LMFDB - Embedded newform 722.6.a.h.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:	$1$
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} - x^{3} - 924x^{2} + 3360x + 110592 $ x^4 - x^3 - 924x^2 + 3360x + 110592
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$25.4173$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +25.4173 q^{3} +16.0000 q^{4} +17.9284 q^{5} -101.669 q^{6} -245.183 q^{7} -64.0000 q^{8} +403.039 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +25.4173 q^{3} +16.0000 q^{4} +17.9284 q^{5} -101.669 q^{6} -245.183 q^{7} -64.0000 q^{8} +403.039 q^{9} -71.7138 q^{10} +534.575 q^{11} +406.677 q^{12} -550.039 q^{13} +980.731 q^{14} +455.693 q^{15} +256.000 q^{16} +611.688 q^{17} -1612.16 q^{18} +286.855 q^{20} -6231.89 q^{21} -2138.30 q^{22} -3791.01 q^{23} -1626.71 q^{24} -2803.57 q^{25} +2200.16 q^{26} +4067.77 q^{27} -3922.93 q^{28} +4661.18 q^{29} -1822.77 q^{30} +8546.14 q^{31} -1024.00 q^{32} +13587.5 q^{33} -2446.75 q^{34} -4395.75 q^{35} +6448.63 q^{36} -2219.74 q^{37} -13980.5 q^{39} -1147.42 q^{40} -2941.14 q^{41} +24927.5 q^{42} -5235.83 q^{43} +8553.20 q^{44} +7225.87 q^{45} +15164.0 q^{46} -3719.17 q^{47} +6506.83 q^{48} +43307.6 q^{49} +11214.3 q^{50} +15547.5 q^{51} -8800.63 q^{52} -38673.1 q^{53} -16271.1 q^{54} +9584.10 q^{55} +15691.7 q^{56} -18644.7 q^{58} +18437.5 q^{59} +7291.08 q^{60} -42937.9 q^{61} -34184.6 q^{62} -98818.3 q^{63} +4096.00 q^{64} -9861.35 q^{65} -54349.8 q^{66} -24416.7 q^{67} +9787.01 q^{68} -96357.2 q^{69} +17583.0 q^{70} -48916.1 q^{71} -25794.5 q^{72} -417.051 q^{73} +8878.97 q^{74} -71259.2 q^{75} -131069. q^{77} +55922.1 q^{78} +45679.8 q^{79} +4589.68 q^{80} +5453.09 q^{81} +11764.6 q^{82} +8558.17 q^{83} -99710.2 q^{84} +10966.6 q^{85} +20943.3 q^{86} +118475. q^{87} -34212.8 q^{88} -69581.9 q^{89} -28903.5 q^{90} +134860. q^{91} -60656.1 q^{92} +217220. q^{93} +14876.7 q^{94} -26027.3 q^{96} -109082. q^{97} -173230. q^{98} +215455. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + q^{3} + 64 q^{4} - 14 q^{5} - 4 q^{6} + 97 q^{7} - 256 q^{8} + 877 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + q^3 + 64 * q^4 - 14 * q^5 - 4 * q^6 + 97 * q^7 - 256 * q^8 + 877 * q^9	\( 4 q - 16 q^{2} + q^{3} + 64 q^{4} - 14 q^{5} - 4 q^{6} + 97 q^{7} - 256 q^{8} + 877 q^{9} + 56 q^{10} + 758 q^{11} + 16 q^{12} - 1465 q^{13} - 388 q^{14} + 926 q^{15} + 1024 q^{16} + 599 q^{17} - 3508 q^{18} - 224 q^{20} - 7199 q^{21} - 3032 q^{22} - 3651 q^{23} - 64 q^{24} - 418 q^{25} + 5860 q^{26} - 7793 q^{27} + 1552 q^{28} + 12451 q^{29} - 3704 q^{30} - 3038 q^{31} - 4096 q^{32} - 9590 q^{33} - 2396 q^{34} - 20302 q^{35} + 14032 q^{36} - 10282 q^{37} + 7403 q^{39} + 896 q^{40} - 6520 q^{41} + 28796 q^{42} - 