	$-0.101016\pi$
$727$	2.70782e7	1.90013	0.950066	+	0.312051i	$0.101016\pi$
$728$	−6.56461e7	−4.59072
$729$	531441.	0.0370370
$730$	−5.79962e7	−4.02803
$731$	0	0
$732$	2.81164e7	1.93947
$733$	−8.82069e6	−0.606377	−0.303188	−	0.952931i	$-0.598051\pi$
$733$	−8.82069e6	−0.606377	−0.303188	+	0.952931i	$0.598051\pi$
$734$	−3.07783e7	−2.10865
$735$	−4.87466e6	−0.332833
$736$	−4.05378e7	−2.75845
$737$	−5.19527e6	−0.352322
$738$	2.39624e6	0.161953
$739$	341575.	0.0230078	0.0115039	−	0.999934i	$-0.496338\pi$
$739$	341575.	0.0230078	0.0115039	+	0.999934i	$0.496338\pi$
$740$	1.19058e8	7.99245
$741$	−6.30604e6	−0.421902
$742$	1.53039e7	1.02045
$743$	4.99443e6	0.331905	0.165952	−	0.986134i	$-0.446930\pi$
$743$	4.99443e6	0.331905	0.165952	+	0.986134i	$0.446930\pi$
$744$	−3.32448e7	−2.20187
$745$	−8.47489e6	−0.559427
$746$	−3.16509e7	−2.08228
$747$	9.07607e6	0.595109
$748$	0	0
$749$	−1.28777e7	−0.838750
$750$	2.15096e7	1.39630
$751$	−8.56359e6	−0.554059	−0.277030	−	0.960861i	$-0.589350\pi$
$751$	−8.56359e6	−0.554059	−0.277030	+	0.960861i	$0.589350\pi$
$752$	9.53973e6	0.615165
$753$	1.20569e7	0.774907
$754$	−3.53158e7	−2.26225
$755$	3.18736e7	2.03500
$756$	8.51520e6	0.541864
$757$	−1.35001e7	−0.856241	−0.428120	−	0.903722i	$-0.640824\pi$
$757$	−1.35001e7	−0.856241	−0.428120	+	0.903722i	$0.640824\pi$
$758$	−2.93063e7	−1.85262
$759$	−8.31939e6	−0.524188
$760$	−3.42461e7	−2.15069
$761$	−2.63436e7	−1.64898	−0.824488	−	0.565880i	$-0.808537\pi$
$761$	−2.63436e7	−1.64898	−0.824488	+	0.565880i	$0.808537\pi$
$762$	1.03039e7	0.642859
$763$	−2.64625e7	−1.64558
$764$	−1.14062e7	−0.706983
$765$	0	0
$766$	−3.45146e7	−2.12535
$767$	2.39538e7	1.47024
$768$	−8.57334e6	−0.524502
$769$	−1.82395e7	−1.11224	−0.556118	−	0.831103i	$-0.687710\pi$
$769$	−1.82395e7	−1.11224	−0.556118	+	0.831103i	$0.687710\pi$
$770$	−3.72488e7	−2.26405
$771$	2.37253e6	0.143739
$772$	−6.53856e7	−3.94856
$773$	5.51471e6	0.331951	0.165976	−	0.986130i	$-0.446923\pi$
$773$	5.51471e6	0.331951	0.165976	+	0.986130i	$0.446923\pi$
$774$	−5.07508e6	−0.304502
$775$	4.30318e7	2.57357
$776$	−6.56729e7	−3.91500
$777$	−2.22454e7	−1.32187
$778$	−4.65411e7	−2.75669
$779$	2.16874e6	0.128045
$780$	−5.94980e7	−3.50159
$781$	6.80281e6	0.399081
$782$	0	0
$783$	2.69367e6	0.157015
$784$	1.46565e7	0.851609
$785$	−7.05301e6	−0.408508
$786$	6.51540e6	0.376170
$787$	2.58185e7	1.48592	0.742959	−	0.669337i	$-0.233422\pi$
$787$	2.58185e7	1.48592	0.742959	+	0.669337i	$0.233422\pi$
$788$	−2.47553e7	−1.42021
$789$	−1.15954e6	−0.0663121
