LMFDB - Embedded newform 722.6.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,6,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	722.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:	$115.797117905$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 382x^{2} - 1336x + 14544 $ x^4 - 2x^3 - 382x^2 - 1336*x + 14544
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$21.3388$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +24.3388 q^{3} +16.0000 q^{4} +57.3176 q^{5} +97.3553 q^{6} +33.7394 q^{7} +64.0000 q^{8} +349.379 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +24.3388 q^{3} +16.0000 q^{4} +57.3176 q^{5} +97.3553 q^{6} +33.7394 q^{7} +64.0000 q^{8} +349.379 q^{9} +229.271 q^{10} +296.625 q^{11} +389.421 q^{12} +720.786 q^{13} +134.958 q^{14} +1395.04 q^{15} +256.000 q^{16} +666.983 q^{17} +1397.52 q^{18} +917.082 q^{20} +821.179 q^{21} +1186.50 q^{22} +2665.88 q^{23} +1557.69 q^{24} +160.312 q^{25} +2883.14 q^{26} +2589.14 q^{27} +539.831 q^{28} -7526.47 q^{29} +5580.18 q^{30} -2859.79 q^{31} +1024.00 q^{32} +7219.51 q^{33} +2667.93 q^{34} +1933.86 q^{35} +5590.06 q^{36} -15179.2 q^{37} +17543.1 q^{39} +3668.33 q^{40} +1848.72 q^{41} +3284.71 q^{42} -21230.0 q^{43} +4746.00 q^{44} +20025.6 q^{45} +10663.5 q^{46} +23244.8 q^{47} +6230.74 q^{48} -15668.7 q^{49} +641.246 q^{50} +16233.6 q^{51} +11532.6 q^{52} -13367.1 q^{53} +10356.6 q^{54} +17001.8 q^{55} +2159.32 q^{56} -30105.9 q^{58} +7992.98 q^{59} +22320.7 q^{60} -48395.8 q^{61} -11439.1 q^{62} +11787.8 q^{63} +4096.00 q^{64} +41313.7 q^{65} +28878.0 q^{66} -20034.1 q^{67} +10671.7 q^{68} +64884.3 q^{69} +7735.46 q^{70} +16029.6 q^{71} +22360.3 q^{72} +34481.2 q^{73} -60717.0 q^{74} +3901.80 q^{75} +10008.0 q^{77} +70172.3 q^{78} +62928.4 q^{79} +14673.3 q^{80} -21882.4 q^{81} +7394.86 q^{82} +81255.2 q^{83} +13138.9 q^{84} +38229.9 q^{85} -84920.1 q^{86} -183186. q^{87} +18984.0 q^{88} -51908.7 q^{89} +80102.3 q^{90} +24318.9 q^{91} +42654.0 q^{92} -69603.9 q^{93} +92979.2 q^{94} +24923.0 q^{96} +171538. q^{97} -62674.6 q^{98} +103635. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} + 14 q^{3} + 64 q^{4} + 36 q^{5} + 56 q^{6} + 38 q^{7} + 256 q^{8} - 156 q^{9}+O(q^{10}) $ 4 * q + 16 * q^2 + 14 * q^3 + 64 * q^4 + 36 * q^5 + 56 * q^6 + 38 * q^7 + 256 * q^8 - 156 * q^9	\( 4 q + 16 q^{2} + 14 q^{3} + 64 q^{4} + 36 q^{5} + 56 q^{6} + 38 q^{7} + 256 q^{8} - 156 q^{9} + 144 q^{10} + 72 q^{11} + 224 q^{12} + 674 q^{13} + 152 q^{14} + 20 q^{15} + 1024 q^{16} - 522 q^{17} - 624 q^{18} + 576 q^{20} + 770 q^{21} + 288 q^{22} + 204 q^{23} + 896 q^{24} + 2158 q^{25} + 2696 q^{26} + 6578 q^{27} + 608 q^{28} + 5712 q^{29} + 80 q^{30} - 1162 q^{31} + 4096 q^{32} + 15650 q^{33} - 2088 q^{34} + 4188 q^{35} - 2496 q^{36} - 12754 q^{37} + 22078 q^{39} + 2304 q^{40} + 3480 q^{41} + 3080 q^{42} - 4066 q^{43} + 1152 q^{44} + 25780 q^{45} + 816 q^{46} + 45768 q^{47} + 3584 q^{48} + 708 q^{49} + 8632 q^{50} - 1506 q^{51} + 10784 q^{52} - 45654 q^{53} + 26312 q^{54} - 36570 q^{55} + 2432 q^{56} + 22848 q^{58} + 84006 q^{59} + 320 q^{60} + 14012 q^{61} - 4648 q^{62} + 15128 q^{63} + 16384 q^{64} - 2010 q^{65} + 62600 q^{66} + 19046 q^{67} - 8352 q^{68} + 55796 q^{69} + 16752 q^{70} + 53274 q^{71} - 9984 q^{72} + 41084 q^{73} - 51016 q^{74} + 76608 q^{75} + 135762 q^{77} + 88312 q^{78} + 54170 q^{79} + 9216 q^{80} + 9528 q^{81} + 13920 q^{82} + 26196 q^{83} + 12320 q^{84} + 221850 q^{85} - 16264 q^{86} - 228560 q^{87} + 4608 q^{88} + 137862 q^{89} + 103120 q^{90} - 308516 q^{91} + 3264 q^{92} - 112746 q^{93} + 183072 q^{94} + 14336 q^{96} + 292388 q^{97} + 2832 q^{98} + 138328 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 14 * q^3 + 64 * q^4 + 36 * q^5 + 56 * q^6 + 38 * q^7 + 256 * q^8 - 156 * q^9 + 144 * q^10 + 72 * q^11 + 224 * q^12 + 674 * q^13 + 152 * q^14 + 20 * q^15 + 1024 * q^16 - 522 * q^17 - 624 * q^18 + 576 * q^20 + 770 * q^21 + 288 * q^22 + 204 * q^23 + 896 * q^24 + 2158 * q^25 + 2696 * q^26 + 6578 * q^27 + 608 * q^28 + 5712 * q^29 + 80 * q^30 - 1162 * q^31 + 4096 * q^32 + 15650 * q^33 - 2088 * q^34 + 4188 * q^35 - 2496 * q^36 - 12754 * q^37 + 22078 * q^39 + 2304 * q^40 + 3480 * q^41 + 3080 * q^42 - 4066 * q^43 + 1152 * q^44 + 25780 * q^45 + 816 * q^46 + 45768 * q^47 + 3584 * q^48 + 708 * q^49 + 8632 * q^50 - 1506 * q^51 + 10784 * q^52 - 45654 * q^53 + 26312 * q^54 - 36570 * q^55 + 2432 * q^56 + 22848 * q^58 + 84006 * q^59 + 320 * q^60 + 14012 * q^61 - 4648 * q^62 + 15128 * q^63 + 16384 * q^64 - 2010 * q^65 + 62600 * q^66 + 19046 * q^67 - 8352 * q^68 + 55796 * q^69 + 16752 * q^70 + 53274 * q^71 - 9984 * q^72 + 41084 * q^73 - 51016 * q^74 + 76608 * q^75 + 135762 * q^77 + 88312 * q^78 + 54170 * q^79 + 9216 * q^80 + 9528 * q^81 + 13920 * q^82 + 26196 * q^83 + 12320 * q^84 + 221850 * q^85 - 16264 * q^86 - 228560 * q^87 + 4608 * q^88 + 137862 * q^89 + 103120 * q^90 - 308516 * q^91 + 3264 * q^92 - 112746 * q^93 + 183072 * q^94 + 14336 * q^96 + 292388 * q^97 + 2832 * q^98 + 138328 * 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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	24.3388	1.56134	0.780669	−	0.624945i	$-0.214879\pi$
$3$	24.3388	1.56134	0.780669	+	0.624945i	$0.214879\pi$
$4$	16.0000	0.500000
$5$	57.3176	1.02533	0.512665	−	0.858589i	$-0.328658\pi$
$5$	57.3176	1.02533	0.512665	+	0.858589i	$0.328658\pi$
$6$	97.3553	1.10403
$7$	33.7394	0.260251	0.130126	−	0.991498i	$-0.458462\pi$
$7$	33.7394	0.260251	0.130126	+	0.991498i	$0.458462\pi$
$8$	64.0000	0.353553
$9$	349.379	1.43777
$10$	229.271	0.725017
$11$	296.625	0.739139	0.369569	−	0.929203i	$-0.379505\pi$
$11$	296.625	0.739139	0.369569	+	0.929203i	$0.379505\pi$
$12$	389.421	0.780669
$13$	720.786	1.18290	0.591450	−	0.806342i	$-0.298556\pi$
$13$	720.786	1.18290	0.591450	+	0.806342i	$0.298556\pi$
$14$	134.958	0.184025
$15$	1395.04	1.60088
$16$	256.000	0.250000
$17$	666.983	0.559748	0.279874	−	0.960037i	$-0.409707\pi$
$17$	666.983	0.559748	0.279874	+	0.960037i	$0.409707\pi$
$18$	1397.52	1.01666
$19$	0	0
$19$	0	0
$20$	917.082	0.512665
$21$	821.179	0.406340
$22$	1186.50	0.522650
$23$	2665.88	1.05080	0.525401	−	0.850855i	$-0.323915\pi$
$23$	2665.88	1.05080	0.525401	+	0.850855i	$0.323915\pi$
$24$	1557.69	0.552016
$25$	160.312	0.0512997
$26$	2883.14	0.836436
$27$	2589.14	0.683512
$28$	539.831	0.130126
$29$	−7526.47	−1.66187	−0.830934	−	0.556371i	$-0.812193\pi$