2330 q^{43} + 12128 q^{44} - 43708 q^{45} + 14604 q^{46} + 12760 q^{47} + 256 q^{48} + 49263 q^{49} + 1672 q^{50} + 72111 q^{51} - 23440 q^{52} - 78509 q^{53} + 31172 q^{54} - 4840 q^{55} - 6208 q^{56} - 49804 q^{58} + 20605 q^{59} + 14816 q^{60} + 36040 q^{61} + 12152 q^{62} - 22226 q^{63} + 16384 q^{64} + 45766 q^{65} + 38360 q^{66} - 42707 q^{67} + 9584 q^{68} - 42827 q^{69} + 81208 q^{70} + 24000 q^{71} - 56128 q^{72} - 55595 q^{73} + 41128 q^{74} - 140365 q^{75} - 135836 q^{77} - 29612 q^{78} - 81936 q^{79} - 3584 q^{80} + 143716 q^{81} + 26080 q^{82} - 173966 q^{83} - 115184 q^{84} + 188508 q^{85} + 9320 q^{86} + 190339 q^{87} - 48512 q^{88} - 35682 q^{89} + 174832 q^{90} + 7967 q^{91} - 58416 q^{92} + 278686 q^{93} - 51040 q^{94} - 1024 q^{96} - 44748 q^{97} - 197052 q^{98} + 575764 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + q^3 + 64 * q^4 - 14 * q^5 - 4 * q^6 + 97 * q^7 - 256 * q^8 + 877 * q^9 + 56 * q^10 + 758 * q^11 + 16 * q^12 - 1465 * q^13 - 388 * q^14 + 926 * q^15 + 1024 * q^16 + 599 * q^17 - 3508 * q^18 - 224 * q^20 - 7199 * q^21 - 3032 * q^22 - 3651 * q^23 - 64 * q^24 - 418 * q^25 + 5860 * q^26 - 7793 * q^27 + 1552 * q^28 + 12451 * q^29 - 3704 * q^30 - 3038 * q^31 - 4096 * q^32 - 9590 * q^33 - 2396 * q^34 - 20302 * q^35 + 14032 * q^36 - 10282 * q^37 + 7403 * q^39 + 896 * q^40 - 6520 * q^41 + 28796 * q^42 - 2330 * q^43 + 12128 * q^44 - 43708 * q^45 + 14604 * q^46 + 12760 * q^47 + 256 * q^48 + 49263 * q^49 + 1672 * q^50 + 72111 * q^51 - 23440 * q^52 - 78509 * q^53 + 31172 * q^54 - 4840 * q^55 - 6208 * q^56 - 49804 * q^58 + 20605 * q^59 + 14816 * q^60 + 36040 * q^61 + 12152 * q^62 - 22226 * q^63 + 16384 * q^64 + 45766 * q^65 + 38360 * q^66 - 42707 * q^67 + 9584 * q^68 - 42827 * q^69 + 81208 * q^70 + 24000 * q^71 - 56128 * q^72 - 55595 * q^73 + 41128 * q^74 - 140365 * q^75 - 135836 * q^77 - 29612 * q^78 - 81936 * q^79 - 3584 * q^80 + 143716 * q^81 + 26080 * q^82 - 173966 * q^83 - 115184 * q^84 + 188508 * q^85 + 9320 * q^86 + 190339 * q^87 - 48512 * q^88 - 35682 * q^89 + 174832 * q^90 + 7967 * q^91 - 58416 * q^92 + 278686 * q^93 - 51040 * q^94 - 1024 * q^96 - 44748 * q^97 - 197052 * q^98 + 575764 * 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
$3$	25.4173	1.63052	0.815260	−	0.579095i	$-0.196594\pi$
$3$	25.4173	1.63052	0.815260	+	0.579095i	$0.196594\pi$
$4$	16.0000	0.500000
$5$	17.9284	0.320714	0.160357	−	0.987059i	$-0.448735\pi$
$5$	17.9284	0.320714	0.160357	+	0.987059i	$0.448735\pi$
$6$	−101.669	−1.15295
$7$	−245.183	−1.89123	−0.945616	−	0.325284i	$-0.894540\pi$
$7$	−245.183	−1.89123	−0.945616	+	0.325284i	$0.894540\pi$
$8$	−64.0000	−0.353553
$9$	403.039	1.65860
$10$	−71.7138	−0.226779
$11$	534.575	1.33207	0.666035	−	0.745920i	$-0.267990\pi$
