LMFDB - Embedded newform 867.6.a.l.1.2

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			1.2
Root			$-7.67568$ 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)

$f(q)$	$=$	$q-7.67568 q^{2} -9.00000 q^{3} +26.9161 q^{4} -1.48858 q^{5} +69.0811 q^{6} +193.858 q^{7} +39.0226 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-7.67568 q^{2} -9.00000 q^{3} +26.9161 q^{4} -1.48858 q^{5} +69.0811 q^{6} +193.858 q^{7} +39.0226 q^{8} +81.0000 q^{9} +11.4259 q^{10} -127.651 q^{11} -242.245 q^{12} -734.225 q^{13} -1488.00 q^{14} +13.3973 q^{15} -1160.84 q^{16} -621.730 q^{18} +1078.65 q^{19} -40.0668 q^{20} -1744.73 q^{21} +979.811 q^{22} -2251.55 q^{23} -351.203 q^{24} -3122.78 q^{25} +5635.68 q^{26} -729.000 q^{27} +5217.91 q^{28} +3357.43 q^{29} -102.833 q^{30} -1690.66 q^{31} +7661.51 q^{32} +1148.86 q^{33} -288.574 q^{35} +2180.20 q^{36} +14617.1 q^{37} -8279.35 q^{38} +6608.03 q^{39} -58.0884 q^{40} +2994.66 q^{41} +13392.0 q^{42} -11675.7 q^{43} -3435.87 q^{44} -120.575 q^{45} +17282.2 q^{46} +23780.7 q^{47} +10447.6 q^{48} +20774.1 q^{49} +23969.5 q^{50} -19762.5 q^{52} +776.369 q^{53} +5595.57 q^{54} +190.020 q^{55} +7564.86 q^{56} -9707.82 q^{57} -25770.5 q^{58} -32794.6 q^{59} +360.601 q^{60} +23081.2 q^{61} +12976.9 q^{62} +15702.5 q^{63} -21660.4 q^{64} +1092.96 q^{65} -8818.30 q^{66} -70077.2 q^{67} +20263.9 q^{69} +2215.00 q^{70} +5541.70 q^{71} +3160.83 q^{72} -28413.2 q^{73} -112196. q^{74} +28105.1 q^{75} +29032.9 q^{76} -24746.3 q^{77} -50721.1 q^{78} -49442.7 q^{79} +1728.01 q^{80} +6561.00 q^{81} -22986.1 q^{82} +107691. q^{83} -46961.2 q^{84} +89618.9 q^{86} -30216.8 q^{87} -4981.29 q^{88} -25681.6 q^{89} +925.497 q^{90} -142336. q^{91} -60602.8 q^{92} +15215.9 q^{93} -182533. q^{94} -1605.66 q^{95} -68953.6 q^{96} +66430.5 q^{97} -159455. q^{98} -10339.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−7.67568	−1.35688	−0.678441	−	0.734655i	$-0.737344\pi$
$2$	−7.67568	−1.35688	−0.678441	+	0.734655i	$0.737344\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	26.9161	0.841127
$5$	−1.48858	−0.0266286	−0.0133143	−	0.999911i	$-0.504238\pi$
$5$	−1.48858	−0.0266286	−0.0133143	+	0.999911i	$0.504238\pi$
$6$	69.0811	0.783396
$7$	193.858	1.49534	0.747669	−	0.664071i	$-0.231173\pi$
$7$	193.858	1.49534	0.747669	+	0.664071i	$0.231173\pi$
$8$	39.0226	0.215571
$9$	81.0000	0.333333
$10$	11.4259	0.0361318
$11$	−127.651	−0.318085	−0.159043	−	0.987272i	$-0.550841\pi$
$11$	−127.651	−0.318085	−0.159043	+	0.987272i	$0.550841\pi$
$12$	−242.245	−0.485625
$13$	−734.225	−1.20496	−0.602478	−	0.798136i	$-0.705820\pi$
$13$	−734.225	−1.20496	−0.602478	+	0.798136i	$0.705820\pi$
$14$	−1488.00	−2.02900
$15$	13.3973	0.0153740
$16$	−1160.84	−1.13363
$17$	0	0
$17$	0	0
$18$	−621.730	−0.452294
$19$	1078.65	0.685481	0.342740	−	0.939430i	$-0.388645\pi$
$19$	1078.65	0.685481	0.342740	+	0.939430i	$0.388645\pi$
$20$	−40.0668	−0.0223980
$21$	−1744.73	−0.863334
$22$	979.811	0.431604
$23$	−2251.55	−0.887487	−0.443743	−	0.896154i	$-0.646350\pi$
$23$	−2251.55	−0.887487	−0.443743	+	0.896154i	$0.646350\pi$
$24$	−351.203	−0.124460
$25$	−3122.78	−0.999291
$26$	5635.68	1.63498
$27$	−729.000	−0.192450
$28$	5217.91	1.25777
$29$	3357.43	0.741330	0.370665	−	0.928767i	$-0.379130\pi$
$29$	3357.43	0.741330	0.370665	+	0.928767i	$0.379130\pi$
$30$	−102.833	−0.0208607
$31$	−1690.66	−0.315974	−0.157987	−	0.987441i	$-0.550500\pi$
$31$	−1690.66	−0.315974	−0.157987	+	0.987441i	$0.550500\pi$
$32$	7661.51	1.32263
$33$	1148.86	0.183647
$34$	0	0
$35$	−288.574	−0.0398188
$36$	2180.20	0.280376
$37$	14617.1	1.75533	0.877663	−	0.479278i	$-0.159102\pi$
$37$	14617.1	1.75533	0.877663	+	0.479278i	$0.159102\pi$
$38$	−8279.35	−0.930116
$39$	6608.03	0.695681
$40$	−58.0884	−0.00574037
$41$	2994.66	0.278220	0.139110	−	0.990277i	$-0.455576\pi$
$41$	2994.66	0.278220	0.139110	+	0.990277i	$0.455576\pi$
$42$	13392.0	1.17144
$43$	−11675.7	−0.962968	−0.481484	−	0.876455i	$-0.659902\pi$
$43$	−11675.7	−0.962968	−0.481484	+	0.876455i	$0.659902\pi$
$44$	−3435.87	−0.267550
$45$	−120.575	−0.00887620
$46$	17282.2	1.20421
$47$	23780.7	1.57029	0.785146	−	0.619311i	$-0.212588\pi$
$47$	23780.7	1.57029	0.785146	+	0.619311i	$0.212588\pi$
$48$	10447.6	0.654503
$49$	20774.1	1.23604
$50$	23969.5	1.35592
$51$	0	0
$52$	−19762.5	−1.01352
$53$	776.369	0.0379646	0.0189823	−	0.999820i	$-0.493957\pi$
$53$	776.369	0.0379646	0.0189823	+	0.999820i	$0.493957\pi$
$54$	5595.57	0.261132
$55$	190.020	0.00847016
$56$	7564.86	0.322352
$57$	−9707.82	−0.395763
$58$	−25770.5	−1.00590
$59$	−32794.6	−1.22651	−0.613257	−	0.789884i	$-0.710141\pi$
$59$	−32794.6	−1.22651	−0.613257	+	0.789884i	$0.710141\pi$
$60$	360.601	0.0129315
$61$	23081.2	0.794208	0.397104	−	0.917774i	$-0.370015\pi$
$61$	23081.2	0.794208	0.397104	+	0.917774i	$0.370015\pi$
$62$	12976.9	0.428739
$63$	15702.5	0.498446
$64$	−21660.4	−0.661024
$65$	1092.96	0.0320863
$66$	−8818.30	−0.249187
$67$	−70077.2	−1.90717	−0.953586	−	0.301120i	$-0.902640\pi$
$67$	−70077.2	−1.90717	−0.953586	+	0.301120i	$0.902640\pi$
$68$	0	0
$69$	20263.9	0.512391
$70$	2215.00	0.0540293
$71$	5541.70	0.130466	0.0652329	−	0.997870i	$-0.479221\pi$
$71$	5541.70	0.130466	0.0652329	+	0.997870i	$0.479221\pi$
$72$	3160.83	0.0718572
$73$	−28413.2	−0.624041	−0.312020	−	0.950075i	$-0.601006\pi$
$73$	−28413.2	−0.624041	−0.312020	+	0.950075i	$0.601006\pi$
$74$	−112196.	−2.38177
$75$	28105.1	0.576941
$76$	29032.9	0.576577
$77$	−24746.3	−0.475645
$78$	−50721.1	−0.943957
$79$	−49442.7	−0.891322	−0.445661	−	0.895202i	$-0.647031\pi$
$79$	−49442.7	−0.891322	−0.445661	+	0.895202i	$0.647031\pi$