$790$	−2.17865e6	−0.124200
$791$	−8.07401e6	−0.458826
$792$	9.82593e6	0.556622
$793$	3.67070e7	2.07284
$794$	2.47627e7	1.39395
$795$	8.15614e6	0.457685
$796$	9.98188e6	0.558379
$797$	1.07961e7	0.602033	0.301017	−	0.953619i	$-0.402674\pi$
$797$	1.07961e7	0.602033	0.301017	+	0.953619i	$0.402674\pi$
$798$	1.08818e7	0.604916
$799$	0	0
$800$	−6.19738e7	−3.42360
$801$	837157.	0.0461026
$802$	5.14735e7	2.82584
$803$	1.50605e7	0.824235
$804$	1.43200e7	0.781275
$805$	−5.11158e7	−2.78013
$806$	−7.38111e7	−4.00206
$807$	1.27267e7	0.687912
$808$	−5.06231e7	−2.72785
$809$	−3.30006e7	−1.77276	−0.886380	−	0.462958i	$-0.846788\pi$
$809$	−3.30006e7	−1.77276	−0.886380	+	0.462958i	$0.846788\pi$
$810$	6.40778e6	0.343159
$811$	1.85573e7	0.990748	0.495374	−	0.868680i	$-0.335031\pi$
$811$	1.85573e7	0.990748	0.495374	+	0.868680i	$0.335031\pi$
$812$	4.31603e7	2.29718
$813$	1.60854e7	0.853504
$814$	−4.36545e7	−2.30923
$815$	2.97846e7	1.57072
$816$	0	0
$817$	−4.59326e6	−0.240750
$818$	−5.58287e7	−2.91725
$819$	1.11169e7	0.579126
$820$	2.04622e7	1.06272
$821$	−2.02654e6	−0.104929	−0.0524647	−	0.998623i	$-0.516708\pi$
$821$	−2.02654e6	−0.104929	−0.0524647	+	0.998623i	$0.516708\pi$
$822$	7.72553e6	0.398794
$823$	1.08486e7	0.558309	0.279155	−	0.960246i	$-0.409946\pi$
$823$	1.08486e7	0.558309	0.279155	+	0.960246i	$0.409946\pi$
$824$	5.30116e7	2.71990
$825$	−1.27186e7	−0.650586
$826$	−4.13353e7	−2.10800
$827$	−1.19289e7	−0.606506	−0.303253	−	0.952910i	$-0.598073\pi$
$827$	−1.19289e7	−0.606506	−0.303253	+	0.952910i	$0.598073\pi$
$828$	2.29312e7	1.16239
$829$	1.23292e7	0.623086	0.311543	−	0.950232i	$-0.399154\pi$
$829$	1.23292e7	0.623086	0.311543	+	0.950232i	$0.399154\pi$
$830$	1.09434e8	5.51385
$831$	−1.80408e6	−0.0906259
$832$	3.26017e7	1.63280
$833$	0	0
$834$	−1.57469e7	−0.783935
$835$	−2.10038e7	−1.04251
$836$	1.51238e7	0.748421
$837$	5.62986e6	0.277769
$838$	−3.87224e7	−1.90481
$839$	−3.09681e7	−1.51883	−0.759415	−	0.650607i	$-0.774515\pi$
$839$	−3.09681e7	−1.51883	−0.759415	+	0.650607i	$0.774515\pi$
$840$	6.03723e7	2.95216
$841$	−6.85795e6	−0.334352
$842$	−6.93497e6	−0.337105
$843$	−1.28919e7	−0.624811
$844$	7.45723e7	3.60347
$845$	−4.30505e7	−2.07413
$846$	−3.20667e6	−0.154038
$847$	−1.45464e7	−0.696703
$848$	−2.45229e7	−1.17107
$849$	1.62329e6	0.0772908
$850$	0	0
$851$	−5.99062e7	−2.83562
$852$	−1.87510e7	−0.884963
$853$	1.32944e7	0.625601	0.312800	−	0.949819i	$-0.398733\pi$
$853$	1.32944e7	0.625601	0.312800	+	0.949819i	$0.398733\pi$
$854$	−6.33423e7	−2.97200
$855$	5.79943e6	0.271313