$11$	534.575	1.33207	0.666035	+	0.745920i	$0.267990\pi$
$12$	406.677	0.815260
$13$	−550.039	−0.902683	−0.451342	−	0.892351i	$-0.649054\pi$
$13$	−550.039	−0.902683	−0.451342	+	0.892351i	$0.649054\pi$
$14$	980.731	1.33730
$15$	455.693	0.522931
$16$	256.000	0.250000
$17$	611.688	0.513343	0.256671	−	0.966499i	$-0.417374\pi$
$17$	611.688	0.513343	0.256671	+	0.966499i	$0.417374\pi$
$18$	−1612.16	−1.17281
$19$	0	0
$19$	0	0
$20$	286.855	0.160357
$21$	−6231.89	−3.08369
$22$	−2138.30	−0.941916
$23$	−3791.01	−1.49429	−0.747145	−	0.664661i	$-0.768576\pi$
$23$	−3791.01	−1.49429	−0.747145	+	0.664661i	$0.768576\pi$
$24$	−1626.71	−0.576476
$25$	−2803.57	−0.897143
$26$	2200.16	0.638293
$27$	4067.77	1.07386
$28$	−3922.93	−0.945616
$29$	4661.18	1.02920	0.514601	−	0.857430i	$-0.327940\pi$
$29$	4661.18	1.02920	0.514601	+	0.857430i	$0.327940\pi$
$30$	−1822.77	−0.369768
$31$	8546.14	1.59722	0.798612	−	0.601846i	$-0.205568\pi$
$31$	8546.14	1.59722	0.798612	+	0.601846i	$0.205568\pi$
$32$	−1024.00	−0.176777
$33$	13587.5	2.17197
$34$	−2446.75	−0.362988
$35$	−4395.75	−0.606544
$36$	6448.63	0.829299
$37$	−2219.74	−0.266562	−0.133281	−	0.991078i	$-0.542551\pi$
$37$	−2219.74	−0.266562	−0.133281	+	0.991078i	$0.542551\pi$
$38$	0	0
$39$	−13980.5	−1.47184
$40$	−1147.42	−0.113389
$41$	−2941.14	−0.273247	−0.136624	−	0.990623i	$-0.543625\pi$
$41$	−2941.14	−0.273247	−0.136624	+	0.990623i	$0.543625\pi$
$42$	24927.5	2.18050
$43$	−5235.83	−0.431832	−0.215916	−	0.976412i	$-0.569274\pi$
$43$	−5235.83	−0.431832	−0.215916	+	0.976412i	$0.569274\pi$
$44$	8553.20	0.666035
$45$	7225.87	0.531935
$46$	15164.0	1.05662
$47$	−3719.17	−0.245585	−0.122792	−	0.992432i	$-0.539185\pi$
$47$	−3719.17	−0.245585	−0.122792	+	0.992432i	$0.539185\pi$
$48$	6506.83	0.407630
$49$	43307.6	2.57676
$50$	11214.3	0.634376
$51$	15547.5	0.837016
$52$	−8800.63	−0.451342
$53$	−38673.1	−1.89112	−0.945561	−	0.325445i	$-0.894486\pi$
$53$	−38673.1	−1.89112	−0.945561	+	0.325445i	$0.894486\pi$
$54$	−16271.1	−0.759332
$55$	9584.10	0.427213
$56$	15691.7	0.668652
$57$	0	0
$58$	−18644.7	−0.727756
$59$	18437.5	0.689559	0.344780	−	0.938684i	$-0.387954\pi$
$59$	18437.5	0.689559	0.344780	+	0.938684i	$0.387954\pi$
$60$	7291.08	0.261465
$61$	−42937.9	−1.47746	−0.738731	−	0.674001i	$-0.764574\pi$
$61$	−42937.9	−1.47746	−0.738731	+	0.674001i	$0.764574\pi$
$62$	−34184.6	−1.12941
$63$	−98818.3	−3.13679
$64$	4096.00	0.125000
$65$	−9861.35	−0.289503
$66$	−54349.8	−1.53581
$67$	−24416.7	−0.664508	−0.332254	−	0.943190i	$-0.607809\pi$
$67$	−24416.7	−0.664508	−0.332254	+	0.943190i	$0.607809\pi$
$68$	9787.01	0.256671
$69$	−96357.2	−2.43647
$70$	17583.0	0.428892
$71$	−48916.1	−1.15161	−0.575805	−	0.817587i	$-0.695311\pi$
$71$	−48916.1	−1.15161	−0.575805	+	0.817587i	$0.695311\pi$