$80$	1728.01	0.0301870
$81$	6561.00	0.111111
$82$	−22986.1	−0.377511
$83$	107691.	1.71587	0.857935	−	0.513758i	$-0.171747\pi$
$83$	107691.	1.71587	0.857935	+	0.513758i	$0.171747\pi$
$84$	−46961.2	−0.726174
$85$	0	0
$86$	89618.9	1.30663
$87$	−30216.8	−0.428007
$88$	−4981.29	−0.0685701
$89$	−25681.6	−0.343675	−0.171837	−	0.985125i	$-0.554970\pi$
$89$	−25681.6	−0.343675	−0.171837	+	0.985125i	$0.554970\pi$
$90$	925.497	0.0120439
$91$	−142336.	−1.80182
$92$	−60602.8	−0.746489
$93$	15215.9	0.182428
$94$	−182533.	−2.13070
$95$	−1605.66	−0.0182534
$96$	−68953.6	−0.763623
$97$	66430.5	0.716866	0.358433	−	0.933555i	$-0.383311\pi$
$97$	66430.5	0.716866	0.358433	+	0.933555i	$0.383311\pi$
$98$	−159455.	−1.67716
$99$	−10339.8	−0.106028
$100$	−84053.1	−0.840531
$101$	75142.6	0.732964	0.366482	−	0.930425i	$-0.380562\pi$
$101$	75142.6	0.732964	0.366482	+	0.930425i	$0.380562\pi$
$102$	0	0
$103$	117077.	1.08737	0.543685	−	0.839289i	$-0.317029\pi$
$103$	117077.	1.08737	0.543685	+	0.839289i	$0.317029\pi$
$104$	−28651.4	−0.259754
$105$	2597.17	0.0229894
$106$	−5959.16	−0.0515134
$107$	−108171.	−0.913383	−0.456691	−	0.889625i	$-0.650966\pi$
$107$	−108171.	−0.913383	−0.456691	+	0.889625i	$0.650966\pi$
$108$	−19621.8	−0.161875
$109$	−49927.8	−0.402509	−0.201255	−	0.979539i	$-0.564502\pi$
$109$	−49927.8	−0.402509	−0.201255	+	0.979539i	$0.564502\pi$
$110$	−1458.53	−0.0114930
$111$	−131554.	−1.01344
$112$	−225038.	−1.69516
$113$	114429.	0.843025	0.421512	−	0.906823i	$-0.361499\pi$
$113$	114429.	0.843025	0.421512	+	0.906823i	$0.361499\pi$
$114$	74514.2	0.537003
$115$	3351.62	0.0236325
$116$	90368.7	0.623553
$117$	−59472.3	−0.401652
$118$	251721.	1.66423
$119$	0	0
$120$	522.796	0.00331420
$121$	−144756.	−0.898822
$122$	−177164.	−1.07765
$123$	−26951.9	−0.160630
$124$	−45505.8	−0.265774
$125$	9300.35	0.0532383
$126$	−120528.	−0.676332
$127$	4300.41	0.0236592	0.0118296	−	0.999930i	$-0.496234\pi$
$127$	4300.41	0.0236592	0.0118296	+	0.999930i	$0.496234\pi$
$128$	−78909.7	−0.425702
$129$	105081.	0.555970
$130$	−8389.18	−0.0435373
$131$	370088.	1.88420	0.942099	−	0.335334i	$-0.108849\pi$
$131$	370088.	1.88420	0.942099	+	0.335334i	$0.108849\pi$
$132$	30922.9	0.154470
$133$	209105.	1.02503
$134$	537891.	2.58781
$135$	1085.18	0.00512467
$136$	0	0
$137$	−102169.	−0.465070	−0.232535	−	0.972588i	$-0.574702\pi$
$137$	−102169.	−0.465070	−0.232535	+	0.972588i	$0.574702\pi$
$138$	−155540.	−0.695253
$139$	290209.	1.27402	0.637008	−	0.770858i	$-0.280172\pi$
$139$	290209.	1.27402	0.637008	+	0.770858i	$0.280172\pi$
$140$	−7767.29	−0.0334926
$141$	−214026.	−0.906608
$142$	−42536.3	−0.177027
$143$	93724.9	0.383279
$144$	−94028.0	−0.377877
$145$	−4997.81	−0.0197406
$146$	218091.	0.846749
$147$	−186967.	−0.713626
$148$	393436.	1.47645
$149$	−482274.	−1.77962	−0.889811	−	0.456329i	$-0.849164\pi$
$149$	−482274.	−1.77962	−0.889811	+	0.456329i	$0.849164\pi$
$150$	−215725.	−0.782840
$151$	157139.	0.560842	0.280421	−	0.959877i	$-0.409526\pi$
$151$	157139.	0.560842	0.280421	+	0.959877i	$0.409526\pi$
$152$	42091.6	0.147770
$153$	0	0
$154$	189945.	0.645394
$155$	2516.68	0.00841394
$156$	177862.	0.585157
$157$	−345343.	−1.11815	−0.559077	−	0.829115i	$-0.688845\pi$
$157$	−345343.	−1.11815	−0.559077	+	0.829115i	$0.688845\pi$
$158$	379506.	1.20942
$159$	−6987.32	−0.0219189
$160$	−11404.8	−0.0352199
$161$	−436482.	−1.32709
$162$	−50360.1	−0.150765
$163$	−625607.	−1.84431	−0.922153	−	0.386826i	$-0.873571\pi$
$163$	−625607.	−1.84431	−0.922153	+	0.386826i	$0.873571\pi$
$164$	80604.5	0.234018
$165$	−1710.18	−0.00489025
$166$	−826602.	−2.32823
$167$	−198869.	−0.551793	−0.275896	−	0.961187i	$-0.588975\pi$
$167$	−198869.	−0.551793	−0.275896	+	0.961187i	$0.588975\pi$
$168$	−68083.7	−0.186110
$169$	167794.	0.451918
$170$	0	0
$171$	87370.4	0.228494
$172$	−314264.	−0.809979
$173$	463629.	1.17776	0.588878	−	0.808222i	$-0.299570\pi$
$173$	463629.	1.17776	0.588878	+	0.808222i	$0.299570\pi$
$174$	231935.	0.580755
$175$	−605378.	−1.49428
$176$	148183.	0.360592
$177$	295151.	0.708128
$178$	197124.	0.466326
$179$	694729.	1.62063	0.810313	−	0.585998i	$-0.199297\pi$
$179$	694729.	1.62063	0.810313	+	0.585998i	$0.199297\pi$
$180$	−3245.41	−0.00746601
$181$	−13390.5	−0.0303809	−0.0151905	−	0.999885i	$-0.504835\pi$
$181$	−13390.5	−0.0303809	−0.0151905	+	0.999885i	$0.504835\pi$
$182$	1.09252e6	2.44485
$183$	−207731.	−0.458536
$184$	−87861.3	−0.191317
$185$	−21758.8	−0.0467419
$186$	−116792.	−0.247533
$187$	0	0
$188$	640084.	1.32082
$189$	−141323.	−0.287778
$190$	12324.5	0.0247677
$191$	−762091.	−1.51155	−0.755777	−	0.654829i	$-0.772740\pi$
$191$	−762091.	−1.51155	−0.755777	+	0.654829i	$0.772740\pi$
$192$	194944.	0.381642
$193$	−703785.	−1.36002	−0.680012	−	0.733201i	$-0.738026\pi$
$193$	−703785.	−1.36002	−0.680012	+	0.733201i	$0.738026\pi$
$194$	−509899.	−0.972703
$195$	−9836.60	−0.0185250
$196$	559156.	1.03966
$197$	−153005.	−0.280892	−0.140446	−	0.990088i	$-0.544854\pi$
$197$	−153005.	−0.280892	−0.140446	+	0.990088i	$0.544854\pi$
$198$	79364.7	0.143868
$199$	−212361.	−0.380139	−0.190070	−	0.981771i	$-0.560871\pi$
$199$	−212361.	−0.380139	−0.190070	+	0.981771i	$0.560871\pi$
$200$	−121859.	−0.215419
$201$	630695.	1.10111
$202$	−576770.	−0.994545
$203$	650865.	1.10854
$204$	0	0
$205$	−4457.80	−0.00740860
$206$	−898643.	−1.47543
$207$	−182375.	−0.295829
$208$	852318.	1.36598
$209$	−137691.	−0.218041
$210$	−19935.0	−0.0311938
$211$	−562613.	−0.869968	−0.434984	−	0.900438i	$-0.643246\pi$
$211$	−562613.	−0.869968	−0.434984	+	0.900438i	$0.643246\pi$
$212$	20896.8	0.0319330
$213$	−49875.3	−0.0753245
$214$	830289.	1.23935