$29$	−7526.47	−1.66187	−0.830934	+	0.556371i	$0.812193\pi$
$30$	5580.18	1.13200
$31$	−2859.79	−0.534477	−0.267239	−	0.963630i	$-0.586111\pi$
$31$	−2859.79	−0.534477	−0.267239	+	0.963630i	$0.586111\pi$
$32$	1024.00	0.176777
$33$	7219.51	1.15405
$34$	2667.93	0.395801
$35$	1933.86	0.266843
$36$	5590.06	0.718887
$37$	−15179.2	−1.82283	−0.911415	−	0.411489i	$-0.865009\pi$
$37$	−15179.2	−1.82283	−0.911415	+	0.411489i	$0.865009\pi$
$38$	0	0
$39$	17543.1	1.84690
$40$	3668.33	0.362509
$41$	1848.72	0.171755	0.0858777	−	0.996306i	$-0.472631\pi$
$41$	1848.72	0.171755	0.0858777	+	0.996306i	$0.472631\pi$
$42$	3284.71	0.287326
$43$	−21230.0	−1.75097	−0.875487	−	0.483242i	$-0.839459\pi$
$43$	−21230.0	−1.75097	−0.875487	+	0.483242i	$0.839459\pi$
$44$	4746.00	0.369569
$45$	20025.6	1.47419
$46$	10663.5	0.743029
$47$	23244.8	1.53490	0.767452	−	0.641106i	$-0.221524\pi$
$47$	23244.8	1.53490	0.767452	+	0.641106i	$0.221524\pi$
$48$	6230.74	0.390334
$49$	−15668.7	−0.932269
$50$	641.246	0.0362744
$51$	16233.6	0.873955
$52$	11532.6	0.591450
$53$	−13367.1	−0.653654	−0.326827	−	0.945084i	$-0.605980\pi$
$53$	−13367.1	−0.653654	−0.326827	+	0.945084i	$0.605980\pi$
$54$	10356.6	0.483316
$55$	17001.8	0.757861
$56$	2159.32	0.0920127
$57$	0	0
$58$	−30105.9	−1.17512
$59$	7992.98	0.298936	0.149468	−	0.988767i	$-0.452244\pi$
$59$	7992.98	0.298936	0.149468	+	0.988767i	$0.452244\pi$
$60$	22320.7	0.800442
$61$	−48395.8	−1.66526	−0.832632	−	0.553827i	$-0.813167\pi$
$61$	−48395.8	−1.66526	−0.832632	+	0.553827i	$0.813167\pi$
$62$	−11439.1	−0.377933
$63$	11787.8	0.374182
$64$	4096.00	0.125000
$65$	41313.7	1.21286
$66$	28878.0	0.816033
$67$	−20034.1	−0.545234	−0.272617	−	0.962123i	$-0.587889\pi$
$67$	−20034.1	−0.545234	−0.272617	+	0.962123i	$0.587889\pi$
$68$	10671.7	0.279874
$69$	64884.3	1.64065
$70$	7735.46	0.188687
$71$	16029.6	0.377378	0.188689	−	0.982037i	$-0.439576\pi$
$71$	16029.6	0.377378	0.188689	+	0.982037i	$0.439576\pi$
$72$	22360.3	0.508330
$73$	34481.2	0.757312	0.378656	−	0.925538i	$-0.376386\pi$
$73$	34481.2	0.757312	0.378656	+	0.925538i	$0.376386\pi$
$74$	−60717.0	−1.28893
$75$	3901.80	0.0800962
$76$	0	0
$77$	10008.0	0.192362
$78$	70172.3	1.30596
$79$	62928.4	1.13443	0.567216	−	0.823569i	$-0.308020\pi$
$79$	62928.4	1.13443	0.567216	+	0.823569i	$0.308020\pi$
$80$	14673.3	0.256332
$81$	−21882.4	−0.370581
$82$	7394.86	0.121449
$83$	81255.2	1.29466	0.647330	−	0.762210i	$-0.275885\pi$
$83$	81255.2	1.29466	0.647330	+	0.762210i	$0.275885\pi$
$84$	13138.9	0.203170
$85$	38229.9	0.573926
$86$	−84920.1	−1.23813
$87$	−183186.	−2.59474
$88$	18984.0	0.261325
$89$	−51908.7	−0.694649	−0.347324	−	0.937745i	$-0.612910\pi$
$89$	−51908.7	−0.694649	−0.347324	+	0.937745i	$0.612910\pi$
$90$	80102.3	1.04241
$91$	24318.9	0.307851
$92$	42654.0	0.525401
$93$	−69603.9	−0.834499
$94$	92979.2	1.08534
$95$	0	0
$96$	24923.0	0.276008
$97$	171538.	1.85111	0.925554	−	0.378616i	$-0.123600\pi$
$97$	171538.	1.85111	0.925554	+	0.378616i	$0.123600\pi$
$98$	−62674.6	−0.659214
$99$	103635.	1.06271
$100$	2564.99	0.0256499
$101$	40325.0	0.393343	0.196671	−	0.980469i	$-0.436987\pi$
$101$	40325.0	0.393343	0.196671	+	0.980469i	$0.436987\pi$
$102$	64934.3	0.617979
$103$	−145271.	−1.34923	−0.674617	−	0.738168i	$-0.735691\pi$
$103$	−145271.	−1.34923	−0.674617	+	0.738168i	$0.735691\pi$
$104$	46130.3	0.418218
$105$	47068.0	0.416632
$106$	−53468.5	−0.462203
$107$	96115.1	0.811582	0.405791	−	0.913966i	$-0.366996\pi$
$107$	96115.1	0.811582	0.405791	+	0.913966i	$0.366996\pi$
$108$	41426.3	0.341756
$109$	−43657.5	−0.351960	−0.175980	−	0.984394i	$-0.556309\pi$
$109$	−43657.5	−0.351960	−0.175980	+	0.984394i	$0.556309\pi$
$110$	68007.4	0.535888
$111$	−369445.	−2.84605
$112$	8637.29	0.0650628
$113$	38244.2	0.281753	0.140877	−	0.990027i	$-0.455008\pi$
$113$	38244.2	0.281753	0.140877	+	0.990027i	$0.455008\pi$
$114$	0	0
$115$	152802.	1.07742
$116$	−120424.	−0.830934
$117$	251827.	1.70074
$118$	31971.9	0.211380
$119$	22503.6	0.145675
$120$	89282.9	0.565998
$121$	−73064.6	−0.453674
$122$	−193583.	−1.17752
$123$	44995.6	0.268168
$124$	−45756.6	−0.267239
$125$	−169929.	−0.972730
$126$	47151.4	0.264587
$127$	107671.	0.592362	0.296181	−	0.955132i	$-0.404287\pi$
$127$	107671.	0.592362	0.296181	+	0.955132i	$0.404287\pi$
$128$	16384.0	0.0883883
$129$	−516714.	−2.73386
$130$	165255.	0.857622
$131$	148793.	0.757539	0.378770	−	0.925491i	$-0.376347\pi$
$131$	148793.	0.757539	0.378770	+	0.925491i	$0.376347\pi$
$132$	115512.	0.577023
$133$	0	0
$134$	−80136.4	−0.385539
$135$	148403.	0.700825
$136$	42686.9	0.197901
$137$	−11356.4	−0.0516941	−0.0258470	−	0.999666i	$-0.508228\pi$
$137$	−11356.4	−0.0516941	−0.0258470	+	0.999666i	$0.508228\pi$
$138$	259537.	1.16012
$139$	−252781.	−1.10971	−0.554853	−	0.831949i	$-0.687225\pi$
$139$	−252781.	−1.10971	−0.554853	+	0.831949i	$0.687225\pi$
$140$	30941.8	0.133422
$141$	565751.	2.39650
$142$	64118.4	0.266846
$143$	213803.	0.874327
$144$	89441.0	0.359443
$145$	−431400.	−1.70396
$146$	137925.	0.535500
$147$	−381357.	−1.45559
$148$	−242868.	−0.911415
$149$	64886.9	0.239437	0.119718	−	0.992808i	$-0.461801\pi$
$149$	64886.9	0.239437	0.119718	+	0.992808i	$0.461801\pi$
$150$	15607.2	0.0566365
$151$	248902.	0.888353	0.444176	−	0.895939i	$-0.353496\pi$
$151$	248902.	0.888353	0.444176	+	0.895939i	$0.353496\pi$
$152$	0	0
$153$	233030.	0.804791
$154$	40031.8	0.136020
$155$	−163916.	−0.548015
$156$	280689.	0.923452
$157$	−157709.	−0.510631	−0.255315	−	0.966858i	$-0.582179\pi$
$157$	−157709.	−0.510631	−0.255315	+	0.966858i	$0.582179\pi$
$158$	251713.	0.802165
$159$	−325340.	−1.02057
$160$	58693.3	0.181254
$161$	89945.2	0.273472
$162$	−87529.7	−0.262040
$163$	190969.	0.562980	0.281490	−	0.959564i	$-0.409171\pi$
$163$	190969.	0.562980	0.281490	+	0.959564i	$0.409171\pi$
$164$	29579.5	0.0858777
$165$	413805.	1.18328
$166$	325021.	0.915463
$167$	−586104.	−1.62624	−0.813118	−	0.582099i	$-0.802231\pi$
$167$	−586104.	−1.62624	−0.813118	+	0.582099i	$0.802231\pi$
$168$	52555.4	0.143663
$169$	148239.	0.399250
$170$	152920.	0.405827
$171$	0	0
$172$	−339681.	−0.875487
$173$	430660.	1.09401	0.547003	−	0.837131i	$-0.315769\pi$
$173$	430660.	1.09401	0.547003	+	0.837131i	$0.315769\pi$
$174$	−732743.	−1.83476
$175$	5408.82	0.0133508
$176$	75936.0	0.184785
$177$	194540.	0.466741
$178$	−207635.	−0.491191
$179$	−434152.	−1.01277	−0.506383	−	0.862308i	$-0.669018\pi$