$72$	−25794.5	−0.586403
$73$	−417.051	−0.00915972	−0.00457986	−	0.999990i	$-0.501458\pi$
$73$	−417.051	−0.00915972	−0.00457986	+	0.999990i	$0.501458\pi$
$74$	8878.97	0.188488
$75$	−71259.2	−1.46281
$76$	0	0
$77$	−131069.	−2.51925
$78$	55922.1	1.04075
$79$	45679.8	0.823487	0.411744	−	0.911300i	$-0.364920\pi$
$79$	45679.8	0.823487	0.411744	+	0.911300i	$0.364920\pi$
$80$	4589.68	0.0801785
$81$	5453.09	0.0923486
$82$	11764.6	0.193215
$83$	8558.17	0.136360	0.0681798	−	0.997673i	$-0.478281\pi$
$83$	8558.17	0.136360	0.0681798	+	0.997673i	$0.478281\pi$
$84$	−99710.2	−1.54185
$85$	10966.6	0.164636
$86$	20943.3	0.305351
$87$	118475.	1.67814
$88$	−34212.8	−0.470958
$89$	−69581.9	−0.931153	−0.465577	−	0.885008i	$-0.654153\pi$
$89$	−69581.9	−0.931153	−0.465577	+	0.885008i	$0.654153\pi$
$90$	−28903.5	−0.376135
$91$	134860.	1.70718
$92$	−60656.1	−0.747145
$93$	217220.	2.60431
$94$	14876.7	0.173655
$95$	0	0
$96$	−26027.3	−0.288238
$97$	−109082.	−1.17713	−0.588565	−	0.808450i	$-0.700307\pi$
$97$	−109082.	−1.17713	−0.588565	+	0.808450i	$0.700307\pi$
$98$	−173230.	−1.82204
$99$	215455.	2.20937
$100$	−44857.1	−0.448571
$101$	−14109.3	−0.137627	−0.0688134	−	0.997630i	$-0.521921\pi$
$101$	−14109.3	−0.137627	−0.0688134	+	0.997630i	$0.521921\pi$
$102$	−62189.8	−0.591860
$103$	−183135.	−1.70090	−0.850448	−	0.526059i	$-0.823669\pi$
$103$	−183135.	−1.70090	−0.850448	+	0.526059i	$0.823669\pi$
$104$	35202.5	0.319147
$105$	−111728.	−0.988983
$106$	154692.	1.33722
$107$	1779.11	0.0150226	0.00751128	−	0.999972i	$-0.497609\pi$
$107$	1779.11	0.0150226	0.00751128	+	0.999972i	$0.497609\pi$
$108$	65084.2	0.536929
$109$	108438.	0.874210	0.437105	−	0.899411i	$-0.356004\pi$
$109$	108438.	0.874210	0.437105	+	0.899411i	$0.356004\pi$
$110$	−38336.4	−0.302085
$111$	−56419.9	−0.434635
$112$	−62766.8	−0.472808
$113$	−160010.	−1.17883	−0.589414	−	0.807831i	$-0.700641\pi$
$113$	−160010.	−1.17883	−0.589414	+	0.807831i	$0.700641\pi$
$114$	0	0
$115$	−67966.9	−0.479240
$116$	74578.9	0.514601
$117$	−221687.	−1.49719
$118$	−73749.9	−0.487592
$119$	−149975.	−0.970851
$120$	−29164.3	−0.184884
$121$	124720.	0.774410
$122$	171752.	1.04472
$123$	−74755.8	−0.445535
$124$	136738.	0.798612
$125$	−106290.	−0.608440
$126$	395273.	2.21805
$127$	177239.	0.975101	0.487551	−	0.873095i	$-0.337890\pi$
$127$	177239.	0.975101	0.487551	+	0.873095i	$0.337890\pi$
$128$	−16384.0	−0.0883883
$129$	−133081.	−0.704111
$130$	39445.4	0.204709
$131$	−193868.	−0.987024	−0.493512	−	0.869739i	$-0.664287\pi$
$131$	−193868.	−0.987024	−0.493512	+	0.869739i	$0.664287\pi$
$132$	217399.	1.08598
$133$	0	0
$134$	97666.9	0.469878
$135$	72928.7	0.344401
$136$	−39148.0	−0.181494
$137$	49526.5	0.225443	0.112721	−	0.993627i	$-0.464043\pi$