$856$	4.09592e7	1.91059
$857$	2.13174e7	0.991475	0.495737	−	0.868472i	$-0.334898\pi$
$857$	2.13174e7	0.991475	0.495737	+	0.868472i	$0.334898\pi$
$858$	2.18158e7	1.01170
$859$	2.78369e7	1.28718	0.643588	−	0.765372i	$-0.277445\pi$
$859$	2.78369e7	1.28718	0.643588	+	0.765372i	$0.277445\pi$
$860$	−4.33377e7	−1.99811
$861$	−3.82326e6	−0.175762
$862$	7.99888e7	3.66658
$863$	−3.02799e7	−1.38397	−0.691986	−	0.721911i	$-0.743264\pi$
$863$	−3.02799e7	−1.38397	−0.691986	+	0.721911i	$0.743264\pi$
$864$	−8.10805e6	−0.369515
$865$	1.49489e7	0.679311
$866$	1.68788e7	0.764800
$867$	0	0
$868$	9.02064e7	4.06385
$869$	565755.	0.0254144
$870$	3.24786e7	1.45479
$871$	1.86953e7	0.835000
$872$	8.41677e7	3.74847
$873$	1.11214e7	0.493884
$874$	2.93045e7	1.29764
$875$	−3.43192e7	−1.51536
$876$	−4.15122e7	−1.82774
$877$	−4.00270e7	−1.75734	−0.878668	−	0.477434i	$-0.841567\pi$
$877$	−4.00270e7	−1.75734	−0.878668	+	0.477434i	$0.841567\pi$
$878$	6.84362e6	0.299605
$879$	1.78893e7	0.780948
$880$	5.96872e7	2.59821
$881$	−4.34972e7	−1.88809	−0.944044	−	0.329821i	$-0.893012\pi$
$881$	−4.34972e7	−1.88809	−0.944044	+	0.329821i	$0.893012\pi$
$882$	−4.92662e6	−0.213245
$883$	4.60169e6	0.198617	0.0993083	−	0.995057i	$-0.468337\pi$
$883$	4.60169e6	0.198617	0.0993083	+	0.995057i	$0.468337\pi$
$884$	0	0
$885$	−2.20295e7	−0.945465
$886$	−5.85932e7	−2.50763
$887$	−3.85846e7	−1.64666	−0.823332	−	0.567560i	$-0.807888\pi$
$887$	−3.85846e7	−1.64666	−0.823332	+	0.567560i	$0.807888\pi$
$888$	7.07546e7	3.01108
$889$	−1.64402e7	−0.697674
$890$	1.00939e7	0.427154
$891$	−1.66398e6	−0.0702188
$892$	−7.84567e6	−0.330155
$893$	−2.90224e6	−0.121788
$894$	−8.56523e6	−0.358423
$895$	1.01864e7	0.425072
$896$	−2.73581e6	−0.113846
$897$	2.99375e7	1.24232
$898$	3.38333e7	1.40008
$899$	2.85356e7	1.17757
$900$	3.50570e7	1.44268
$901$	0	0
$902$	−7.50279e6	−0.307048
$903$	8.09743e6	0.330467
$904$	2.56805e7	1.04516
$905$	1.73524e7	0.704269
$906$	3.22134e7	1.30382
$907$	1.56249e7	0.630666	0.315333	−	0.948981i	$-0.397884\pi$
$907$	1.56249e7	0.630666	0.315333	+	0.948981i	$0.397884\pi$
$908$	1.79084e7	0.720843
$909$	8.57281e6	0.344123
$910$	1.34040e8	5.36577
$911$	−1.03725e7	−0.414083	−0.207042	−	0.978332i	$-0.566384\pi$
$911$	−1.03725e7	−0.414083	−0.207042	+	0.978332i	$0.566384\pi$
$912$	−1.74370e7	−0.694200
$913$	−2.84178e7	−1.12827
$914$	−1.28869e7	−0.510249
$915$	−3.37580e7	−1.33298
$916$	−4.71798e7	−1.85788
$917$	−1.03955e7	−0.408246
$918$	0	0
$919$	2.52456e7	0.986045	0.493023	−	0.870016i	$-0.335892\pi$