$215$	17380.3	0.0256425
$216$	−28447.5	−0.0414868
$217$	−327748.	−0.472488
$218$	383230.	0.546158
$219$	255719.	0.360290
$220$	5114.58	0.00712449
$221$	0	0
$222$	1.00977e6	1.37512
$223$	1.30341e6	1.75516	0.877582	−	0.479427i	$-0.159156\pi$
$223$	1.30341e6	1.75516	0.877582	+	0.479427i	$0.159156\pi$
$224$	1.48525e6	1.97778
$225$	−252946.	−0.333097
$226$	−878321.	−1.14388
$227$	870252.	1.12094	0.560468	−	0.828176i	$-0.310621\pi$
$227$	870252.	1.12094	0.560468	+	0.828176i	$0.310621\pi$
$228$	−261296.	−0.332887
$229$	439654.	0.554016	0.277008	−	0.960868i	$-0.410657\pi$
$229$	439654.	0.554016	0.277008	+	0.960868i	$0.410657\pi$
$230$	−25726.0	−0.0320665
$231$	222717.	0.274614
$232$	131015.	0.159810
$233$	−28513.5	−0.0344081	−0.0172041	−	0.999852i	$-0.505476\pi$
$233$	−28513.5	−0.0344081	−0.0172041	+	0.999852i	$0.505476\pi$
$234$	456490.	0.544994
$235$	−35399.6	−0.0418147
$236$	−882702.	−1.03165
$237$	444984.	0.514605
$238$	0	0
$239$	616903.	0.698590	0.349295	−	0.937013i	$-0.386421\pi$
$239$	616903.	0.698590	0.349295	+	0.937013i	$0.386421\pi$
$240$	−15552.1	−0.0174285
$241$	1.21440e6	1.34685	0.673423	−	0.739258i	$-0.264823\pi$
$241$	1.21440e6	1.34685	0.673423	+	0.739258i	$0.264823\pi$
$242$	1.11110e6	1.21959
$243$	−59049.0	−0.0641500
$244$	621256.	0.668030
$245$	−30923.9	−0.0329139
$246$	206874.	0.217956
$247$	−791970.	−0.825974
$248$	−65973.8	−0.0681150
$249$	−969219.	−0.990658
$250$	−71386.5	−0.0722381
$251$	1.96202e6	1.96571	0.982854	−	0.184388i	$-0.0590303\pi$
$251$	1.96202e6	1.96571	0.982854	+	0.184388i	$0.0590303\pi$
$252$	422650.	0.419257
$253$	287413.	0.282296
$254$	−33008.5	−0.0321027
$255$	0	0
$256$	1.29882e6	1.23865
$257$	−548268.	−0.517797	−0.258899	−	0.965904i	$-0.583360\pi$
$257$	−548268.	−0.517797	−0.258899	+	0.965904i	$0.583360\pi$
$258$	−806571.	−0.754385
$259$	2.83365e6	2.62481
$260$	29418.1	0.0269886
$261$	271951.	0.247110
$262$	−2.84068e6	−2.55663
$263$	1.05688e6	0.942186	0.471093	−	0.882084i	$-0.343860\pi$
$263$	1.05688e6	0.942186	0.471093	+	0.882084i	$0.343860\pi$
$264$	44831.6	0.0395890
$265$	−1155.69	−0.00101094
$266$	−1.60502e6	−1.39084
$267$	231135.	0.198421
$268$	−1.88620e6	−1.60417
$269$	−2.08910e6	−1.76027	−0.880134	−	0.474724i	$-0.842548\pi$
$269$	−2.08910e6	−1.76027	−0.880134	+	0.474724i	$0.842548\pi$
$270$	−8329.47	−0.00695358
$271$	−730661.	−0.604355	−0.302178	−	0.953252i	$-0.597714\pi$
$271$	−730661.	−0.604355	−0.302178	+	0.953252i	$0.597714\pi$
$272$	0	0
$273$	1.28102e6	1.04028
$274$	784217.	0.631044
$275$	398628.	0.317860
$276$	545426.	0.430986
$277$	134326.	0.105187	0.0525933	−	0.998616i	$-0.483251\pi$
$277$	134326.	0.105187	0.0525933	+	0.998616i	$0.483251\pi$
$278$	−2.22756e6	−1.72869
$279$	−136943.	−0.105325
$280$	−11260.9	−0.00858379
$281$	1.92136e6	1.45159	0.725795	−	0.687911i	$-0.241472\pi$
$281$	1.92136e6	1.45159	0.725795	+	0.687911i	$0.241472\pi$
$282$	1.64280e6	1.23016
$283$	642789.	0.477092	0.238546	−	0.971131i	$-0.423329\pi$
$283$	642789.	0.477092	0.238546	+	0.971131i	$0.423329\pi$
$284$	149161.	0.109738
$285$	14450.9	0.0105386
$286$	−719402.	−0.520064
$287$	580540.	0.416033
$288$	620582.	0.440878
$289$	0	0
$290$	38361.6	0.0267856
$291$	−597875.	−0.413883
$292$	−764771.	−0.524898
$293$	626538.	0.426362	0.213181	−	0.977013i	$-0.431618\pi$
$293$	626538.	0.426362	0.213181	+	0.977013i	$0.431618\pi$
$294$	1.43510e6	0.968306
$295$	48817.5	0.0326603
$296$	570398.	0.378398
$297$	93057.8	0.0612155
$298$	3.70178e6	2.41474
$299$	1.65314e6	1.06938
$300$	756478.	0.485281
$301$	−2.26343e6	−1.43996
$302$	−1.20615e6	−0.760996
$303$	−676283.	−0.423177
$304$	−1.25214e6	−0.777083
$305$	−34358.3	−0.0211486
$306$	0	0
$307$	985319.	0.596665	0.298333	−	0.954462i	$-0.403570\pi$
$307$	985319.	0.596665	0.298333	+	0.954462i	$0.403570\pi$
$308$	−666073.	−0.400078
$309$	−1.05369e6	−0.627793
$310$	−19317.3	−0.0114167
$311$	3.10948e6	1.82300	0.911500	−	0.411299i	$-0.134925\pi$
$311$	3.10948e6	1.82300	0.911500	+	0.411299i	$0.134925\pi$
$312$	257863.	0.149969
$313$	−1.48857e6	−0.858830	−0.429415	−	0.903107i	$-0.641280\pi$
$313$	−1.48857e6	−0.858830	−0.429415	+	0.903107i	$0.641280\pi$
$314$	2.65075e6	1.51720
$315$	−23374.5	−0.0132729
$316$	−1.33080e6	−0.749715
$317$	−2.88282e6	−1.61128	−0.805638	−	0.592408i	$-0.798177\pi$
$317$	−2.88282e6	−1.61128	−0.805638	+	0.592408i	$0.798177\pi$
$318$	53632.4	0.0297413
$319$	−428580.	−0.235806
$320$	32243.4	0.0176021
$321$	973542.	0.527342
$322$	3.35029e6	1.80071
$323$	0	0
$324$	176596.	0.0934586
$325$	2.29283e6	1.20410
$326$	4.80196e6	2.50250
$327$	449350.	0.232389
$328$	116859.	0.0599762
$329$	4.61009e6	2.34812
$330$	13126.8	0.00663549
$331$	2.89258e6	1.45116	0.725581	−	0.688137i	$-0.241571\pi$
$331$	2.89258e6	1.45116	0.725581	+	0.688137i	$0.241571\pi$
$332$	2.89862e6	1.44326
$333$	1.18399e6	0.585109
$334$	1.52646e6	0.748717
$335$	104316.	0.0507853
$336$	2.02535e6	0.978703
$337$	−2.17131e6	−1.04147	−0.520736	−	0.853718i	$-0.674342\pi$
$337$	−2.17131e6	−1.04147	−0.520736	+	0.853718i	$0.674342\pi$
$338$	−1.28793e6	−0.613199
$339$	−1.02986e6	−0.486721
$340$	0	0
$341$	215815.	0.100507
$342$	−670627.	−0.310039
$343$	769051.	0.352955
$344$	−455616.	−0.207588
$345$	−30164.6	−0.0136442
$346$	−3.55867e6	−1.59808
$347$	−2.89517e6	−1.29077	−0.645387	−	0.763856i	$-0.723304\pi$
$347$	−2.89517e6	−1.29077	−0.645387	+	0.763856i	$0.723304\pi$
$348$	−813318.	−0.360008
$349$	602825.	0.264928	0.132464	−	0.991188i	$-0.457711\pi$
$349$	602825.	0.264928	0.132464	+	0.991188i	$0.457711\pi$
$350$	4.64669e6	2.02756
$351$	535250.	0.231894
$352$	−978002.	−0.420710
$353$	2.31232e6	0.987670	0.493835	−	0.869556i	$-0.335595\pi$