$137$	49526.5	0.225443	0.112721	+	0.993627i	$0.464043\pi$
$138$	385429.	1.72285
$139$	279493.	1.22697	0.613485	−	0.789706i	$-0.289767\pi$
$139$	279493.	1.22697	0.613485	+	0.789706i	$0.289767\pi$
$140$	−70332.0	−0.303272
$141$	−94531.4	−0.400431
$142$	195664.	0.814312
$143$	−294037.	−1.20244
$144$	103178.	0.414649
$145$	83567.7	0.330080
$146$	1668.21	0.00647690
$147$	1.10076e6	4.20146
$148$	−35515.9	−0.133281
$149$	−259988.	−0.959375	−0.479687	−	0.877439i	$-0.659250\pi$
$149$	−259988.	−0.959375	−0.479687	+	0.877439i	$0.659250\pi$
$150$	285037.	1.03436
$151$	−393002.	−1.40266	−0.701330	−	0.712837i	$-0.747410\pi$
$151$	−393002.	−1.40266	−0.701330	+	0.712837i	$0.747410\pi$
$152$	0	0
$153$	246534.	0.851429
$154$	524275.	1.78138
$155$	153219.	0.512252
$156$	−223688.	−0.735922
$157$	300552.	0.973130	0.486565	−	0.873644i	$-0.338250\pi$
$157$	300552.	0.973130	0.486565	+	0.873644i	$0.338250\pi$
$158$	−182719.	−0.582293
$159$	−982966.	−3.08351
$160$	−18358.7	−0.0566947
$161$	929490.	2.82605
$162$	−21812.4	−0.0653003
$163$	−189222.	−0.557831	−0.278916	−	0.960316i	$-0.589975\pi$
$163$	−189222.	−0.557831	−0.278916	+	0.960316i	$0.589975\pi$
$164$	−47058.2	−0.136624
$165$	243602.	0.696580
$166$	−34232.7	−0.0964208
$167$	−386465.	−1.07231	−0.536153	−	0.844121i	$-0.680123\pi$
$167$	−386465.	−1.07231	−0.536153	+	0.844121i	$0.680123\pi$
$168$	398841.	1.09025
$169$	−68749.8	−0.185163
$170$	−43866.5	−0.116415
$171$	0	0
$172$	−83773.3	−0.215916
$173$	−21910.8	−0.0556600	−0.0278300	−	0.999613i	$-0.508860\pi$
$173$	−21910.8	−0.0556600	−0.0278300	+	0.999613i	$0.508860\pi$
$174$	−473899.	−1.18662
$175$	687387.	1.69671
$176$	136851.	0.333017
$177$	468631.	1.12434
$178$	278328.	0.658425
$179$	−211720.	−0.493890	−0.246945	−	0.969030i	$-0.579427\pi$
$179$	−211720.	−0.493890	−0.246945	+	0.969030i	$0.579427\pi$
$180$	115614.	0.265968
$181$	−168642.	−0.382622	−0.191311	−	0.981529i	$-0.561274\pi$
$181$	−168642.	−0.382622	−0.191311	+	0.981529i	$0.561274\pi$
$182$	−539441.	−1.20716
$183$	−1.09137e6	−2.40903
$184$	242625.	0.528312
$185$	−39796.5	−0.0854901
$186$	−868880.	−1.84152
$187$	326993.	0.683809
$188$	−59506.8	−0.122792
$189$	−997346.	−2.03091
$190$	0	0
$191$	584476.	1.15927	0.579633	−	0.814877i	$-0.303196\pi$
$191$	584476.	1.15927	0.579633	+	0.814877i	$0.303196\pi$
$192$	104109.	0.203815
$193$	490746.	0.948339	0.474170	−	0.880434i	$-0.342748\pi$
$193$	490746.	0.948339	0.474170	+	0.880434i	$0.342748\pi$
$194$	436328.	0.832356
$195$	−250649.	−0.472041
$196$	692922.	1.28838
$197$	437638.	0.803432	0.401716	−	0.915764i	$-0.368414\pi$
$197$	437638.	0.803432	0.401716	+	0.915764i	$0.368414\pi$
$198$	−861819.	−1.56226
$199$	−636970.	−1.14021	−0.570107	−	0.821571i	$-0.693098\pi$
$199$	−636970.	−1.14021	−0.570107	+	0.821571i	$0.693098\pi$