$919$	2.52456e7	0.986045	0.493023	+	0.870016i	$0.335892\pi$
$920$	1.62581e8	6.33286
$921$	696401.	0.0270527
$922$	3.61610e7	1.40092
$923$	−2.44800e7	−0.945818
$924$	−2.66617e7	−1.02733
$925$	−9.15842e7	−3.51938
$926$	−2.42778e7	−0.930426
$927$	−8.97729e6	−0.343120
$928$	−4.10966e7	−1.56652
$929$	2.21061e6	0.0840374	0.0420187	−	0.999117i	$-0.486621\pi$
$929$	2.21061e6	0.0840374	0.0420187	+	0.999117i	$0.486621\pi$
$930$	6.78813e7	2.57361
$931$	−4.45889e6	−0.168598
$932$	7.99301e6	0.301419
$933$	2.13949e7	0.804649
$934$	1.37204e6	0.0514636
$935$	0	0
$936$	−3.53588e7	−1.31919
$937$	−1.30558e7	−0.485796	−0.242898	−	0.970052i	$-0.578098\pi$
$937$	−1.30558e7	−0.485796	−0.242898	+	0.970052i	$0.578098\pi$
$938$	−3.22610e7	−1.19721
$939$	2.50779e7	0.928169
$940$	−2.73828e7	−1.01078
$941$	−5.55338e6	−0.204448	−0.102224	−	0.994761i	$-0.532596\pi$
$941$	−5.55338e6	−0.204448	−0.102224	+	0.994761i	$0.532596\pi$
$942$	−7.12820e6	−0.261730
$943$	−1.02959e7	−0.377039
$944$	6.62354e7	2.41913
$945$	−1.02238e7	−0.372419
$946$	1.58904e7	0.577309
$947$	4.09126e7	1.48246	0.741229	−	0.671252i	$-0.234243\pi$
$947$	4.09126e7	1.48246	0.741229	+	0.671252i	$0.234243\pi$
$948$	−1.55942e6	−0.0563564
$949$	−5.41955e7	−1.95343
$950$	4.48005e7	1.61055
$951$	−2.62631e7	−0.941663
$952$	0	0
$953$	2.90924e7	1.03764	0.518821	−	0.854883i	$-0.326371\pi$
$953$	2.90924e7	1.03764	0.518821	+	0.854883i	$0.326371\pi$
$954$	8.24309e6	0.293237
$955$	1.36949e7	0.485904
$956$	−6.66786e6	−0.235962
$957$	−8.43408e6	−0.297685
$958$	4.73551e7	1.66707
$959$	−1.23263e7	−0.432798
$960$	−2.99826e7	−1.05000
$961$	3.10111e7	1.08320
$962$	1.57091e8	5.47287
$963$	−6.93626e6	−0.241024
$964$	3.85752e7	1.33695
$965$	7.85052e7	2.71382
$966$	−5.16607e7	−1.78122
$967$	4.25989e7	1.46498	0.732491	−	0.680777i	$-0.238358\pi$
$967$	4.25989e7	1.46498	0.732491	+	0.680777i	$0.238358\pi$
$968$	4.62669e7	1.58702
$969$	0	0
$970$	1.34095e8	4.57597
$971$	3.79024e7	1.29009	0.645043	−	0.764146i	$-0.276840\pi$
$971$	3.79024e7	1.29009	0.645043	+	0.764146i	$0.276840\pi$
$972$	4.58652e6	0.155710
$973$	2.51246e7	0.850780
$974$	−3.43777e7	−1.16113
$975$	4.57682e7	1.54188
$976$	1.01499e8	3.41066
$977$	3.41918e7	1.14600	0.573000	−	0.819555i	$-0.305779\pi$
$977$	3.41918e7	1.14600	0.573000	+	0.819555i	$0.305779\pi$
$978$	3.01021e7	1.00635
$979$	−2.62120e6	−0.0874063
$980$	−4.20700e7	−1.39929
$981$	−1.42534e7	−0.472876
$982$	−9.42343e7	−3.11839
$983$	4.95502e7	1.63554	0.817770	−	0.575545i	$-0.195210\pi$
$983$	4.95502e7	1.63554	0.817770	+	0.575545i	$0.195210\pi$