$353$	2.31232e6	0.987670	0.493835	+	0.869556i	$0.335595\pi$
$354$	−2.26549e6	−0.960845
$355$	−8249.28	−0.00347412
$356$	−691249.	−0.289074
$357$	0	0
$358$	−5.33252e6	−2.19900
$359$	492715.	0.201771	0.100886	−	0.994898i	$-0.467832\pi$
$359$	492715.	0.201771	0.100886	+	0.994898i	$0.467832\pi$
$360$	−4705.16	−0.00191346
$361$	−1.31262e6	−0.530116
$362$	102781.	0.0412233
$363$	1.30281e6	0.518935
$364$	−3.83112e6	−1.51556
$365$	42295.4	0.0166173
$366$	1.59448e6	0.622179
$367$	−2.90364e6	−1.12533	−0.562663	−	0.826686i	$-0.690223\pi$
$367$	−2.90364e6	−1.12533	−0.562663	+	0.826686i	$0.690223\pi$
$368$	2.61369e6	1.00608
$369$	242567.	0.0927399
$370$	167014.	0.0634232
$371$	150506.	0.0567699
$372$	409552.	0.153445
$373$	4.70576e6	1.75129	0.875645	−	0.482955i	$-0.160437\pi$
$373$	4.70576e6	1.75129	0.875645	+	0.482955i	$0.160437\pi$
$374$	0	0
$375$	−83703.1	−0.0307371
$376$	927986.	0.338510
$377$	−2.46511e6	−0.893269
$378$	1.08475e6	0.390481
$379$	−471049.	−0.168449	−0.0842244	−	0.996447i	$-0.526841\pi$
$379$	−471049.	−0.168449	−0.0842244	+	0.996447i	$0.526841\pi$
$380$	−43218.0	−0.0153534
$381$	−38703.7	−0.0136596
$382$	5.84957e6	2.05100
$383$	−1.25455e6	−0.437011	−0.218506	−	0.975836i	$-0.570118\pi$
$383$	−1.25455e6	−0.437011	−0.218506	+	0.975836i	$0.570118\pi$
$384$	710187.	0.245779
$385$	36836.9	0.0126658
$386$	5.40203e6	1.84539
$387$	−945732.	−0.320989
$388$	1.78805e6	0.602976
$389$	12276.7	0.00411345	0.00205673	−	0.999998i	$-0.499345\pi$
$389$	12276.7	0.00411345	0.00205673	+	0.999998i	$0.499345\pi$
$390$	75502.6	0.0251363
$391$	0	0
$392$	810659.	0.266454
$393$	−3.33079e6	−1.08784
$394$	1.17442e6	0.381137
$395$	73599.6	0.0237346
$396$	−278306.	−0.0891834
$397$	2.36101e6	0.751832	0.375916	−	0.926654i	$-0.377328\pi$
$397$	2.36101e6	0.751832	0.375916	+	0.926654i	$0.377328\pi$
$398$	1.63002e6	0.515804
$399$	−1.88194e6	−0.591799
$400$	3.62505e6	1.13283
$401$	5.95964e6	1.85080	0.925399	−	0.378995i	$-0.123730\pi$
$401$	5.95964e6	1.85080	0.925399	+	0.378995i	$0.123730\pi$
$402$	−4.84101e6	−1.49407
$403$	1.24132e6	0.380734
$404$	2.02254e6	0.616516
$405$	−9766.60	−0.00295873
$406$	−4.99583e6	−1.50416
$407$	−1.86590e6	−0.558343
$408$	0	0
$409$	−2.38028e6	−0.703591	−0.351796	−	0.936077i	$-0.614429\pi$
$409$	−2.38028e6	−0.703591	−0.351796	+	0.936077i	$0.614429\pi$
$410$	34216.7	0.0100526
$411$	919521.	0.268508
$412$	3.15124e6	0.914617
$413$	−6.35751e6	−1.83405
$414$	1.39986e6	0.401405
$415$	−160307.	−0.0456912
$416$	−5.62527e6	−1.59371
$417$	−2.61189e6	−0.735553
$418$	1.05687e6	0.295856
$419$	−5.31984e6	−1.48035	−0.740174	−	0.672416i	$-0.765257\pi$
$419$	−5.31984e6	−1.48035	−0.740174	+	0.672416i	$0.765257\pi$
$420$	69905.6	0.0193370
$421$	−5.78519e6	−1.59079	−0.795394	−	0.606093i	$-0.792736\pi$
$421$	−5.78519e6	−1.59079	−0.795394	+	0.606093i	$0.792736\pi$
$422$	4.31843e6	1.18044
$423$	1.92624e6	0.523431
$424$	30295.9	0.00818408
$425$	0	0
$426$	382827.	0.102206
$427$	4.47449e6	1.18761
$428$	−2.91155e6	−0.768271
$429$	−843524.	−0.221286
$430$	−133405.	−0.0347938
$431$	239883.	0.0622023	0.0311011	−	0.999516i	$-0.490099\pi$
$431$	239883.	0.0622023	0.0311011	+	0.999516i	$0.490099\pi$
$432$	846252.	0.218168
$433$	109058.	0.0279537	0.0139768	−	0.999902i	$-0.495551\pi$
$433$	109058.	0.0279537	0.0139768	+	0.999902i	$0.495551\pi$
$434$	2.51569e6	0.641110
$435$	44980.3	0.0113972
$436$	−1.34386e6	−0.338562
$437$	−2.42863e6	−0.608355
$438$	−1.96282e6	−0.488871
$439$	−3.03252e6	−0.751003	−0.375502	−	0.926822i	$-0.622530\pi$
$439$	−3.03252e6	−0.751003	−0.375502	+	0.926822i	$0.622530\pi$
$440$	7415.06	0.00182593
$441$	1.68270e6	0.412012
$442$	0	0
$443$	6.16761e6	1.49316	0.746582	−	0.665294i	$-0.231694\pi$
$443$	6.16761e6	1.49316	0.746582	+	0.665294i	$0.231694\pi$
$444$	−3.54092e6	−0.852430
$445$	38229.3	0.00915158
$446$	−1.00045e7	−2.38155
$447$	4.34046e6	1.02747
$448$	−4.19906e6	−0.988455
$449$	6.35197e6	1.48694	0.743468	−	0.668771i	$-0.233179\pi$
$449$	6.35197e6	1.48694	0.743468	+	0.668771i	$0.233179\pi$
$450$	1.94153e6	0.451973
$451$	−382272.	−0.0884976
$452$	3.07998e6	0.709091
$453$	−1.41425e6	−0.323802
$454$	−6.67978e6	−1.52098
$455$	211879.	0.0479798
$456$	−378825.	−0.0853151
$457$	956581.	0.214255	0.107128	−	0.994245i	$-0.465835\pi$
$457$	956581.	0.214255	0.107128	+	0.994245i	$0.465835\pi$
$458$	−3.37464e6	−0.751734
$459$	0	0
$460$	90212.4	0.0198780
$461$	7.26726e6	1.59264	0.796322	−	0.604873i	$-0.206776\pi$
$461$	7.26726e6	1.59264	0.796322	+	0.604873i	$0.206776\pi$
$462$	−1.70950e6	−0.372618
$463$	327118.	0.0709174	0.0354587	−	0.999371i	$-0.488711\pi$
$463$	327118.	0.0709174	0.0354587	+	0.999371i	$0.488711\pi$
$464$	−3.89743e6	−0.840395
$465$	−22650.1	−0.00485779
$466$	218861.	0.0466878
$467$	8.41231e6	1.78494	0.892469	−	0.451109i	$-0.148971\pi$
$467$	8.41231e6	1.78494	0.892469	+	0.451109i	$0.148971\pi$
$468$	−1.60076e6	−0.337840
$469$	−1.35851e7	−2.85187
$470$	271716.	0.0567375
$471$	3.10809e6	0.645567
$472$	−1.27973e6	−0.264401
$473$	1.49042e6	0.306306
$474$	−3.41556e6	−0.698258
$475$	−3.36838e6	−0.684995
$476$	0	0
$477$	62885.9	0.0126549
$478$	−4.73515e6	−0.947903
$479$	−5.42134e6	−1.07961	−0.539806	−	0.841790i	$-0.681502\pi$
$479$	−5.42134e6	−1.07961	−0.539806	+	0.841790i	$0.681502\pi$
$480$	102643.	0.0203342
$481$	−1.07323e7	−2.11509
$482$	−9.32132e6	−1.82751
$483$	3.92833e6	0.766197
$484$	−3.89627e6	−0.756023
$485$	−98887.4	−0.0190891
$486$	453241.	0.0870440
$487$	3.36457e6	0.642846	0.321423	−	0.946936i	$-0.395839\pi$
$487$	3.36457e6	0.642846	0.321423	+	0.946936i	$0.395839\pi$
$488$	900690.	0.171209
$489$	5.63047e6	1.06481