$200$	179429.	0.317188
$201$	−620607.	−1.08349
$202$	56437.3	0.0973169
$203$	−1.14284e6	−1.94646
$204$	248759.	0.418508
$205$	−52730.0	−0.0876342
$206$	732539.	1.20272
$207$	−1.52792e6	−2.47843
$208$	−140810.	−0.225671
$209$	0	0
$210$	446912.	0.699317
$211$	413314.	0.639107	0.319554	−	0.947568i	$-0.396467\pi$
$211$	413314.	0.639107	0.319554	+	0.947568i	$0.396467\pi$
$212$	−618770.	−0.945561
$213$	−1.24331e6	−1.87772
$214$	−7116.45	−0.0106225
$215$	−93870.3	−0.138494
$216$	−260337.	−0.379666
$217$	−2.09537e6	−3.02072
$218$	−433752.	−0.618159
$219$	−10600.3	−0.0149351
$220$	153346.	0.213607
$221$	−336452.	−0.463386
$222$	225679.	0.307333
$223$	−834346.	−1.12353	−0.561764	−	0.827297i	$-0.689877\pi$
$223$	−834346.	−1.12353	−0.561764	+	0.827297i	$0.689877\pi$
$224$	251067.	0.334326
$225$	−1.12995e6	−1.48800
$226$	640039.	0.833557
$227$	−717734.	−0.924483	−0.462242	−	0.886754i	$-0.652955\pi$
$227$	−717734.	−0.924483	−0.462242	+	0.886754i	$0.652955\pi$
$228$	0	0
$229$	872518.	1.09948	0.549738	−	0.835337i	$-0.314728\pi$
$229$	872518.	1.09948	0.549738	+	0.835337i	$0.314728\pi$
$230$	271868.	0.338874
$231$	−3.33141e6	−4.10770
$232$	−298316.	−0.363878
$233$	1.42996e6	1.72558	0.862790	−	0.505562i	$-0.168715\pi$
$233$	1.42996e6	1.72558	0.862790	+	0.505562i	$0.168715\pi$
$234$	886750.	1.05867
$235$	−66679.0	−0.0787625
$236$	295000.	0.344780
$237$	1.16106e6	1.34271
$238$	599901.	0.686495
$239$	−296348.	−0.335589	−0.167795	−	0.985822i	$-0.553665\pi$
$239$	−296348.	−0.335589	−0.167795	+	0.985822i	$0.553665\pi$
$240$	116657.	0.130733
$241$	1.63514e6	1.81348	0.906738	−	0.421694i	$-0.138564\pi$
$241$	1.63514e6	1.81348	0.906738	+	0.421694i	$0.138564\pi$
$242$	−498878.	−0.547591
$243$	−849864.	−0.923281
$244$	−687006.	−0.738731
$245$	776438.	0.826403
$246$	299023.	0.315041
$247$	0	0
$248$	−546953.	−0.564704
$249$	217526.	0.222337
$250$	425160.	0.430232
$251$	55651.1	0.0557558	0.0278779	−	0.999611i	$-0.491125\pi$
$251$	55651.1	0.0557558	0.0278779	+	0.999611i	$0.491125\pi$
$252$	−1.58109e6	−1.56840
$253$	−2.02658e6	−1.99050
$254$	−708956.	−0.689501
$255$	278742.	0.268443
$256$	65536.0	0.0625000
$257$	−1.03705e6	−0.979417	−0.489708	−	0.871886i	$-0.662897\pi$
$257$	−1.03705e6	−0.979417	−0.489708	+	0.871886i	$0.662897\pi$
$258$	532323.	0.497881
$259$	544243.	0.504131
$260$	−157782.	−0.144751
$261$	1.87864e6	1.70703
$262$	775472.	0.697932
$263$	970479.	0.865161	0.432581	−	0.901595i	$-0.357603\pi$
$263$	970479.	0.865161	0.432581	+	0.901595i	$0.357603\pi$
$264$	−869597.	−0.767907
$265$	−693349.	−0.606509
$266$	0	0
$267$	−1.76858e6	−1.51826
$268$	−390667.	−0.332254
$269$	−1.23851e6	−1.04357	−0.521783	−	0.853078i	$-0.674733\pi$
$269$	−1.23851e6	−1.04357	−0.521783	+	0.853078i	$0.674733\pi$