$179$	−434152.	−1.01277	−0.506383	+	0.862308i	$0.669018\pi$
$180$	320409.	0.737096
$181$	348244.	0.790109	0.395055	−	0.918658i	$-0.370726\pi$
$181$	348244.	0.790109	0.395055	+	0.918658i	$0.370726\pi$
$182$	97275.6	0.217683
$183$	−1.17790e6	−2.60004
$184$	170616.	0.371514
$185$	−870039.	−1.86900
$186$	−278415.	−0.590080
$187$	197844.	0.413731
$188$	371917.	0.767452
$189$	87356.1	0.177885
$190$	0	0
$191$	608995.	1.20790	0.603949	−	0.797023i	$-0.293593\pi$
$191$	608995.	1.20790	0.603949	+	0.797023i	$0.293593\pi$
$192$	99691.9	0.195167
$193$	−936113.	−1.80898	−0.904492	−	0.426490i	$-0.859750\pi$
$193$	−936113.	−1.80898	−0.904492	+	0.426490i	$0.859750\pi$
$194$	686153.	1.30893
$195$	1.00553e6	1.89368
$196$	−250698.	−0.466135
$197$	488265.	0.896375	0.448188	−	0.893940i	$-0.352070\pi$
$197$	488265.	0.896375	0.448188	+	0.893940i	$0.352070\pi$
$198$	414538.	0.751453
$199$	511508.	0.915629	0.457815	−	0.889048i	$-0.348632\pi$
$199$	511508.	0.915629	0.457815	+	0.889048i	$0.348632\pi$
$200$	10259.9	0.0181372
$201$	−487607.	−0.851294
$202$	161300.	0.278135
$203$	−253939.	−0.432503
$204$	259737.	0.436977
$205$	105964.	0.176106
$206$	−581086.	−0.954052
$207$	931401.	1.51081
$208$	184521.	0.295725
$209$	0	0
$210$	188272.	0.294603
$211$	−110779.	−0.171297	−0.0856487	−	0.996325i	$-0.527296\pi$
$211$	−110779.	−0.171297	−0.0856487	+	0.996325i	$0.527296\pi$
$212$	−213874.	−0.326827
$213$	390142.	0.589214
$214$	384461.	0.573875
$215$	−1.21686e6	−1.79532
$216$	165705.	0.241658
$217$	−96487.6	−0.139098
$218$	−174630.	−0.248873
$219$	839231.	1.18242
$220$	272030.	0.378930
$221$	480752.	0.662125
$222$	−1.47778e6	−2.01246
$223$	−653521.	−0.880030	−0.440015	−	0.897990i	$-0.645027\pi$
$223$	−653521.	−0.880030	−0.440015	+	0.897990i	$0.645027\pi$
$224$	34549.2	0.0460063
$225$	56009.5	0.0737574
$226$	152977.	0.199230
$227$	−407748.	−0.525203	−0.262601	−	0.964904i	$-0.584580\pi$
$227$	−407748.	−0.525203	−0.262601	+	0.964904i	$0.584580\pi$
$228$	0	0
$229$	−512836.	−0.646234	−0.323117	−	0.946359i	$-0.604731\pi$
$229$	−512836.	−0.646234	−0.323117	+	0.946359i	$0.604731\pi$
$230$	611207.	0.761849
$231$	243582.	0.300342
$232$	−481694.	−0.587559
$233$	954851.	1.15225	0.576124	−	0.817363i	$-0.304565\pi$
$233$	954851.	1.15225	0.576124	+	0.817363i	$0.304565\pi$
$234$	1.00731e6	1.20261
$235$	1.33234e6	1.57378
$236$	127888.	0.149468
$237$	1.53160e6	1.77123
$238$	90014.5	0.103008
$239$	−529252.	−0.599332	−0.299666	−	0.954044i	$-0.596875\pi$
$239$	−529252.	−0.599332	−0.299666	+	0.954044i	$0.596875\pi$
$240$	357131.	0.400221
$241$	108692.	0.120546	0.0602732	−	0.998182i	$-0.480803\pi$
$241$	108692.	0.120546	0.0602732	+	0.998182i	$0.480803\pi$
$242$	−292258.	−0.320796
$243$	−1.16175e6	−1.26211
$244$	−774333.	−0.832632
$245$	−898090.	−0.955883
$246$	179982.	0.189624
$247$	0	0
$248$	−183026.	−0.188966
$249$	1.97766e6	2.02140
$250$	−679716.	−0.687824
$251$	−509528.	−0.510485	−0.255243	−	0.966877i	$-0.582155\pi$
$251$	−509528.	−0.510485	−0.255243	+	0.966877i	$0.582155\pi$
$252$	188606.	0.187091
$253$	790766.	0.776688
$254$	430682.	0.418863
$255$	930471.	0.896091
$256$	65536.0	0.0625000
$257$	−1.29857e6	−1.22640	−0.613201	−	0.789927i	$-0.710118\pi$
$257$	−1.29857e6	−1.22640	−0.613201	+	0.789927i	$0.710118\pi$
$258$	−2.06686e6	−1.93313
$259$	−512139.	−0.474393
$260$	661020.	0.606430
$261$	−2.62959e6	−2.38939
$262$	595173.	0.535661
$263$	−784882.	−0.699705	−0.349853	−	0.936805i	$-0.613768\pi$
$263$	−784882.	−0.699705	−0.349853	+	0.936805i	$0.613768\pi$
$264$	462049.	0.408017
$265$	−766172.	−0.670211
$266$	0	0
$267$	−1.26340e6	−1.08458
$268$	−320546.	−0.272617
$269$	2.00724e6	1.69129	0.845645	−	0.533746i	$-0.179216\pi$
$269$	2.00724e6	1.69129	0.845645	+	0.533746i	$0.179216\pi$
$270$	593614.	0.495558
$271$	−624304.	−0.516384	−0.258192	−	0.966094i	$-0.583127\pi$
$271$	−624304.	−0.516384	−0.258192	+	0.966094i	$0.583127\pi$
$272$	170748.	0.139937
$273$	591894.	0.480659
$274$	−45425.8	−0.0365532
$275$	47552.4	0.0379176
$276$	1.03815e6	0.820327
$277$	−245409.	−0.192173	−0.0960863	−	0.995373i	$-0.530632\pi$
$277$	−245409.	−0.192173	−0.0960863	+	0.995373i	$0.530632\pi$
$278$	−1.01112e6	−0.784680
$279$	−999149.	−0.768457
$280$	123767.	0.0943433
$281$	1.21139e6	0.915204	0.457602	−	0.889157i	$-0.348708\pi$
$281$	1.21139e6	0.915204	0.457602	+	0.889157i	$0.348708\pi$
$282$	2.26301e6	1.69458
$283$	61542.1	0.0456779	0.0228389	−	0.999739i	$-0.492730\pi$
$283$	61542.1	0.0456779	0.0228389	+	0.999739i	$0.492730\pi$
$284$	256473.	0.188689
$285$	0	0
$286$	855212.	0.618242
$287$	62374.6	0.0446995
$288$	357764.	0.254165
$289$	−974991.	−0.686682
$290$	−1.72560e6	−1.20488
$291$	4.17504e6	2.89020
$292$	551698.	0.378656
$293$	−78019.4	−0.0530926	−0.0265463	−	0.999648i	$-0.508451\pi$
$293$	−78019.4	−0.0530926	−0.0265463	+	0.999648i	$0.508451\pi$
$294$	−1.52543e6	−1.02926
$295$	458139.	0.306508
$296$	−971472.	−0.644467
$297$	768004.	0.505211
$298$	259547.	0.169307
$299$	1.92153e6	1.24299
$300$	62428.8	0.0400481
$301$	−716289.	−0.455693
$302$	995607.	0.628160
$303$	981464.	0.614140
$304$	0	0
$305$	−2.77393e6	−1.70744
$306$	932119.	0.569073
$307$	−794710.	−0.481241	−0.240620	−	0.970619i	$-0.577351\pi$
$307$	−794710.	−0.481241	−0.240620	+	0.970619i	$0.577351\pi$
$308$	160127.	0.0961809
$309$	−3.53574e6	−2.10661
$310$	−655665.	−0.387505
$311$	3.23144e6	1.89450	0.947251	−	0.320492i	$-0.103848\pi$
$311$	3.23144e6	1.89450	0.947251	+	0.320492i	$0.103848\pi$
$312$	1.12276e6	0.652979
$313$	1.04864e6	0.605017	0.302509	−	0.953147i	$-0.402176\pi$
$313$	1.04864e6	0.605017	0.302509	+	0.953147i	$0.402176\pi$
$314$	−630835.	−0.361070
$315$	675652.	0.383660
$316$	1.00685e6	0.567216
$317$	−307309.	−0.171762	−0.0858809	−	0.996305i	$-0.527370\pi$
$317$	−307309.	−0.171762	−0.0858809	+	0.996305i	$0.527370\pi$
$318$	−1.30136e6	−0.721655
$319$	−2.23254e6	−1.22835
$320$	234773.	0.128166
$321$	2.33933e6	1.26715
$322$	359781.	0.193374
$323$	0	0
$324$	−350119.	−0.185290
$325$	115550.	0.0606824
$326$	763875.	0.398087
$327$	−1.06257e6	−0.549528
$328$	118318.	0.0607247
$329$	784266.	0.399461
$330$	1.65522e6	0.836702
$331$	−249620.	−0.125230	−0.0626151	−	0.998038i	$-0.519944\pi$
$331$	−249620.	−0.125230	−0.0626151	+	0.998038i	$0.519944\pi$
$332$	1.30008e6	0.647330
$333$	−5.30331e6	−2.62082
$334$	−2.34442e6	−1.14992
$335$	−1.14831e6	−0.559044
$336$	210222.	0.101585