$490$	237362.	0.0446603
$491$	−1.90967e6	−0.357482	−0.178741	−	0.983896i	$-0.557202\pi$
$491$	−1.90967e6	−0.357482	−0.178741	+	0.983896i	$0.557202\pi$
$492$	−725440.	−0.135110
$493$	0	0
$494$	6.07891e6	1.12075
$495$	15391.6	0.00282339
$496$	1.96258e6	0.358198
$497$	1.07430e6	0.195091
$498$	7.43942e6	1.34421
$499$	7.06926e6	1.27093	0.635467	−	0.772128i	$-0.280808\pi$
$499$	7.06926e6	1.27093	0.635467	+	0.772128i	$0.280808\pi$
$500$	250329.	0.0447802
$501$	1.78982e6	0.318578
$502$	−1.50598e7	−2.66723
$503$	−1.70388e6	−0.300275	−0.150138	−	0.988665i	$-0.547972\pi$
$503$	−1.70388e6	−0.300275	−0.150138	+	0.988665i	$0.547972\pi$
$504$	612754.	0.107451
$505$	−111856.	−0.0195178
$506$	−2.20609e6	−0.383043
$507$	−1.51015e6	−0.260915
$508$	115750.	0.0199004
$509$	7.42527e6	1.27033	0.635167	−	0.772375i	$-0.280931\pi$
$509$	7.42527e6	1.27033	0.635167	+	0.772375i	$0.280931\pi$
$510$	0	0
$511$	−5.50814e6	−0.933152
$512$	−7.44421e6	−1.25500
$513$	−786334.	−0.131921
$514$	4.20833e6	0.702590
$515$	−174278.	−0.0289551
$516$	2.82838e6	0.467641
$517$	−3.03564e6	−0.499487
$518$	−2.17502e7	−3.56155
$519$	−4.17266e6	−0.679978
$520$	42650.0	0.00691689
$521$	4.40734e6	0.711347	0.355674	−	0.934610i	$-0.384251\pi$
$521$	4.40734e6	0.711347	0.355674	+	0.934610i	$0.384251\pi$
$522$	−2.08741e6	−0.335299
$523$	−8.63390e6	−1.38023	−0.690117	−	0.723697i	$-0.742441\pi$
$523$	−8.63390e6	−1.38023	−0.690117	+	0.723697i	$0.742441\pi$
$524$	9.96131e6	1.58485
$525$	5.44840e6	0.862722
$526$	−8.11228e6	−1.27843
$527$	0	0
$528$	−1.33364e6	−0.208188
$529$	−1.36687e6	−0.212368
$530$	8870.71	0.00137173
$531$	−2.65636e6	−0.408838
$532$	5.62828e6	0.862177
$533$	−2.19876e6	−0.335242
$534$	−1.77412e6	−0.269234
$535$	161022.	0.0243221
$536$	−2.73460e6	−0.411132
$537$	−6.25256e6	−0.935669
$538$	1.60353e7	2.38848
$539$	−2.65184e6	−0.393165
$540$	29208.7	0.00431050
$541$	3.00246e6	0.441047	0.220523	−	0.975382i	$-0.429223\pi$
$541$	3.00246e6	0.441047	0.220523	+	0.975382i	$0.429223\pi$
$542$	5.60832e6	0.820039
$543$	120515.	0.0175404
$544$	0	0
$545$	74321.7	0.0107183
$546$	−9.83271e6	−1.41154
$547$	−1.59825e6	−0.228389	−0.114195	−	0.993458i	$-0.536429\pi$
$547$	−1.59825e6	−0.228389	−0.114195	+	0.993458i	$0.536429\pi$
$548$	−2.74999e6	−0.391183
$549$	1.86958e6	0.264736
$550$	−3.05974e6	−0.431298
$551$	3.62148e6	0.508167
$552$	790752.	0.110457
$553$	−9.58488e6	−1.33283
$554$	−1.03104e6	−0.142726
$555$	195829.	0.0269864
$556$	7.81130e6	1.07161
$557$	8.98070e6	1.22651	0.613257	−	0.789884i	$-0.289859\pi$
$557$	8.98070e6	1.22651	0.613257	+	0.789884i	$0.289859\pi$
$558$	1.05113e6	0.142913
$559$	8.57260e6	1.16033
$560$	334989.	0.0451398
$561$	0	0
$562$	−1.47478e7	−1.96964
$563$	1.24536e7	1.65586	0.827931	−	0.560830i	$-0.189518\pi$
$563$	1.24536e7	1.65586	0.827931	+	0.560830i	$0.189518\pi$
$564$	−5.76075e6	−0.762573
$565$	−170337.	−0.0224486
$566$	−4.93384e6	−0.647358
$567$	1.27190e6	0.166149
$568$	216251.	0.0281247
$569$	−6.18204e6	−0.800481	−0.400241	−	0.916410i	$-0.631073\pi$
$569$	−6.18204e6	−0.800481	−0.400241	+	0.916410i	$0.631073\pi$
$570$	−110921.	−0.0142996
$571$	−1.14477e7	−1.46936	−0.734681	−	0.678413i	$-0.762668\pi$
$571$	−1.14477e7	−1.46936	−0.734681	+	0.678413i	$0.762668\pi$
$572$	2.52270e6	0.322386
$573$	6.85882e6	0.872696
$574$	−4.45604e6	−0.564507
$575$	7.03110e6	0.886857
$576$	−1.75450e6	−0.220341
$577$	5.62673e6	0.703585	0.351793	−	0.936078i	$-0.385572\pi$
$577$	5.62673e6	0.703585	0.351793	+	0.936078i	$0.385572\pi$
$578$	0	0
$579$	6.33407e6	0.785211
$580$	−134521.	−0.0166043
$581$	2.08768e7	2.56581
$582$	4.58909e6	0.561590
$583$	−99104.5	−0.0120760
$584$	−1.10876e6	−0.134525
$585$	88529.4	0.0106954
$586$	−4.80910e6	−0.578522
$587$	−7.87112e6	−0.942847	−0.471423	−	0.881907i	$-0.656260\pi$
$587$	−7.87112e6	−0.942847	−0.471423	+	0.881907i	$0.656260\pi$
$588$	−5.03241e6	−0.600251
$589$	−1.82362e6	−0.216594
$590$	−374707.	−0.0443162
$591$	1.37704e6	0.162173
$592$	−1.69681e7	−1.98989
$593$	1.43001e7	1.66995	0.834975	−	0.550288i	$-0.185482\pi$
$593$	1.43001e7	1.66995	0.834975	+	0.550288i	$0.185482\pi$
$594$	−714282.	−0.0830622
$595$	0	0
$596$	−1.29809e7	−1.49689
$597$	1.91125e6	0.219473
$598$	−1.26890e7	−1.45102
$599$	−7.61723e6	−0.867421	−0.433710	−	0.901052i	$-0.642796\pi$
$599$	−7.61723e6	−0.867421	−0.433710	+	0.901052i	$0.642796\pi$
$600$	1.09673e6	0.124372
$601$	−4.13592e6	−0.467075	−0.233537	−	0.972348i	$-0.575030\pi$
$601$	−4.13592e6	−0.467075	−0.233537	+	0.972348i	$0.575030\pi$
$602$	1.73734e7	1.95386
$603$	−5.67626e6	−0.635724
$604$	4.22955e6	0.471739
$605$	215482.	0.0239344
$606$	5.19093e6	0.574201
$607$	1.32634e7	1.46111	0.730555	−	0.682853i	$-0.239261\pi$
$607$	1.32634e7	1.46111	0.730555	+	0.682853i	$0.239261\pi$
$608$	8.26406e6	0.906640
$609$	−5.85779e6	−0.640015
$610$	263724.	0.0286962
$611$	−1.74604e7	−1.89213
$612$	0	0
$613$	6.96884e6	0.749048	0.374524	−	0.927217i	$-0.377806\pi$
$613$	6.96884e6	0.749048	0.374524	+	0.927217i	$0.377806\pi$
$614$	−7.56299e6	−0.809604
$615$	40120.2	0.00427736
$616$	−965664.	−0.102536
$617$	3.25250e6	0.343958	0.171979	−	0.985101i	$-0.444984\pi$
$617$	3.25250e6	0.343958	0.171979	+	0.985101i	$0.444984\pi$
$618$	8.08779e6	0.851841
$619$	8.06355e6	0.845862	0.422931	−	0.906162i	$-0.361001\pi$
$619$	8.06355e6	0.845862	0.422931	+	0.906162i	$0.361001\pi$
$620$	67739.2	0.00707719
$621$	1.64138e6	0.170797
$622$	−2.38674e7	−2.47360
$623$	−4.97860e6	−0.513910
$624$	−7.67086e6	−0.788647
$625$	9.74486e6	0.997873
$626$	1.14258e7	1.16533
$627$	1.23922e6	0.125886
$628$	−9.29529e6	−0.940510
$629$	0	0
$630$	179415.	0.0180098