$270$	−291715.	−0.243528
$271$	−58008.3	−0.0479807	−0.0239904	−	0.999712i	$-0.507637\pi$
$271$	−58008.3	−0.0479807	−0.0239904	+	0.999712i	$0.507637\pi$
$272$	156592.	0.128336
$273$	3.42778e6	2.78360
$274$	−198106.	−0.159412
$275$	−1.49872e6	−1.19506
$276$	−1.54172e6	−1.21824
$277$	62624.6	0.0490395	0.0245197	−	0.999699i	$-0.492194\pi$
$277$	62624.6	0.0490395	0.0245197	+	0.999699i	$0.492194\pi$
$278$	−1.11797e6	−0.867599
$279$	3.44443e6	2.64915
$280$	281328.	0.214446
$281$	−2.06854e6	−1.56278	−0.781392	−	0.624040i	$-0.785490\pi$
$281$	−2.06854e6	−1.56278	−0.781392	+	0.624040i	$0.785490\pi$
$282$	378125.	0.283148
$283$	−474899.	−0.352480	−0.176240	−	0.984347i	$-0.556394\pi$
$283$	−474899.	−0.352480	−0.176240	+	0.984347i	$0.556394\pi$
$284$	−782657.	−0.575805
$285$	0	0
$286$	1.17615e6	0.850251
$287$	721117.	0.516774
$288$	−412712.	−0.293201
$289$	−1.04570e6	−0.736479
$290$	−334271.	−0.233401
$291$	−2.77257e6	−1.91933
$292$	−6672.82	−0.00457986
$293$	54130.7	0.0368362	0.0184181	−	0.999830i	$-0.494137\pi$
$293$	54130.7	0.0368362	0.0184181	+	0.999830i	$0.494137\pi$
$294$	−4.40305e6	−2.97088
$295$	330555.	0.221151
$296$	142063.	0.0942439
$297$	2.17453e6	1.43045
$298$	1.03995e6	0.678380
$299$	2.08520e6	1.34887
$300$	−1.14015e6	−0.731405
$301$	1.28374e6	0.816694
$302$	1.57201e6	0.991830
$303$	−358621.	−0.224403
$304$	0	0
$305$	−769810.	−0.473842
$306$	−986137.	−0.602051
$307$	2.77928e6	1.68301	0.841503	−	0.540252i	$-0.181671\pi$
$307$	2.77928e6	1.68301	0.841503	+	0.540252i	$0.181671\pi$
$308$	−2.09710e6	−1.25963
$309$	−4.65479e6	−2.77335
$310$	−612876.	−0.362217
$311$	2.32320e6	1.36202	0.681012	−	0.732272i	$-0.261540\pi$
$311$	2.32320e6	1.36202	0.681012	+	0.732272i	$0.261540\pi$
$312$	894753.	0.520375
$313$	244046.	0.140803	0.0704013	−	0.997519i	$-0.477572\pi$
$313$	244046.	0.140803	0.0704013	+	0.997519i	$0.477572\pi$
$314$	−1.20221e6	−0.688107
$315$	−1.77166e6	−1.00601
$316$	730877.	0.411744
$317$	−2.07136e6	−1.15773	−0.578864	−	0.815424i	$-0.696504\pi$
$317$	−2.07136e6	−1.15773	−0.578864	+	0.815424i	$0.696504\pi$
$318$	3.93186e6	2.18037
$319$	2.49175e6	1.37097
$320$	73434.9	0.0400892
$321$	45220.2	0.0244946
$322$	−3.71796e6	−1.99832
$323$	0	0
$324$	87249.5	0.0461743
$325$	1.54207e6	0.809835
$326$	756888.	0.394446
$327$	2.75620e6	1.42542
$328$	188233.	0.0966075
$329$	911877.	0.464458
$330$	−974408.	−0.492556
$331$	138623.	0.0695448	0.0347724	−	0.999395i	$-0.488929\pi$
$331$	138623.	0.0695448	0.0347724	+	0.999395i	$0.488929\pi$
$332$	136931.	0.0681798
$333$	−894643.	−0.442119
$334$	1.54586e6	0.758236
$335$	−437754.	−0.213117
$336$	−1.59536e6	−0.770923
$337$	−720956.	−0.345807	−0.172903	−	0.984939i	$-0.555315\pi$
$337$	−720956.	−0.345807	−0.172903	+	0.984939i	$0.555315\pi$