$337$	3.72828e6	1.78827	0.894137	−	0.447794i	$-0.147790\pi$
$337$	3.72828e6	1.78827	0.894137	+	0.447794i	$0.147790\pi$
$338$	592956.	0.282313
$339$	930818.	0.439912
$340$	611678.	0.286963
$341$	−848284.	−0.395053
$342$	0	0
$343$	−1.09571e6	−0.502875
$344$	−1.35872e6	−0.619063
$345$	3.71902e6	1.68221
$346$	1.72264e6	0.773579
$347$	3.90382e6	1.74047	0.870233	−	0.492640i	$-0.163968\pi$
$347$	3.90382e6	1.74047	0.870233	+	0.492640i	$0.163968\pi$
$348$	−2.93097e6	−1.29737
$349$	1.31205e6	0.576617	0.288308	−	0.957538i	$-0.406907\pi$
$349$	1.31205e6	0.576617	0.288308	+	0.957538i	$0.406907\pi$
$350$	21635.3	0.00944045
$351$	1.86622e6	0.808526
$352$	303744.	0.130663
$353$	1.61557e6	0.690062	0.345031	−	0.938591i	$-0.387868\pi$
$353$	1.61557e6	0.690062	0.345031	+	0.938591i	$0.387868\pi$
$354$	778160.	0.330035
$355$	918778.	0.386937
$356$	−830539.	−0.347324
$357$	547712.	0.227448
$358$	−1.73661e6	−0.716134
$359$	954354.	0.390817	0.195408	−	0.980722i	$-0.437397\pi$
$359$	954354.	0.390817	0.195408	+	0.980722i	$0.437397\pi$
$360$	1.28164e6	0.521205
$361$	0	0
$362$	1.39298e6	0.558692
$363$	−1.77831e6	−0.708338
$364$	389102.	0.153925
$365$	1.97638e6	0.776494
$366$	−4.71159e6	−1.83850
$367$	3.34153e6	1.29503	0.647516	−	0.762052i	$-0.275808\pi$
$367$	3.34153e6	1.29503	0.647516	+	0.762052i	$0.275808\pi$
$368$	682464.	0.262700
$369$	645902.	0.246945
$370$	−3.48015e6	−1.32158
$371$	−450999.	−0.170114
$372$	−1.11366e6	−0.417250
$373$	1.61445e6	0.600830	0.300415	−	0.953809i	$-0.402875\pi$
$373$	1.61445e6	0.600830	0.300415	+	0.953809i	$0.402875\pi$
$374$	791375.	0.292552
$375$	−4.13587e6	−1.51876
$376$	1.48767e6	0.542670
$377$	−5.42497e6	−1.96582
$378$	349425.	0.125784
$379$	−363580.	−0.130017	−0.0650087	−	0.997885i	$-0.520708\pi$
$379$	−363580.	−0.130017	−0.0650087	+	0.997885i	$0.520708\pi$
$380$	0	0
$381$	2.62058e6	0.924877
$382$	2.43598e6	0.854112
$383$	−2.27621e6	−0.792894	−0.396447	−	0.918058i	$-0.629757\pi$
$383$	−2.27621e6	−0.792894	−0.396447	+	0.918058i	$0.629757\pi$
$384$	398768.	0.138004
$385$	573633.	0.197234
$386$	−3.74445e6	−1.27915
$387$	−7.41733e6	−2.51750
$388$	2.74461e6	0.925554
$389$	1.94441e6	0.651498	0.325749	−	0.945456i	$-0.394384\pi$
$389$	1.94441e6	0.651498	0.325749	+	0.945456i	$0.394384\pi$
$390$	4.02211e6	1.33904
$391$	1.77809e6	0.588184
$392$	−1.00279e6	−0.329607
$393$	3.62146e6	1.18277
$394$	1.95306e6	0.633833
$395$	3.60691e6	1.16317
$396$	1.65815e6	0.531357
$397$	93849.7	0.0298852	0.0149426	−	0.999888i	$-0.495243\pi$
$397$	93849.7	0.0298852	0.0149426	+	0.999888i	$0.495243\pi$
$398$	2.04603e6	0.647448
$399$	0	0
$400$	41039.8	0.0128249
$401$	4.12081e6	1.27974	0.639871	−	0.768483i	$-0.278988\pi$
$401$	4.12081e6	1.27974	0.639871	+	0.768483i	$0.278988\pi$
$402$	−1.95043e6	−0.601956
$403$	−2.06129e6	−0.632233
$404$	645200.	0.196671
$405$	−1.25425e6	−0.379967
$406$	−1.01576e6	−0.305826
$407$	−4.50254e6	−1.34732
$408$	1.03895e6	0.308990
$409$	−4.55917e6	−1.34765	−0.673825	−	0.738891i	$-0.735350\pi$
$409$	−4.55917e6	−1.34765	−0.673825	+	0.738891i	$0.735350\pi$
$410$	423856.	0.124526
$411$	−276403.	−0.0807119
$412$	−2.32434e6	−0.674617
$413$	269679.	0.0777985
$414$	3.72561e6	1.06831
$415$	4.65736e6	1.32745
$416$	738084.	0.209109
$417$	−6.15240e6	−1.73262
$418$	0	0
$419$	5.22672e6	1.45444	0.727218	−	0.686407i	$-0.240813\pi$
$419$	5.22672e6	1.45444	0.727218	+	0.686407i	$0.240813\pi$
$420$	753088.	0.208316
$421$	−3.94648e6	−1.08519	−0.542594	−	0.839995i	$-0.682558\pi$
$421$	−3.94648e6	−1.08519	−0.542594	+	0.839995i	$0.682558\pi$
$422$	−443116.	−0.121126
$423$	8.12125e6	2.20684
$424$	−855496.	−0.231102
$425$	106925.	0.0287149
$426$	1.56057e6	0.416637
$427$	−1.63285e6	−0.433387
$428$	1.53784e6	0.405791
$429$	5.20372e6	1.36512
$430$	−4.86742e6	−1.26949
$431$	−704636.	−0.182714	−0.0913569	−	0.995818i	$-0.529120\pi$
$431$	−704636.	−0.182714	−0.0913569	+	0.995818i	$0.529120\pi$
$432$	662820.	0.170878
$433$	−7.12384e6	−1.82597	−0.912986	−	0.407990i	$-0.866230\pi$
$433$	−7.12384e6	−1.82597	−0.912986	+	0.407990i	$0.866230\pi$
$434$	−385950.	−0.0983574
$435$	−1.04998e7	−2.66046
$436$	−698521.	−0.175980
$437$	0	0
$438$	3.35692e6	0.836096
$439$	−7.67127e6	−1.89979	−0.949896	−	0.312567i	$-0.898811\pi$
$439$	−7.67127e6	−1.89979	−0.949896	+	0.312567i	$0.898811\pi$
$440$	1.08812e6	0.267944
$441$	−5.47430e6	−1.34039
$442$	1.92301e6	0.468193
$443$	−4.09669e6	−0.991800	−0.495900	−	0.868380i	$-0.665162\pi$
$443$	−4.09669e6	−0.991800	−0.495900	+	0.868380i	$0.665162\pi$
$444$	−5.91112e6	−1.42303
$445$	−2.97528e6	−0.712243
$446$	−2.61409e6	−0.622275
$447$	1.57927e6	0.373842
$448$	138197.	0.0325314
$449$	4.01682e6	0.940301	0.470151	−	0.882586i	$-0.344200\pi$
$449$	4.01682e6	0.940301	0.470151	+	0.882586i	$0.344200\pi$
$450$	224038.	0.0521543
$451$	548375.	0.126951
$452$	611907.	0.140877
$453$	6.05798e6	1.38702
$454$	−1.63099e6	−0.371375
$455$	1.39390e6	0.315648
$456$	0	0
$457$	−8.59295e6	−1.92465	−0.962325	−	0.271900i	$-0.912348\pi$
$457$	−8.59295e6	−1.92465	−0.962325	+	0.271900i	$0.912348\pi$
$458$	−2.05134e6	−0.456956
$459$	1.72691e6	0.382594
$460$	2.44483e6	0.538708
$461$	−4.10402e6	−0.899408	−0.449704	−	0.893178i	$-0.648471\pi$
$461$	−4.10402e6	−0.899408	−0.449704	+	0.893178i	$0.648471\pi$
$462$	974328.	0.212374
$463$	−4.50635e6	−0.976950	−0.488475	−	0.872578i	$-0.662447\pi$
$463$	−4.50635e6	−0.976950	−0.488475	+	0.872578i	$0.662447\pi$
$464$	−1.92678e6	−0.415467
$465$	−3.98953e6	−0.855636
$466$	3.81940e6	0.814762
$467$	4.26366e6	0.904669	0.452335	−	0.891848i	$-0.350591\pi$
$467$	4.26366e6	0.904669	0.452335	+	0.891848i	$0.350591\pi$
$468$	4.02924e6	0.850371
$469$	−675940.	−0.141898
$470$	5.32935e6	1.11283
$471$	−3.83845e6	−0.797266
$472$	511551.	0.105690
$473$	−6.29736e6	−1.29421
$474$	6.12641e6	1.25245
$475$	0	0
$476$	360058.	0.0728375
$477$	−4.67019e6	−0.939807
$478$	−2.11701e6	−0.423792
$479$	−2.11480e6	−0.421144	−0.210572	−	0.977578i	$-0.567533\pi$
$479$	−2.11480e6	−0.421144	−0.210572	+	0.977578i	$0.567533\pi$
$480$	1.42853e6	0.282999
$481$	−1.09410e7	−2.15622
$482$	434767.	0.0852392
$483$	2.18916e6	0.426982
$484$	−1.16903e6	−0.226837
$485$	9.83217e6	1.89799
$486$	−4.64702e6	−0.892449
$487$	−1.97866e6	−0.378050	−0.189025	−	0.981972i	$-0.560533\pi$
$487$	−1.97866e6	−0.378050	−0.189025	+	0.981972i	$0.560533\pi$
$488$	−3.09733e6	−0.588760
$489$	4.64796e6	0.879002
$490$	−3.59236e6	−0.675911