$631$	8.43316e6	0.843173	0.421587	−	0.906788i	$-0.361473\pi$
$631$	8.43316e6	0.843173	0.421587	+	0.906788i	$0.361473\pi$
$632$	−1.92938e6	−0.192144
$633$	5.06351e6	0.502276
$634$	2.21276e7	2.18631
$635$	−6401.51	−0.000630011 0
$636$	−188071.	−0.0184365
$637$	−1.52529e7	−1.48937
$638$	3.28964e6	0.319961
$639$	448877.	0.0434886
$640$	117464.	0.0113358
$641$	4.82074e6	0.463413	0.231707	−	0.972786i	$-0.425569\pi$
$641$	4.82074e6	0.463413	0.231707	+	0.972786i	$0.425569\pi$
$642$	−7.47260e6	−0.715540
$643$	7.09861e6	0.677089	0.338544	−	0.940950i	$-0.390065\pi$
$643$	7.09861e6	0.677089	0.338544	+	0.940950i	$0.390065\pi$
$644$	−1.17484e7	−1.11625
$645$	−156422.	−0.0148047
$646$	0	0
$647$	−3.40075e6	−0.319385	−0.159692	−	0.987167i	$-0.551050\pi$
$647$	−3.40075e6	−0.319385	−0.159692	+	0.987167i	$0.551050\pi$
$648$	256027.	0.0239524
$649$	4.18627e6	0.390136
$650$	−1.75990e7	−1.63382
$651$	2.94973e6	0.272791
$652$	−1.68389e7	−1.55130
$653$	1.55468e7	1.42679	0.713393	−	0.700764i	$-0.247158\pi$
$653$	1.55468e7	1.42679	0.713393	+	0.700764i	$0.247158\pi$
$654$	−3.44907e6	−0.315324
$655$	−550907.	−0.0501736
$656$	−3.47632e6	−0.315399
$657$	−2.30147e6	−0.208014
$658$	−3.53856e7	−3.18612
$659$	2.54476e6	0.228262	0.114131	−	0.993466i	$-0.463592\pi$
$659$	2.54476e6	0.228262	0.114131	+	0.993466i	$0.463592\pi$
$660$	−46031.2	−0.00411332
$661$	1.25876e6	0.112057	0.0560287	−	0.998429i	$-0.482156\pi$
$661$	1.25876e6	0.112057	0.0560287	+	0.998429i	$0.482156\pi$
$662$	−2.22025e7	−1.96905
$663$	0	0
$664$	4.20239e6	0.369893
$665$	−311270.	−0.0272950
$666$	−9.08791e6	−0.793923
$667$	−7.55941e6	−0.657920
$668$	−5.35277e6	−0.464128
$669$	−1.17307e7	−1.01334
$670$	−800695.	−0.0689097
$671$	−2.94635e6	−0.252626
$672$	−1.33672e7	−1.14187
$673$	1.20292e7	1.02376	0.511880	−	0.859057i	$-0.328949\pi$
$673$	1.20292e7	1.02376	0.511880	+	0.859057i	$0.328949\pi$
$674$	1.66663e7	1.41315
$675$	2.27651e6	0.192314
$676$	4.51635e6	0.380120
$677$	−3.80892e6	−0.319396	−0.159698	−	0.987166i	$-0.551052\pi$
$677$	−3.80892e6	−0.319396	−0.159698	+	0.987166i	$0.551052\pi$
$678$	7.90489e6	0.660422
$679$	1.28781e7	1.07196
$680$	0	0
$681$	−7.83227e6	−0.647172
$682$	−1.65652e6	−0.136376
$683$	5.09029e6	0.417533	0.208767	−	0.977965i	$-0.433055\pi$
$683$	5.09029e6	0.417533	0.208767	+	0.977965i	$0.433055\pi$
$684$	2.35167e6	0.192192
$685$	152087.	0.0123841
$686$	−5.90299e6	−0.478918
$687$	−3.95689e6	−0.319861
$688$	1.35536e7	1.09165
$689$	−570030.	−0.0457456
$690$	231534.	0.0185136
$691$	−100601.	−0.00801506	−0.00400753	−	0.999992i	$-0.501276\pi$
$691$	−100601.	−0.00801506	−0.00400753	+	0.999992i	$0.501276\pi$
$692$	1.24791e7	0.990643
$693$	−2.00445e6	−0.158548
$694$	2.22224e7	1.75143
$695$	−432001.	−0.0339252
$696$	−1.17914e6	−0.0922661
$697$	0	0
$698$	−4.62710e6	−0.359476
$699$	256622.	0.0198655
$700$	−1.62944e7	−1.25688
$701$	−717527.	−0.0551497	−0.0275749	−	0.999620i	$-0.508778\pi$
$701$	−717527.	−0.0551497	−0.0275749	+	0.999620i	$0.508778\pi$
$702$	−4.10841e6	−0.314652
$703$	1.57667e7	1.20324
$704$	2.76498e6	0.210262
$705$	318596.	0.0241417
$706$	−1.77487e7	−1.34015
$707$	1.45670e7	1.09603
$708$	7.94431e6	0.595626
$709$	−1.67125e7	−1.24861	−0.624304	−	0.781181i	$-0.714618\pi$
$709$	−1.67125e7	−1.24861	−0.624304	+	0.781181i	$0.714618\pi$
$710$	63318.8	0.00471397
$711$	−4.00486e6	−0.297107
$712$	−1.00216e6	−0.0740865
$713$	3.80660e6	0.280423
$714$	0	0
$715$	−139517.	−0.0102062
$716$	1.86994e7	1.36315
$717$	−5.55213e6	−0.403331
$718$	−3.78192e6	−0.273780
$719$	−2.32787e7	−1.67933	−0.839664	−	0.543106i	$-0.817248\pi$
$719$	−2.32787e7	−1.67933	−0.839664	+	0.543106i	$0.817248\pi$
$720$	139969.	0.0100623
$721$	2.26963e7	1.62599
$722$	1.00752e7	0.719304
$723$	−1.09296e7	−0.777602
$724$	−360420.	−0.0255542
$725$	−1.04845e7	−0.740804
$726$	−9.99992e6	−0.704133
$727$	9.37548e6	0.657897	0.328948	−	0.944348i	$-0.393306\pi$
$727$	9.37548e6	0.657897	0.328948	+	0.944348i	$0.393306\pi$
$728$	−5.55431e6	−0.388420
$729$	531441.	0.0370370
$730$	−324646.	−0.0225477
$731$	0	0
$732$	−5.59130e6	−0.385687
$733$	−831478.	−0.0571598	−0.0285799	−	0.999592i	$-0.509099\pi$
$733$	−831478.	−0.0571598	−0.0285799	+	0.999592i	$0.509099\pi$
$734$	2.22874e7	1.52693
$735$	278316.	0.0190029
$736$	−1.72503e7	−1.17382
$737$	8.94545e6	0.606644
$738$	−1.86187e6	−0.125837
$739$	−3.39654e6	−0.228784	−0.114392	−	0.993436i	$-0.536492\pi$
$739$	−3.39654e6	−0.228784	−0.114392	+	0.993436i	$0.536492\pi$
$740$	−585662.	−0.0393158
$741$	7.12773e6	0.476876
$742$	−1.15523e6	−0.0770300
$743$	1.32224e7	0.878694	0.439347	−	0.898317i	$-0.355210\pi$
$743$	1.32224e7	0.878694	0.439347	+	0.898317i	$0.355210\pi$
$744$	593764.	0.0393262
$745$	717905.	0.0473888
$746$	−3.61199e7	−2.37629
$747$	8.72297e6	0.571957
$748$	0	0
$749$	−2.09699e7	−1.36582
$750$	642479.	0.0417067
$751$	−1.33651e7	−0.864716	−0.432358	−	0.901702i	$-0.642318\pi$
$751$	−1.33651e7	−0.864716	−0.432358	+	0.901702i	$0.642318\pi$
$752$	−2.76056e7	−1.78013
$753$	−1.76582e7	−1.13490
$754$	1.89214e7	1.21206
$755$	−233914.	−0.0149344
$756$	−3.80385e6	−0.242058
$757$	−711717.	−0.0451406	−0.0225703	−	0.999745i	$-0.507185\pi$
$757$	−711717.	−0.0451406	−0.0225703	+	0.999745i	$0.507185\pi$
$758$	3.61562e6	0.228565
$759$	−2.58672e6	−0.162984
$760$	−62656.9	−0.00393491
$761$	1.55157e7	0.971201	0.485600	−	0.874181i	$-0.338601\pi$
$761$	1.55157e7	0.971201	0.485600	+	0.874181i	$0.338601\pi$
$762$	297077.	0.0185345
$763$	−9.67892e6	−0.601888
$764$	−2.05125e7	−1.27141
$765$	0	0
$766$	9.62956e6	0.592973
$767$	2.40786e7	1.47789
$768$	−1.16894e7	−0.715135
$769$	1.41937e7	0.865528	0.432764	−	0.901507i	$-0.357538\pi$