$984$	1.21604e7	0.400369
$985$	2.97225e7	0.976101
$986$	0	0
$987$	5.11634e6	0.167173
$988$	−5.44233e7	−1.77375
$989$	2.18062e7	0.708906
$990$	−2.00632e7	−0.650597
$991$	−84722.0	−0.00274039	−0.00137019	−	0.999999i	$-0.500436\pi$
$991$	−84722.0	−0.00274039	−0.00137019	+	0.999999i	$0.500436\pi$
$992$	−8.58932e7	−2.77127
$993$	2.06973e7	0.666102
$994$	4.22433e7	1.35610
$995$	−1.19847e7	−0.383770
$996$	7.83297e7	2.50195
$997$	−3.14915e7	−1.00336	−0.501679	−	0.865054i	$-0.667284\pi$
$997$	−3.14915e7	−1.00336	−0.501679	+	0.865054i	$0.667284\pi$
$998$	−8.47968e7	−2.69496
$999$	−1.19820e7	−0.379852

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	867.a (trivial)

\(f(q)\)	\(=\)	\(q-10.4725 q^{2} +9.00000 q^{3} +77.6731 q^{4} -93.2583 q^{5} -94.2524 q^{6} +150.382 q^{7} -478.312 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.4725 q^{2} +9.00000 q^{3} +77.6731 q^{4} -93.2583 q^{5} -94.2524 q^{6} +150.382 q^{7} -478.312 q^{8} +81.0000 q^{9} +976.647 q^{10} -253.617 q^{11} +699.058 q^{12} +912.644 q^{13} -1574.88 q^{14} -839.325 q^{15} +2523.57 q^{16} -848.272 q^{18} -767.738 q^{19} -7243.66 q^{20} +1353.44 q^{21} +2656.00 q^{22} +3644.78 q^{23} -4304.80 q^{24} +5572.11 q^{25} -9557.66 q^{26} +729.000 q^{27} +11680.7 q^{28} +3695.02 q^{29} +8789.82 q^{30} +7722.71 q^{31} -11122.2 q^{32} -2282.55 q^{33} -14024.4 q^{35} +6291.52 q^{36} -16436.2 q^{37} +8040.13 q^{38} +8213.80 q^{39} +44606.5 q^{40} -2824.85 q^{41} -14173.9 q^{42} +5982.85 q^{43} -19699.2 q^{44} -7553.92 q^{45} -38169.9 q^{46} +3780.24 q^{47} +22712.2 q^{48} +5807.84 q^{49} -58353.9 q^{50} +70887.9 q^{52} -9717.51 q^{53} -7634.45 q^{54} +23651.9 q^{55} -71929.6 q^{56} -6909.64 q^{57} -38696.1 q^{58} +26246.6 q^{59} -65193.0 q^{60} +40220.5 q^{61} -80876.1 q^{62} +12181.0 q^{63} +35722.3 q^{64} -85111.6 q^{65} +23904.0 q^{66} +20484.7 q^{67} +32803.0 q^{69} +146870. q^{70} -26823.2 q^{71} -38743.2 q^{72} -59383.0 q^{73} +172128. q^{74} +50149.0 q^{75} -59632.6 q^{76} -38139.5 q^{77} -86018.9 q^{78} -2230.75 q^{79} -235344. q^{80} +6561.00 q^{81} +29583.2 q^{82} +112050. q^{83} +105126. q^{84} -62655.3 q^{86} +33255.2 q^{87} +121308. q^{88} +10335.3 q^{89} +79108.4 q^{90} +137246. q^{91} +283101. q^{92} +69504.4 q^{93} -39588.6 q^{94} +71597.9 q^{95} -100099. q^{96} +137302. q^{97} -60822.5 q^{98} -20542.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 72 q^{3} + 187 q^{4} + 27 q^{6} - 18 q^{7} + 105 q^{8} + 648 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more