$491$	−6.22636e6	−1.16555	−0.582774	−	0.812634i	$-0.698033\pi$
$491$	−6.22636e6	−1.16555	−0.582774	+	0.812634i	$0.698033\pi$
$492$	719929.	0.134084
$493$	−5.02003e6	−0.930227
$494$	0	0
$495$	5.94009e6	1.08963
$496$	−732105.	−0.133619
$497$	540829.	0.0982130
$498$	7.91063e6	1.42935
$499$	5.00613e6	0.900016	0.450008	−	0.893024i	$-0.351421\pi$
$499$	5.00613e6	0.900016	0.450008	+	0.893024i	$0.351421\pi$
$500$	−2.71886e6	−0.486365
$501$	−1.42651e7	−2.53910
$502$	−2.03811e6	−0.360968
$503$	5.87062e6	1.03458	0.517290	−	0.855810i	$-0.326941\pi$
$503$	5.87062e6	1.03458	0.517290	+	0.855810i	$0.326941\pi$
$504$	754422.	0.132293
$505$	2.31133e6	0.403306
$506$	3.16306e6	0.549201
$507$	3.60796e6	0.623364
$508$	1.72273e6	0.296181
$509$	−4.29379e6	−0.734593	−0.367296	−	0.930104i	$-0.619717\pi$
$509$	−4.29379e6	−0.734593	−0.367296	+	0.930104i	$0.619717\pi$
$510$	3.72188e6	0.633632
$511$	1.16337e6	0.197091
$512$	262144.	0.0441942
$513$	0	0
$514$	−5.19428e6	−0.867197
$515$	−8.32662e6	−1.38341
$516$	−8.26743e6	−1.36693
$517$	6.89499e6	1.13451
$518$	−2.04856e6	−0.335447
$519$	1.04818e7	1.70811
$520$	2.64408e6	0.428811
$521$	−7.53599e6	−1.21631	−0.608157	−	0.793816i	$-0.708091\pi$
$521$	−7.53599e6	−1.21631	−0.608157	+	0.793816i	$0.708091\pi$
$522$	−1.05184e7	−1.68955
$523$	−192070.	−0.0307047	−0.0153523	−	0.999882i	$-0.504887\pi$
$523$	−192070.	−0.0307047	−0.0153523	+	0.999882i	$0.504887\pi$
$524$	2.38069e6	0.378770
$525$	131644.	0.0208451
$526$	−3.13953e6	−0.494766
$527$	−1.90743e6	−0.299173
$528$	1.84819e6	0.288511
$529$	670557.	0.104183
$530$	−3.06469e6	−0.473911
$531$	2.79258e6	0.429803
$532$	0	0
$533$	1.33253e6	0.203169
$534$	−5.05359e6	−0.766914
$535$	5.50909e6	0.832138
$536$	−1.28218e6	−0.192769
$537$	−1.05668e7	−1.58127
$538$	8.02895e6	1.19592
$539$	−4.64771e6	−0.689077
$540$	2.37446e6	0.350412
$541$	−2.22748e6	−0.327205	−0.163602	−	0.986526i	$-0.552311\pi$
$541$	−2.22748e6	−0.327205	−0.163602	+	0.986526i	$0.552311\pi$
$542$	−2.49722e6	−0.365139
$543$	8.47585e6	1.23363
$544$	682990.	0.0989504
$545$	−2.50235e6	−0.360875
$546$	2.36757e6	0.339877
$547$	6.51203e6	0.930568	0.465284	−	0.885161i	$-0.345952\pi$
$547$	6.51203e6	0.930568	0.465284	+	0.885161i	$0.345952\pi$
$548$	−181703.	−0.0258470
$549$	−1.69085e7	−2.39427
$550$	190210.	0.0268118
$551$	0	0
$552$	4.15260e6	0.580059
$553$	2.12317e6	0.295237
$554$	−981637.	−0.135887
$555$	−2.11757e7	−2.91814
$556$	−4.04450e6	−0.554853
$557$	−7.35212e6	−1.00409	−0.502047	−	0.864840i	$-0.667420\pi$
$557$	−7.35212e6	−1.00409	−0.502047	+	0.864840i	$0.667420\pi$
$558$	−3.99660e6	−0.543381
$559$	−1.53023e7	−2.07123
$560$	495069.	0.0667108
$561$	4.81529e6	0.645974
$562$	4.84556e6	0.647147
$563$	−1.07415e7	−1.42822	−0.714110	−	0.700034i	$-0.753168\pi$
$563$	−1.07415e7	−1.42822	−0.714110	+	0.700034i	$0.753168\pi$
$564$	9.05202e6	1.19825
$565$	2.19207e6	0.288890
$566$	246168.	0.0322991
$567$	−738300.	−0.0964440
$568$	1.02589e6	0.133423
$569$	−5.66678e6	−0.733763	−0.366881	−	0.930268i	$-0.619575\pi$
$569$	−5.66678e6	−0.733763	−0.366881	+	0.930268i	$0.619575\pi$
$570$	0	0
$571$	1.46351e7	1.87848	0.939238	−	0.343266i	$-0.111533\pi$
$571$	1.46351e7	1.87848	0.939238	+	0.343266i	$0.111533\pi$
$572$	3.42085e6	0.437163
$573$	1.48222e7	1.88593
$574$	249498.	0.0316074
$575$	427371.	0.0539058
$576$	1.43106e6	0.179722
$577$	1.05971e7	1.32510	0.662550	−	0.749017i	$-0.269474\pi$
$577$	1.05971e7	1.32510	0.662550	+	0.749017i	$0.269474\pi$
$578$	−3.89996e6	−0.485558
$579$	−2.27839e7	−2.82443
$580$	−6.90240e6	−0.851981
$581$	2.74150e6	0.336937
$582$	1.67002e7	2.04368
$583$	−3.96502e6	−0.483141
$584$	2.20679e6	0.267750
$585$	1.44341e7	1.74382
$586$	−312078.	−0.0375421
$587$	1.12648e7	1.34937	0.674683	−	0.738108i	$-0.264281\pi$
$587$	1.12648e7	1.34937	0.674683	+	0.738108i	$0.264281\pi$
$588$	−6.10171e6	−0.727793
$589$	0	0
$590$	1.83256e6	0.216734
$591$	1.18838e7	1.39954
$592$	−3.88589e6	−0.455707
$593$	8.64117e6	1.00910	0.504552	−	0.863381i	$-0.331658\pi$
$593$	8.64117e6	1.00910	0.504552	+	0.863381i	$0.331658\pi$
$594$	3.07202e6	0.357238
$595$	1.28985e6	0.149365
$596$	1.03819e6	0.119718
$597$	1.24495e7	1.42961
$598$	7.68610e6	0.878928
$599$	−3.00195e6	−0.341851	−0.170925	−	0.985284i	$-0.554676\pi$
$599$	−3.00195e6	−0.341851	−0.170925	+	0.985284i	$0.554676\pi$
$600$	249715.	0.0283183
$601$	−1.02562e7	−1.15824	−0.579122	−	0.815241i	$-0.696605\pi$
$601$	−1.02562e7	−1.15824	−0.579122	+	0.815241i	$0.696605\pi$
$602$	−2.86516e6	−0.322224
$603$	−6.99950e6	−0.783923
$604$	3.98243e6	0.444176
$605$	−4.18789e6	−0.465165
$606$	3.92585e6	0.434263
$607$	1.35691e7	1.49479	0.747395	−	0.664380i	$-0.231304\pi$
$607$	1.35691e7	1.49479	0.747395	+	0.664380i	$0.231304\pi$
$608$	0	0
$609$	−6.18058e6	−0.675283
$610$	−1.10957e7	−1.20734
$611$	1.67545e7	1.81564
$612$	3.72848e6	0.402395
$613$	−1.11818e7	−1.20188	−0.600941	−	0.799293i	$-0.705207\pi$
$613$	−1.11818e7	−1.20188	−0.600941	+	0.799293i	$0.705207\pi$
$614$	−3.17884e6	−0.340289
$615$	2.57904e6	0.274961
$616$	640509.	0.0680102
$617$	1.17688e6	0.124457	0.0622283	−	0.998062i	$-0.480179\pi$
$617$	1.17688e6	0.124457	0.0622283	+	0.998062i	$0.480179\pi$
$618$	−1.41430e7	−1.48960
$619$	302723.	0.0317555	0.0158778	−	0.999874i	$-0.494946\pi$
$619$	302723.	0.0317555	0.0158778	+	0.999874i	$0.494946\pi$
$620$	−2.62266e6	−0.274008
$621$	6.90233e6	0.718235
$622$	1.29258e7	1.33962
$623$	−1.75137e6	−0.180783
$624$	4.49103e6	0.461726
$625$	−1.02409e7	−1.04867
$626$	4.19458e6	0.427812
$627$	0	0
$628$	−2.52334e6	−0.255315
$629$	−1.01243e7	−1.02032
$630$	2.70261e6	0.271289
$631$	−6.81671e6	−0.681556	−0.340778	−	0.940144i	$-0.610690\pi$
$631$	−6.81671e6	−0.681556	−0.340778	+	0.940144i	$0.610690\pi$
$632$	4.02742e6	0.401082
$633$	−2.69623e6	−0.267453
$634$	−1.22923e6	−0.121454
$635$	6.17142e6	0.607366
$636$	−5.20544e6	−0.510287
$637$	−1.12937e7	−1.10278
$638$	−8.93016e6	−0.868576
$639$	5.60040e6	0.542584
$640$	939092.	0.0906271
$641$	−8.48338e6	−0.815500	−0.407750	−	0.913094i	$-0.633686\pi$
$641$	−8.48338e6	−0.815500	−0.407750	+	0.913094i	$0.633686\pi$
$642$	9.35732e6	0.896012
$643$	5.45348e6	0.520172	0.260086	−	0.965586i	$-0.416249\pi$
$643$	5.45348e6	0.520172	0.260086	+	0.965586i	$0.416249\pi$
$644$	1.43912e6	0.136736
$645$	−2.96168e7	−2.80311
$646$	0	0
$647$	−1.84581e7	−1.73351	−0.866757	−	0.498731i	$-0.833799\pi$
$647$	−1.84581e7	−1.73351	−0.866757	+	0.498731i	$0.833799\pi$