$769$	1.41937e7	0.865528	0.432764	+	0.901507i	$0.357538\pi$
$770$	−282748.	−0.0171859
$771$	4.93441e6	0.298951
$772$	−1.89431e7	−1.14395
$773$	5.65538e6	0.340419	0.170209	−	0.985408i	$-0.445556\pi$
$773$	5.65538e6	0.340419	0.170209	+	0.985408i	$0.445556\pi$
$774$	7.25913e6	0.435544
$775$	5.27956e6	0.315750
$776$	2.59229e6	0.154536
$777$	−2.55029e7	−1.51543
$778$	−94231.8	−0.00558147
$779$	3.23018e6	0.190714
$780$	−264763.	−0.0155819
$781$	−707405.	−0.0414993
$782$	0	0
$783$	−2.44756e6	−0.142669
$784$	−2.41154e7	−1.40121
$785$	514072.	0.0297749
$786$	2.55661e7	1.47607
$787$	2.28066e6	0.131257	0.0656287	−	0.997844i	$-0.479095\pi$
$787$	2.28066e6	0.131257	0.0656287	+	0.997844i	$0.479095\pi$
$788$	−4.11829e6	−0.236266
$789$	−9.51193e6	−0.543971
$790$	−564927.	−0.0322051
$791$	2.21830e7	1.26061
$792$	−403484.	−0.0228567
$793$	−1.69468e7	−0.956985
$794$	−1.81223e7	−1.02015
$795$	10401.2	0.000583668 0
$796$	−5.71593e6	−0.319745
$797$	−4.16556e6	−0.232288	−0.116144	−	0.993232i	$-0.537053\pi$
$797$	−4.16556e6	−0.232288	−0.116144	+	0.993232i	$0.537053\pi$
$798$	1.44452e7	0.803001
$799$	0	0
$800$	−2.39252e7	−1.32170
$801$	−2.08021e6	−0.114558
$802$	−4.57443e7	−2.51131
$803$	3.62698e6	0.198498
$804$	1.69758e7	0.926171
$805$	649739.	0.0353386
$806$	−9.52800e6	−0.516611
$807$	1.88019e7	1.01629
$808$	2.93226e6	0.158006
$809$	−1.38441e7	−0.743695	−0.371848	−	0.928294i	$-0.621276\pi$
$809$	−1.38441e7	−0.743695	−0.371848	+	0.928294i	$0.621276\pi$
$810$	74965.3	0.00401465
$811$	4.61388e6	0.246328	0.123164	−	0.992386i	$-0.460696\pi$
$811$	4.61388e6	0.246328	0.123164	+	0.992386i	$0.460696\pi$
$812$	1.75187e7	0.932422
$813$	6.57595e6	0.348925
$814$	1.43220e7	0.757606
$815$	931269.	0.0491113
$816$	0	0
$817$	−1.25940e7	−0.660096
$818$	1.82703e7	0.954690
$819$	−1.15292e7	−0.600605
$820$	−119987.	−0.00623157
$821$	2.31578e7	1.19906	0.599528	−	0.800354i	$-0.295355\pi$
$821$	2.31578e7	1.19906	0.599528	+	0.800354i	$0.295355\pi$
$822$	−7.05795e6	−0.364334
$823$	1.42496e7	0.733338	0.366669	−	0.930352i	$-0.380498\pi$
$823$	1.42496e7	0.733338	0.366669	+	0.930352i	$0.380498\pi$
$824$	4.56864e6	0.234406
$825$	−3.58765e6	−0.183516
$826$	4.87982e7	2.48859
$827$	−2.23105e7	−1.13435	−0.567173	−	0.823598i	$-0.691963\pi$
$827$	−2.23105e7	−1.13435	−0.567173	+	0.823598i	$0.691963\pi$
$828$	−4.90883e6	−0.248830
$829$	1.12340e7	0.567737	0.283869	−	0.958863i	$-0.408382\pi$
$829$	1.12340e7	0.567737	0.283869	+	0.958863i	$0.408382\pi$
$830$	1.23047e6	0.0619975
$831$	−1.20893e6	−0.0607295
$832$	1.59036e7	0.796505
$833$	0	0
$834$	2.00480e7	0.998058
$835$	296033.	0.0146935
$836$	−3.70609e6	−0.183401
$837$	1.23249e6	0.0608092
$838$	4.08334e7	2.00866
$839$	2.17970e7	1.06903	0.534516	−	0.845158i	$-0.320494\pi$
$839$	2.17970e7	1.06903	0.534516	+	0.845158i	$0.320494\pi$
$840$	101348.	0.00495585
$841$	−9.23885e6	−0.450430
$842$	4.44053e7	2.15851
$843$	−1.72923e7	−0.838076
$844$	−1.51433e7	−0.731754
$845$	−249775.	−0.0120339
$846$	−1.47852e7	−0.710233
$847$	−2.80622e7	−1.34404
$848$	−901240.	−0.0430379
$849$	−5.78510e6	−0.275449
$850$	0	0
$851$	−3.29112e7	−1.55783
$852$	−1.34245e6	−0.0633575
$853$	−6.80964e6	−0.320443	−0.160222	−	0.987081i	$-0.551221\pi$
$853$	−6.80964e6	−0.320443	−0.160222	+	0.987081i	$0.551221\pi$
$854$	−3.43447e7	−1.61145
$855$	−130058.	−0.00608446
$856$	−4.22113e6	−0.196899
$857$	−155543.	−0.00723432	−0.00361716	−	0.999993i	$-0.501151\pi$
$857$	−155543.	−0.00723432	−0.00361716	+	0.999993i	$0.501151\pi$
$858$	6.47462e6	0.300259
$859$	−648037.	−0.0299652	−0.0149826	−	0.999888i	$-0.504769\pi$
$859$	−648037.	−0.0299652	−0.0149826	+	0.999888i	$0.504769\pi$
$860$	467808.	0.0215686
$861$	−5.22486e6	−0.240197
$862$	−1.84126e6	−0.0844011
$863$	−1.42689e7	−0.652174	−0.326087	−	0.945340i	$-0.605730\pi$
$863$	−1.42689e7	−0.652174	−0.326087	+	0.945340i	$0.605730\pi$
$864$	−5.58524e6	−0.254541
$865$	−690151.	−0.0313620
$866$	−837096.	−0.0379298
$867$	0	0
$868$	−8.82169e6	−0.397422
$869$	6.31143e6	0.283516
$870$	−345254.	−0.0154647
$871$	5.14525e7	2.29806
$872$	−1.94831e6	−0.0867696
$873$	5.38087e6	0.238955
$874$	1.86414e7	0.825466
$875$	1.80295e6	0.0796093
$876$	6.88294e6	0.303050
$877$	1.86999e7	0.820995	0.410497	−	0.911862i	$-0.365355\pi$
$877$	1.86999e7	0.820995	0.410497	+	0.911862i	$0.365355\pi$
$878$	2.32766e7	1.01902
$879$	−5.63884e6	−0.246160
$880$	−220582.	−0.00960205
$881$	−9.98828e6	−0.433562	−0.216781	−	0.976220i	$-0.569556\pi$
$881$	−9.98828e6	−0.433562	−0.216781	+	0.976220i	$0.569556\pi$
$882$	−1.29159e7	−0.559052
$883$	−1.13953e6	−0.0491840	−0.0245920	−	0.999698i	$-0.507829\pi$
$883$	−1.13953e6	−0.0491840	−0.0245920	+	0.999698i	$0.507829\pi$
$884$	0	0
$885$	−439357.	−0.0188564
$886$	−4.73406e7	−2.02605
$887$	−1.02651e7	−0.438080	−0.219040	−	0.975716i	$-0.570293\pi$
$887$	−1.02651e7	−0.438080	−0.219040	+	0.975716i	$0.570293\pi$
$888$	−5.13359e6	−0.218468
$889$	833670.	0.0353785
$890$	−293436.	−0.0124176
$891$	−837520.	−0.0353428
$892$	3.50826e7	1.47632
$893$	2.56510e7	1.07641
$894$	−3.33160e7	−1.39415
$895$	−1.03416e6	−0.0431550
$896$	−1.52973e7	−0.636568
$897$	−1.48783e7	−0.617408
$898$	−4.87557e7	−2.01760
$899$	−5.67625e6	−0.234241
$900$	−6.80830e6	−0.280177
$901$	0	0
$902$	2.93420e6	0.120081
$903$	2.03709e7	0.831363
$904$	4.46532e6	0.181732
$905$	19932.9	0.000809002 0
$906$	1.08553e7	0.439361
$907$	3.52333e7	1.42212	0.711058	−	0.703133i	$-0.248216\pi$
$907$	3.52333e7	1.42212	0.711058	+	0.703133i	$0.248216\pi$
$908$	2.34238e7	0.942849
$909$	6.08655e6	0.244321
$910$	−1.62631e6	−0.0651029
$911$	−6.15016e6	−0.245522	−0.122761	−	0.992436i	$-0.539175\pi$
$911$	−6.15016e6	−0.245522	−0.122761	+	0.992436i	$0.539175\pi$
$912$	1.12692e7	0.448649
$913$	−1.37469e7	−0.545793
$914$	−7.34241e6	−0.290719
$915$	309225.	0.0122102
$916$	1.18338e7	0.465998
$917$	7.17446e7	2.81751
$918$	0	0
$919$	3.41590e7	1.33418	0.667092	−	0.744975i	$-0.267539\pi$
$919$	3.41590e7	1.33418	0.667092	+	0.744975i	$0.267539\pi$
$920$	130789.	0.00509450
$921$	−8.86787e6	−0.344485
$922$	−5.57812e7	−2.16103
$923$	−4.06885e6	−0.157206
$924$	5.99465e6	0.230985
$925$	−4.56461e7	−1.75408
$926$	−2.51086e6	−0.0962265
$927$	9.48321e6	0.362457
$928$	2.57229e7	0.980507
$929$	4.08401e7	1.55256	0.776278	−	0.630391i	$-0.217105\pi$
$929$	4.08401e7	1.55256	0.776278	+	0.630391i	$0.217105\pi$
$930$	173855.	0.00659144
$931$	2.24079e7	0.847280
$932$	−767472.	−0.0289416
$933$	−2.79853e7	−1.05251
$934$	−6.45702e7	−2.42195
$935$	0	0
$936$	−2.32076e6	−0.0865847
$937$	1.09011e7	0.405620	0.202810	−	0.979218i	$-0.434993\pi$
$937$	1.09011e7	0.405620	0.202810	+	0.979218i	$0.434993\pi$
$938$	1.04275e8	3.86965
$939$	1.33971e7	0.495846
$940$	−952818.	−0.0351714
$941$	−8.53215e6	−0.314112	−0.157056	−	0.987590i	$-0.550200\pi$
$941$	−8.53215e6	−0.314112	−0.157056	+	0.987590i	$0.550200\pi$
$942$	−2.38567e7	−0.875958
$943$	−6.74262e6	−0.246916
$944$	3.80693e7	1.39041
$945$	210371.	0.00766312
$946$	−1.14400e7	−0.415621
$947$	3.32382e7	1.20438	0.602189	−	0.798354i	$-0.294295\pi$
$947$	3.32382e7	1.20438	0.602189	+	0.798354i	$0.294295\pi$
$948$	1.19772e7	0.432848
$949$	2.08617e7	0.751941
$950$	2.58546e7	0.929457
$951$	2.59454e7	0.930271
$952$	0	0
$953$	−1.68274e7	−0.600183	−0.300091	−	0.953910i	$-0.597017\pi$
$953$	−1.68274e7	−0.600183	−0.300091	+	0.953910i	$0.597017\pi$
$954$	−482692.	−0.0171711
$955$	1.13444e6	0.0402505
$956$	1.66046e7	0.587603
$957$	3.85722e6	0.136143
$958$	4.16124e7	1.46491
$959$	−1.98063e7	−0.695436
$960$	−290190.	−0.0101626
$961$	−2.57708e7	−0.900161
$962$	8.23775e7	2.86993
$963$	−8.76188e6	−0.304461
$964$	3.26868e7	1.13287
$965$	1.04764e6	0.0362155
$966$	−3.01526e7	−1.03964
$967$	4.06522e6	0.139803	0.0699017	−	0.997554i	$-0.477731\pi$
$967$	4.06522e6	0.139803	0.0699017	+	0.997554i	$0.477731\pi$
$968$	−5.64876e6	−0.193760
$969$	0	0
$970$	759028.	0.0259017
$971$	7.99039e6	0.271969	0.135985	−	0.990711i	$-0.456580\pi$
$971$	7.99039e6	0.271969	0.135985	+	0.990711i	$0.456580\pi$
$972$	−1.58937e6	−0.0539583
$973$	5.62595e7	1.90508
$974$	−2.58254e7	−0.872266
$975$	−2.06354e7	−0.695188
$976$	−2.67936e7	−0.900340
$977$	3.06930e7	1.02873	0.514366	−	0.857571i	$-0.328027\pi$
$977$	3.06930e7	1.02873	0.514366	+	0.857571i	$0.328027\pi$
$978$	−4.32177e7	−1.44482
$979$	3.27830e6	0.109318
$980$	−832351.	−0.0276848
$981$	−4.04415e6	−0.134170
$982$	1.46580e7	0.485060
$983$	3.06021e7	1.01011	0.505054	−	0.863088i	$-0.331473\pi$
$983$	3.06021e7	1.01011	0.505054	+	0.863088i	$0.331473\pi$
$984$	−1.05174e6	−0.0346273
$985$	227760.	0.00747976
$986$	0	0
$987$	−4.14908e7	−1.35569
$988$	−2.13167e7	−0.694749
$989$	2.62884e7	0.854621
$990$	−118141.	−0.00383100
$991$	5.45728e7	1.76519	0.882597	−	0.470131i	$-0.155793\pi$
$991$	5.45728e7	1.76519	0.882597	+	0.470131i	$0.155793\pi$
$992$	−1.29530e7	−0.417917
$993$	−2.60332e7	−0.837828
$994$	−8.24602e6	−0.264715
$995$	316117.	0.0101226
$996$	−2.60876e7	−0.833269
$997$	−2.88163e7	−0.918122	−0.459061	−	0.888405i	$-0.651814\pi$
$997$	−2.88163e7	−0.918122	−0.459061	+	0.888405i	$0.651814\pi$
$998$	−5.42614e7	−1.72451
$999$	−1.06559e7	−0.337813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.6.a.l.1.2	✓	8
17.16	even	2		867.6.a.m.1.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.6.a.l.1.2	✓	8	1.1	even	1	trivial
867.6.a.m.1.2	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)

\(f(q)\)	\(=\)	\(q-7.67568 q^{2} -9.00000 q^{3} +26.9161 q^{4} -1.48858 q^{5} +69.0811 q^{6} +193.858 q^{7} +39.0226 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-7.67568 q^{2} -9.00000 q^{3} +26.9161 q^{4} -1.48858 q^{5} +69.0811 q^{6} +193.858 q^{7} +39.0226 q^{8} +81.0000 q^{9} +11.4259 q^{10} -127.651 q^{11} -242.245 q^{12} -734.225 q^{13} -1488.00 q^{14} +13.3973 q^{15} -1160.84 q^{16} -621.730 q^{18} +1078.65 q^{19} -40.0668 q^{20} -1744.73 q^{21} +979.811 q^{22} -2251.55 q^{23} -351.203 q^{24} -3122.78 q^{25} +5635.68 q^{26} -729.000 q^{27} +5217.91 q^{28} +3357.43 q^{29} -102.833 q^{30} -1690.66 q^{31} +7661.51 q^{32} +1148.86 q^{33} -288.574 q^{35} +2180.20 q^{36} +14617.1 q^{37} -8279.35 q^{38} +6608.03 q^{39} -58.0884 q^{40} +2994.66 q^{41} +13392.0 q^{42} -11675.7 q^{43} -3435.87 q^{44} -120.575 q^{45} +17282.2 q^{46} +23780.7 q^{47} +10447.6 q^{48} +20774.1 q^{49} +23969.5 q^{50} -19762.5 q^{52} +776.369 q^{53} +5595.57 q^{54} +190.020 q^{55} +7564.86 q^{56} -9707.82 q^{57} -25770.5 q^{58} -32794.6 q^{59} +360.601 q^{60} +23081.2 q^{61} +12976.9 q^{62} +15702.5 q^{63} -21660.4 q^{64} +1092.96 q^{65} -8818.30 q^{66} -70077.2 q^{67} +20263.9 q^{69} +2215.00 q^{70} +5541.70 q^{71} +3160.83 q^{72} -28413.2 q^{73} -112196. q^{74} +28105.1 q^{75} +29032.9 q^{76} -24746.3 q^{77} -50721.1 q^{78} -49442.7 q^{79} +1728.01 q^{80} +6561.00 q^{81} -22986.1 q^{82} +107691. q^{83} -46961.2 q^{84} +89618.9 q^{86} -30216.8 q^{87} -4981.29 q^{88} -25681.6 q^{89} +925.497 q^{90} -142336. q^{91} -60602.8 q^{92} +15215.9 q^{93} -182533. q^{94} -1605.66 q^{95} -68953.6 q^{96} +66430.5 q^{97} -159455. q^{98} -10339.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - 72 q^{3} + 187 q^{4} - 27 q^{6} + 18 q^{7} + 105 q^{8} + 648 q^{9}+O(q^{10}) \) 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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