$648$	−1.40047e6	−0.131020
$649$	2.37092e6	0.220956
$650$	462201.	0.0429089
$651$	−2.34839e6	−0.217179
$652$	3.05550e6	0.281490
$653$	6.54167e6	0.600352	0.300176	−	0.953884i	$-0.402955\pi$
$653$	6.54167e6	0.600352	0.300176	+	0.953884i	$0.402955\pi$
$654$	−4.25030e6	−0.388575
$655$	8.52848e6	0.776727
$656$	473271.	0.0429389
$657$	1.20470e7	1.08884
$658$	3.13707e6	0.282461
$659$	−3.55956e6	−0.319288	−0.159644	−	0.987175i	$-0.551035\pi$
$659$	−3.55956e6	−0.319288	−0.159644	+	0.987175i	$0.551035\pi$
$660$	6.62088e6	0.591638
$661$	7.08911e6	0.631085	0.315542	−	0.948911i	$-0.397814\pi$
$661$	7.08911e6	0.631085	0.315542	+	0.948911i	$0.397814\pi$
$662$	−998478.	−0.0885511
$663$	1.17009e7	1.03380
$664$	5.20033e6	0.457732
$665$	0	0
$666$	−2.12132e7	−1.85320
$667$	−2.00647e7	−1.74629
$668$	−9.37766e6	−0.813118
$669$	−1.59060e7	−1.37402
$670$	−4.59323e6	−0.395304
$671$	−1.43554e7	−1.23086
$672$	840887.	0.0718314
$673$	1.96877e6	0.167555	0.0837777	−	0.996484i	$-0.473301\pi$
$673$	1.96877e6	0.167555	0.0837777	+	0.996484i	$0.473301\pi$
$674$	1.49131e7	1.26450
$675$	415069.	0.0350640
$676$	2.37182e6	0.199625
$677$	1.92746e7	1.61627	0.808136	−	0.588996i	$-0.200477\pi$
$677$	1.92746e7	1.61627	0.808136	+	0.588996i	$0.200477\pi$
$678$	3.72327e6	0.311065
$679$	5.78760e6	0.481753
$680$	2.44671e6	0.202913
$681$	−9.92411e6	−0.820019
$682$	−3.39314e6	−0.279345
$683$	−1.67630e7	−1.37499	−0.687496	−	0.726189i	$-0.741290\pi$
$683$	−1.67630e7	−1.37499	−0.687496	+	0.726189i	$0.741290\pi$
$684$	0	0
$685$	−650924.	−0.0530034
$686$	−4.38284e6	−0.355587
$687$	−1.24818e7	−1.00899
$688$	−5.43489e6	−0.437743
$689$	−9.63483e6	−0.773207
$690$	1.48761e7	1.18950
$691$	1.25584e7	1.00055	0.500276	−	0.865866i	$-0.333232\pi$
$691$	1.25584e7	1.00055	0.500276	+	0.865866i	$0.333232\pi$
$692$	6.89056e6	0.547003
$693$	3.49657e6	0.276573
$694$	1.56153e7	1.23070
$695$	−1.44888e7	−1.13781
$696$	−1.17239e7	−0.917378
$697$	1.23306e6	0.0961397
$698$	5.24821e6	0.407730
$699$	2.32400e7	1.79905
$700$	86541.2	0.00667541
$701$	1.73231e7	1.33146	0.665732	−	0.746191i	$-0.268119\pi$
$701$	1.73231e7	1.33146	0.665732	+	0.746191i	$0.268119\pi$
$702$	7.46486e6	0.571714
$703$	0	0
$704$	1.21498e6	0.0923924
$705$	3.24275e7	2.45720
$706$	6.46226e6	0.487947
$707$	1.36054e6	0.102368
$708$	3.11264e6	0.233370
$709$	−8.42109e6	−0.629148	−0.314574	−	0.949233i	$-0.601862\pi$
$709$	−8.42109e6	−0.629148	−0.314574	+	0.949233i	$0.601862\pi$
$710$	3.67511e6	0.273605
$711$	2.19858e7	1.63106
$712$	−3.32216e6	−0.245595
$713$	−7.62384e6	−0.561629
$714$	2.19085e6	0.160830
$715$	1.22547e7	0.896473
$716$	−6.94644e6	−0.506383
$717$	−1.28814e7	−0.935759
$718$	3.81742e6	0.276349
$719$	7.69526e6	0.555138	0.277569	−	0.960706i	$-0.410471\pi$
$719$	7.69526e6	0.555138	0.277569	+	0.960706i	$0.410471\pi$
$720$	5.12655e6	0.368548
$721$	−4.90138e6	−0.351140
$722$	0	0
$723$	2.64543e6	0.188214
$724$	5.57190e6	0.395055
$725$	−1.20658e6	−0.0852534
$726$	−7.11323e6	−0.500870
$727$	−1.31890e7	−0.925502	−0.462751	−	0.886488i	$-0.653138\pi$
$727$	−1.31890e7	−0.925502	−0.462751	+	0.886488i	$0.653138\pi$
$728$	1.55641e6	0.108842
$729$	−2.29583e7	−1.60000
$730$	7.90551e6	0.549064
$731$	−1.41601e7	−0.980104
$732$	−1.88464e7	−1.30002
$733$	−2.42817e7	−1.66924	−0.834622	−	0.550823i	$-0.814314\pi$
$733$	−2.42817e7	−1.66924	−0.834622	+	0.550823i	$0.814314\pi$
$734$	1.33661e7	0.915726
$735$	−2.18585e7	−1.49246
$736$	2.72986e6	0.185757
$737$	−5.94262e6	−0.403004
$738$	2.58361e6	0.174617
$739$	6.91389e6	0.465706	0.232853	−	0.972512i	$-0.425194\pi$
$739$	6.91389e6	0.465706	0.232853	+	0.972512i	$0.425194\pi$
$740$	−1.39206e7	−0.934500
$741$	0	0
$742$	−1.80400e6	−0.120289
$743$	−1.55189e7	−1.03131	−0.515653	−	0.856797i	$-0.672451\pi$
$743$	−1.55189e7	−1.03131	−0.515653	+	0.856797i	$0.672451\pi$
$744$	−4.45465e6	−0.295040
$745$	3.71916e6	0.245502
$746$	6.45779e6	0.424851
$747$	2.83889e7	1.86143
$748$	3.16550e6	0.206866
$749$	3.24287e6	0.211215
$750$	−1.65435e7	−1.07393
$751$	6.26505e6	0.405345	0.202672	−	0.979247i	$-0.435037\pi$
$751$	6.26505e6	0.405345	0.202672	+	0.979247i	$0.435037\pi$
$752$	5.95067e6	0.383726
$753$	−1.24013e7	−0.797040
$754$	−2.16999e7	−1.39005
$755$	1.42665e7	0.910854
$756$	1.39770e6	0.0889424
$757$	1.24885e7	0.792085	0.396042	−	0.918232i	$-0.370383\pi$
$757$	1.24885e7	0.792085	0.396042	+	0.918232i	$0.370383\pi$
$758$	−1.45432e6	−0.0919362
$759$	1.92463e7	1.21267
$760$	0	0
$761$	−3.02820e6	−0.189550	−0.0947749	−	0.995499i	$-0.530213\pi$
$761$	−3.02820e6	−0.189550	−0.0947749	+	0.995499i	$0.530213\pi$
$762$	1.04823e7	0.653987
$763$	−1.47298e6	−0.0915980
$764$	9.74391e6	0.603949
$765$	1.33567e7	0.825175
$766$	−9.10483e6	−0.560661
$767$	5.76123e6	0.353612
$768$	1.59507e6	0.0975836
$769$	−1.09210e7	−0.665958	−0.332979	−	0.942934i	$-0.608054\pi$
$769$	−1.09210e7	−0.665958	−0.332979	+	0.942934i	$0.608054\pi$
$770$	2.29453e6	0.139466
$771$	−3.16057e7	−1.91483
$772$	−1.49778e7	−0.904492
$773$	1.39695e7	0.840877	0.420439	−	0.907321i	$-0.361876\pi$
$773$	1.39695e7	0.840877	0.420439	+	0.907321i	$0.361876\pi$
$774$	−2.96693e7	−1.78014
$775$	−458457.	−0.0274185
$776$	1.09785e7	0.654466
$777$	−1.24649e7	−0.740688
$778$	7.77762e6	0.460678
$779$	0	0
$780$	1.60884e7	0.946842
$781$	4.75478e6	0.278935
$782$	7.11238e6	0.415909
$783$	−1.94871e7	−1.13591
$784$	−4.01117e6	−0.233067
$785$	−9.03950e6	−0.523564
$786$	1.44858e7	0.836348
$787$	−2.60283e7	−1.49799	−0.748996	−	0.662574i	$-0.769464\pi$
$787$	−2.60283e7	−1.49799	−0.748996	+	0.662574i	$0.769464\pi$
$788$	7.81224e6	0.448188
$789$	−1.91031e7	−1.09248
$790$	1.44276e7	0.822483
$791$	1.29034e6	0.0733266
$792$	6.63261e6	0.375726
$793$	−3.48830e7	−1.96984
$794$	375399.	0.0211320
$795$	−1.86477e7	−1.04643
$796$	8.18413e6	0.457815
$797$	1.55129e7	0.865060	0.432530	−	0.901620i	$-0.357621\pi$
$797$	1.55129e7	0.865060	0.432530	+	0.901620i	$0.357621\pi$
$798$	0	0
$799$	1.55039e7	0.859159
$800$	164159.	0.00906859
$801$	−1.81358e7	−0.998747
$802$	1.64833e7	0.904914
$803$	1.02280e7	0.559758
$804$	−7.80171e6	−0.425647
$805$	5.15544e6	0.280399
$806$	−8.24517e6	−0.447056
$807$	4.88538e7	2.64067
$808$	2.58080e6	0.139068
$809$	3.27273e7	1.75808	0.879039	−	0.476750i	$-0.158185\pi$
$809$	3.27273e7	1.75808	0.879039	+	0.476750i	$0.158185\pi$
$810$	−5.01699e6	−0.268677
$811$	−4.48205e6	−0.239290	−0.119645	−	0.992817i	$-0.538176\pi$
$811$	−4.48205e6	−0.239290	−0.119645	+	0.992817i	$0.538176\pi$
$812$	−4.06302e6	−0.216252
$813$	−1.51948e7	−0.806250
$814$	−1.80102e7	−0.952702
$815$	1.09459e7	0.577240
$816$	4.15580e6	0.218489
$817$	0	0
$818$	−1.82367e7	−0.952933
$819$	8.49651e6	0.442620
$820$	1.69542e6	0.0880529
$821$	2.77947e7	1.43914	0.719572	−	0.694418i	$-0.244338\pi$
$821$	2.77947e7	1.43914	0.719572	+	0.694418i	$0.244338\pi$
$822$	−1.10561e6	−0.0570719
$823$	2.45128e7	1.26152	0.630758	−	0.775980i	$-0.282744\pi$
$823$	2.45128e7	1.26152	0.630758	+	0.775980i	$0.282744\pi$
$824$	−9.29737e6	−0.477026
$825$	1.15737e6	0.0592022
$826$	1.07871e6	0.0550119
$827$	2.86478e7	1.45656	0.728278	−	0.685281i	$-0.240321\pi$
$827$	2.86478e7	1.45656	0.728278	+	0.685281i	$0.240321\pi$
$828$	1.49024e7	0.755407
$829$	−1.77619e7	−0.897640	−0.448820	−	0.893622i	$-0.648156\pi$
$829$	−1.77619e7	−0.897640	−0.448820	+	0.893622i	$0.648156\pi$
$830$	1.86294e7	0.938651
$831$	−5.97297e6	−0.300046
$832$	2.95234e6	0.147862
$833$	−1.04507e7	−0.521836
$834$	−2.46096e7	−1.22515
$835$	−3.35941e7	−1.66743
$836$	0	0
$837$	−7.40439e6	−0.365322
$838$	2.09069e7	1.02844
$839$	1.08116e7	0.530253	0.265126	−	0.964214i	$-0.414586\pi$
$839$	1.08116e7	0.530253	0.265126	+	0.964214i	$0.414586\pi$
$840$	3.01235e6	0.147302
$841$	3.61367e7	1.76181
$842$	−1.57859e7	−0.767344
$843$	2.94838e7	1.42894
$844$	−1.77246e6	−0.0856487
$845$	8.49670e6	0.409363
$846$	3.24850e7	1.56047
$847$	−2.46516e6	−0.118069
$848$	−3.42198e6	−0.163414
$849$	1.49786e6	0.0713186
$850$	427700.	0.0203045
$851$	−4.04660e7	−1.91543
$852$	6.24226e6	0.294607
$853$	1.31376e7	0.618221	0.309110	−	0.951026i	$-0.399969\pi$
$853$	1.31376e7	0.618221	0.309110	+	0.951026i	$0.399969\pi$
$854$	−6.53139e6	−0.306451
$855$	0	0
$856$	6.15137e6	0.286937
$857$	−1.60667e7	−0.747264	−0.373632	−	0.927577i	$-0.621888\pi$
$857$	−1.60667e7	−0.747264	−0.373632	+	0.927577i	$0.621888\pi$
$858$	2.08149e7	0.965285
$859$	1.47624e7	0.682611	0.341305	−	0.939953i	$-0.389131\pi$
$859$	1.47624e7	0.682611	0.341305	+	0.939953i	$0.389131\pi$
$860$	−1.94697e7	−0.897662
$861$	1.51813e6	0.0697911
$862$	−2.81854e6	−0.129198
$863$	−1.32374e7	−0.605028	−0.302514	−	0.953145i	$-0.597826\pi$
$863$	−1.32374e7	−0.605028	−0.302514	+	0.953145i	$0.597826\pi$
$864$	2.65128e6	0.120829
$865$	2.46844e7	1.12172
$866$	−2.84953e7	−1.29116
$867$	−2.37301e7	−1.07214
$868$	−1.54380e6	−0.0695492
$869$	1.86661e7	0.838503
$870$	−4.19991e7	−1.88123
$871$	−1.44403e7	−0.644957
$872$	−2.79408e6	−0.124437
$873$	5.99319e7	2.66147
$874$	0	0
$875$	−5.73331e6	−0.253154
$876$	1.34277e7	0.591209
$877$	−1.65954e7	−0.728597	−0.364299	−	0.931282i	$-0.618691\pi$
$877$	−1.65954e7	−0.728597	−0.364299	+	0.931282i	$0.618691\pi$
$878$	−3.06851e7	−1.34336
$879$	−1.89890e6	−0.0828954
$880$	4.35247e6	0.189465
$881$	3.35813e6	0.145766	0.0728832	−	0.997340i	$-0.476780\pi$
$881$	3.35813e6	0.145766	0.0728832	+	0.997340i	$0.476780\pi$
$882$	−2.18972e7	−0.947800
$883$	−1.06193e7	−0.458345	−0.229173	−	0.973386i	$-0.573602\pi$
$883$	−1.06193e7	−0.458345	−0.229173	+	0.973386i	$0.573602\pi$
$884$	7.69203e6	0.331063
$885$	1.11506e7	0.478563
$886$	−1.63868e7	−0.701308
$887$	−7.55855e6	−0.322574	−0.161287	−	0.986908i	$-0.551564\pi$
$887$	−7.55855e6	−0.322574	−0.161287	+	0.986908i	$0.551564\pi$
$888$	−2.36445e7	−1.00623
$889$	3.63274e6	0.154163
$890$	−1.19011e7	−0.503632
$891$	−6.49087e6	−0.273911
$892$	−1.04563e7	−0.440015
$893$	0	0
$894$	6.31708e6	0.264346
$895$	−2.48846e7	−1.03842
$896$	552787.	0.0230032
$897$	4.67677e7	1.94073
$898$	1.60673e7	0.664893
$899$	2.15241e7	0.888231
$900$	896152.	0.0368787
$901$	−8.91564e6	−0.365882
$902$	2.19350e6	0.0897680
$903$	−1.74336e7	−0.711490
$904$	2.44763e6	0.0996148
$905$	1.99605e7	0.810122
$906$	2.42319e7	0.980770
$907$	4.58704e7	1.85146	0.925731	−	0.378184i	$-0.123451\pi$
$907$	4.58704e7	1.85146	0.925731	+	0.378184i	$0.123451\pi$
$908$	−6.52397e6	−0.262601
$909$	1.40887e7	0.565538
$910$	5.57561e6	0.223197
$911$	2.28851e7	0.913601	0.456800	−	0.889569i	$-0.348995\pi$
$911$	2.28851e7	0.913601	0.456800	+	0.889569i	$0.348995\pi$
$912$	0	0
$913$	2.41023e7	0.956934
$914$	−3.43718e7	−1.36093
$915$	−6.75143e7	−2.66589
$916$	−8.20538e6	−0.323117
$917$	5.02020e6	0.197150
$918$	6.90765e6	0.270535
$919$	−3.88644e6	−0.151797	−0.0758985	−	0.997116i	$-0.524182\pi$
$919$	−3.88644e6	−0.151797	−0.0758985	+	0.997116i	$0.524182\pi$
$920$	9.77931e6	0.380924
$921$	−1.93423e7	−0.751379
$922$	−1.64161e7	−0.635978
$923$	1.15539e7	0.446400
$924$	3.89731e6	0.150171
$925$	−2.43341e6	−0.0935106
$926$	−1.80254e7	−0.690808
$927$	−5.07548e7	−1.93989
$928$	−7.70711e6	−0.293780
$929$	−2.67753e6	−0.101787	−0.0508937	−	0.998704i	$-0.516207\pi$
$929$	−2.67753e6	−0.101787	−0.0508937	+	0.998704i	$0.516207\pi$
$930$	−1.59581e7	−0.605026
$931$	0	0
$932$	1.52776e7	0.576124
$933$	7.86495e7	2.95796
$934$	1.70546e7	0.639698
$935$	1.13399e7	0.424211
$936$	1.61170e7	0.601303
$937$	1.13565e7	0.422568	0.211284	−	0.977425i	$-0.432236\pi$
$937$	1.13565e7	0.422568	0.211284	+	0.977425i	$0.432236\pi$
$938$	−2.70376e6	−0.100337
$939$	2.55228e7	0.944636
$940$	2.13174e7	0.786891
$941$	2.55862e7	0.941957	0.470978	−	0.882145i	$-0.343901\pi$
$941$	2.55862e7	0.941957	0.470978	+	0.882145i	$0.343901\pi$
$942$	−1.53538e7	−0.563752
$943$	4.92845e6	0.180481
$944$	2.04620e6	0.0747341
$945$	5.00705e6	0.182391
$946$	−2.51894e7	−0.915147
$947$	1.54082e7	0.558313	0.279157	−	0.960246i	$-0.409945\pi$
$947$	1.54082e7	0.558313	0.279157	+	0.960246i	$0.409945\pi$
$948$	2.45057e7	0.885616
$949$	2.48535e7	0.895823
$950$	0	0
$951$	−7.47953e6	−0.268178
$952$	1.44023e6	0.0515039
$953$	−3.66390e6	−0.130681	−0.0653403	−	0.997863i	$-0.520813\pi$
$953$	−3.66390e6	−0.130681	−0.0653403	+	0.997863i	$0.520813\pi$
$954$	−1.86808e7	−0.664544
$955$	3.49061e7	1.23849
$956$	−8.46803e6	−0.299666
$957$	−5.43374e7	−1.91787
$958$	−8.45920e6	−0.297794
$959$	−383160.	−0.0134534
$960$	5.71410e6	0.200111
$961$	−2.04508e7	−0.714334
$962$	−4.37639e7	−1.52468
$963$	3.35806e7	1.16687
$964$	1.73907e6	0.0602732
$965$	−5.36558e7	−1.85480
$966$	8.75664e6	0.301922
$967$	2.19093e7	0.753464	0.376732	−	0.926322i	$-0.377048\pi$
$967$	2.19093e7	0.753464	0.376732	+	0.926322i	$0.377048\pi$
$968$	−4.67613e6	−0.160398
$969$	0	0
$970$	3.93287e7	1.34209
$971$	3.60912e7	1.22844	0.614220	−	0.789135i	$-0.289471\pi$
$971$	3.60912e7	1.22844	0.614220	+	0.789135i	$0.289471\pi$
$972$	−1.85881e7	−0.631057
$973$	−8.52869e6	−0.288802
$974$	−7.91465e6	−0.267322
$975$	2.81236e6	0.0947457
$976$	−1.23893e7	−0.416316
$977$	4.47841e7	1.50102	0.750512	−	0.660856i	$-0.229807\pi$
$977$	4.47841e7	1.50102	0.750512	+	0.660856i	$0.229807\pi$
$978$	1.85918e7	0.621548
$979$	−1.53974e7	−0.513442
$980$	−1.43694e7	−0.477941
$981$	−1.52530e7	−0.506039
$982$	−2.49054e7	−0.824167
$983$	−2.45566e7	−0.810558	−0.405279	−	0.914193i	$-0.632826\pi$
$983$	−2.45566e7	−0.810558	−0.405279	+	0.914193i	$0.632826\pi$
$984$	2.87972e6	0.0948118
$985$	2.79862e7	0.919079
$986$	−2.00801e7	−0.657770
$987$	1.90881e7	0.623693
$988$	0	0
$989$	−5.65967e7	−1.83992
$990$	2.37604e7	0.770486
$991$	−2.25215e7	−0.728471	−0.364236	−	0.931307i	$-0.618670\pi$
$991$	−2.25215e7	−0.728471	−0.364236	+	0.931307i	$0.618670\pi$
$992$	−2.92842e6	−0.0944831
$993$	−6.07545e6	−0.195526
$994$	2.16332e6	0.0694471
$995$	2.93184e7	0.938821
$996$	3.16425e7	1.01070
$997$	−9.11525e6	−0.290423	−0.145211	−	0.989401i	$-0.546386\pi$
$997$	−9.11525e6	−0.290423	−0.145211	+	0.989401i	$0.546386\pi$
$998$	2.00245e7	0.636408
$999$	−3.93012e7	−1.24593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.j.1.4		4
19.7	even	3		38.6.c.b.11.1	yes	8
19.11	even	3		38.6.c.b.7.1	✓	8
19.18	odd	2		722.6.a.g.1.1		4
57.11	odd	6		342.6.g.d.235.4		8
57.26	odd	6		342.6.g.d.163.4		8
76.7	odd	6		304.6.i.b.49.4		8
76.11	odd	6		304.6.i.b.273.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.b.7.1	✓	8	19.11	even	3
38.6.c.b.11.1	yes	8	19.7	even	3
304.6.i.b.49.4		8	76.7	odd	6
304.6.i.b.273.4		8	76.11	odd	6
342.6.g.d.163.4		8	57.26	odd	6
342.6.g.d.235.4		8	57.11	odd	6
722.6.a.g.1.1		4	19.18	odd	2
722.6.a.j.1.4		4	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +24.3388 q^{3} +16.0000 q^{4} +57.3176 q^{5} +97.3553 q^{6} +33.7394 q^{7} +64.0000 q^{8} +349.379 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +24.3388 q^{3} +16.0000 q^{4} +57.3176 q^{5} +97.3553 q^{6} +33.7394 q^{7} +64.0000 q^{8} +349.379 q^{9} +229.271 q^{10} +296.625 q^{11} +389.421 q^{12} +720.786 q^{13} +134.958 q^{14} +1395.04 q^{15} +256.000 q^{16} +666.983 q^{17} +1397.52 q^{18} +917.082 q^{20} +821.179 q^{21} +1186.50 q^{22} +2665.88 q^{23} +1557.69 q^{24} +160.312 q^{25} +2883.14 q^{26} +2589.14 q^{27} +539.831 q^{28} -7526.47 q^{29} +5580.18 q^{30} -2859.79 q^{31} +1024.00 q^{32} +7219.51 q^{33} +2667.93 q^{34} +1933.86 q^{35} +5590.06 q^{36} -15179.2 q^{37} +17543.1 q^{39} +3668.33 q^{40} +1848.72 q^{41} +3284.71 q^{42} -21230.0 q^{43} +4746.00 q^{44} +20025.6 q^{45} +10663.5 q^{46} +23244.8 q^{47} +6230.74 q^{48} -15668.7 q^{49} +641.246 q^{50} +16233.6 q^{51} +11532.6 q^{52} -13367.1 q^{53} +10356.6 q^{54} +17001.8 q^{55} +2159.32 q^{56} -30105.9 q^{58} +7992.98 q^{59} +22320.7 q^{60} -48395.8 q^{61} -11439.1 q^{62} +11787.8 q^{63} +4096.00 q^{64} +41313.7 q^{65} +28878.0 q^{66} -20034.1 q^{67} +10671.7 q^{68} +64884.3 q^{69} +7735.46 q^{70} +16029.6 q^{71} +22360.3 q^{72} +34481.2 q^{73} -60717.0 q^{74} +3901.80 q^{75} +10008.0 q^{77} +70172.3 q^{78} +62928.4 q^{79} +14673.3 q^{80} -21882.4 q^{81} +7394.86 q^{82} +81255.2 q^{83} +13138.9 q^{84} +38229.9 q^{85} -84920.1 q^{86} -183186. q^{87} +18984.0 q^{88} -51908.7 q^{89} +80102.3 q^{90} +24318.9 q^{91} +42654.0 q^{92} -69603.9 q^{93} +92979.2 q^{94} +24923.0 q^{96} +171538. q^{97} -62674.6 q^{98} +103635. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} + 14 q^{3} + 64 q^{4} + 36 q^{5} + 56 q^{6} + 38 q^{7} + 256 q^{8} - 156 q^{9}+O(q^{10}) \) 4 * q + 16 * q^2 + 14 * q^3 + 64 * q^4 + 36 * q^5 + 56 * q^6 + 38 * q^7 + 256 * q^8 - 156 * q^9	\( 4 q + 16 q^{2} + 14 q^{3} + 64 q^{4} + 36 q^{5} + 56 q^{6} + 38 q^{7} + 256 q^{8} - 156 q^{9} + 144 q^{10} + 72 q^{11} + 224 q^{12} + 674 q^{13} + 152 q^{14} + 20 q^{15} + 1024 q^{16} - 522 q^{17} - 624 q^{18} + 576 q^{20} + 770 q^{21} + 288 q^{22} + 204 q^{23} + 896 q^{24} + 2158 q^{25} + 2696 q^{26} + 6578 q^{27} + 608 q^{28} + 5712 q^{29} + 80 q^{30} - 1162 q^{31} + 4096 q^{32} + 15650 q^{33} - 2088 q^{34} + 4188 q^{35} - 2496 q^{36} - 12754 q^{37} + 22078 q^{39} + 2304 q^{40} + 3480 q^{41} + 3080 q^{42} - 4066 q^{43} + 1152 q^{44} + 25780 q^{45} + 816 q^{46} + 45768 q^{47} + 3584 q^{48} + 708 q^{49} + 8632 q^{50} - 1506 q^{51} + 10784 q^{52} - 45654 q^{53} + 26312 q^{54} - 36570 q^{55} + 2432 q^{56} + 22848 q^{58} + 84006 q^{59} + 320 q^{60} + 14012 q^{61} - 4648 q^{62} + 15128 q^{63} + 16384 q^{64} - 2010 q^{65} + 62600 q^{66} + 19046 q^{67} - 8352 q^{68} + 55796 q^{69} + 16752 q^{70} + 53274 q^{71} - 9984 q^{72} + 41084 q^{73} - 51016 q^{74} + 76608 q^{75} + 135762 q^{77} + 88312 q^{78} + 54170 q^{79} + 9216 q^{80} + 9528 q^{81} + 13920 q^{82} + 26196 q^{83} + 12320 q^{84} + 221850 q^{85} - 16264 q^{86} - 228560 q^{87} + 4608 q^{88} + 137862 q^{89} + 103120 q^{90} - 308516 q^{91} + 3264 q^{92} - 112746 q^{93} + 183072 q^{94} + 14336 q^{96} + 292388 q^{97} + 2832 q^{98} + 138328 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 14 * q^3 + 64 * q^4 + 36 * q^5 + 56 * q^6 + 38 * q^7 + 256 * q^8 - 156 * q^9 + 144 * q^10 + 72 * q^11 + 224 * q^12 + 674 * q^13 + 152 * q^14 + 20 * q^15 + 1024 * q^16 - 522 * q^17 - 624 * q^18 + 576 * q^20 + 770 * q^21 + 288 * q^22 + 204 * q^23 + 896 * q^24 + 2158 * q^25 + 2696 * q^26 + 6578 * q^27 + 608 * q^28 + 5712 * q^29 + 80 * q^30 - 1162 * q^31 + 4096 * q^32 + 15650 * q^33 - 2088 * q^34 + 4188 * q^35 - 2496 * q^36 - 12754 * q^37 + 22078 * q^39 + 2304 * q^40 + 3480 * q^41 + 3080 * q^42 - 4066 * q^43 + 1152 * q^44 + 25780 * q^45 + 816 * q^46 + 45768 * q^47 + 3584 * q^48 + 708 * q^49 + 8632 * q^50 - 1506 * q^51 + 10784 * q^52 - 45654 * q^53 + 26312 * q^54 - 36570 * q^55 + 2432 * q^56 + 22848 * q^58 + 84006 * q^59 + 320 * q^60 + 14012 * q^61 - 4648 * q^62 + 15128 * q^63 + 16384 * q^64 - 2010 * q^65 + 62600 * q^66 + 19046 * q^67 - 8352 * q^68 + 55796 * q^69 + 16752 * q^70 + 53274 * q^71 - 9984 * q^72 + 41084 * q^73 - 51016 * q^74 + 76608 * q^75 + 135762 * q^77 + 88312 * q^78 + 54170 * q^79 + 9216 * q^80 + 9528 * q^81 + 13920 * q^82 + 26196 * q^83 + 12320 * q^84 + 221850 * q^85 - 16264 * q^86 - 228560 * q^87 + 4608 * q^88 + 137862 * q^89 + 103120 * q^90 - 308516 * q^91 + 3264 * q^92 - 112746 * q^93 + 183072 * q^94 + 14336 * q^96 + 292388 * q^97 + 2832 * q^98 + 138328 * q^99

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