$338$	274999.	0.130930
$339$	−4.06702e6	−1.92210
$340$	175466.	0.0823181
$341$	4.56856e6	2.12761
$342$	0	0
$343$	−6.49750e6	−2.98202
$344$	335093.	0.152676
$345$	−1.72753e6	−0.781410
$346$	87643.3	0.0393576
$347$	874897.	0.390062	0.195031	−	0.980797i	$-0.437519\pi$
$347$	874897.	0.390062	0.195031	+	0.980797i	$0.437519\pi$
$348$	1.89559e6	0.839068
$349$	−161839.	−0.0711247	−0.0355623	−	0.999367i	$-0.511322\pi$
$349$	−161839.	−0.0711247	−0.0355623	+	0.999367i	$0.511322\pi$
$350$	−2.74955e6	−1.19975
$351$	−2.23743e6	−0.969353
$352$	−547405.	−0.235479
$353$	3.17966e6	1.35814	0.679070	−	0.734074i	$-0.262383\pi$
$353$	3.17966e6	1.35814	0.679070	+	0.734074i	$0.262383\pi$
$354$	−1.87452e6	−0.795029
$355$	−876989.	−0.369337
$356$	−1.11331e6	−0.465577
$357$	−3.81197e6	−1.58299
$358$	846882.	0.349233
$359$	−1.97645e6	−0.809374	−0.404687	−	0.914455i	$-0.632619\pi$
$359$	−1.97645e6	−0.809374	−0.404687	+	0.914455i	$0.632619\pi$
$360$	−462456.	−0.188067
$361$	0	0
$362$	674569.	0.270555
$363$	3.17004e6	1.26269
$364$	2.15776e6	0.853592
$365$	−7477.08	−0.00293765
$366$	4.36546e6	1.70344
$367$	−3.14180e6	−1.21762	−0.608812	−	0.793314i	$-0.708354\pi$
$367$	−3.14180e6	−1.21762	−0.608812	+	0.793314i	$0.708354\pi$
$368$	−970498.	−0.373573
$369$	−1.18539e6	−0.453207
$370$	159186.	0.0604506
$371$	9.48198e6	3.57655
$372$	3.47552e6	1.30215
$373$	1.37871e6	0.513097	0.256548	−	0.966531i	$-0.417415\pi$
$373$	1.37871e6	0.513097	0.256548	+	0.966531i	$0.417415\pi$
$374$	−1.30797e6	−0.483526
$375$	−2.70161e6	−0.992074
$376$	238027.	0.0868274
$377$	−2.56383e6	−0.929044
$378$	3.98938e6	1.43607
$379$	−3.81997e6	−1.36603	−0.683017	−	0.730402i	$-0.739333\pi$
$379$	−3.81997e6	−1.36603	−0.683017	+	0.730402i	$0.739333\pi$
$380$	0	0
$381$	4.50493e6	1.58992
$382$	−2.33790e6	−0.819725
$383$	−4.57039e6	−1.59205	−0.796025	−	0.605264i	$-0.793067\pi$
$383$	−4.57039e6	−1.59205	−0.796025	+	0.605264i	$0.793067\pi$
$384$	−416437.	−0.144119
$385$	−2.34986e6	−0.807960
$386$	−1.96298e6	−0.670577
$387$	−2.11025e6	−0.716235
$388$	−1.74531e6	−0.588565
$389$	534267.	0.179013	0.0895065	−	0.995986i	$-0.471471\pi$
$389$	534267.	0.179013	0.0895065	+	0.995986i	$0.471471\pi$
$390$	1.00260e6	0.333783
$391$	−2.31891e6	−0.767083
$392$	−2.77169e6	−0.911022
$393$	−4.92760e6	−1.60936
$394$	−1.75055e6	−0.568112
$395$	818969.	0.264104
$396$	3.44728e6	1.10468
$397$	−3.48177e6	−1.10872	−0.554362	−	0.832276i	$-0.687038\pi$
$397$	−3.48177e6	−1.10872	−0.554362	+	0.832276i	$0.687038\pi$
$398$	2.54788e6	0.806253
$399$	0	0
$400$	−717714.	−0.224286
$401$	1.61009e6	0.500022	0.250011	−	0.968243i	$-0.419566\pi$
$401$	1.61009e6	0.500022	0.250011	+	0.968243i	$0.419566\pi$
$402$	2.48243e6	0.766146
$403$	−4.70071e6	−1.44179
$404$	−225749.	−0.0688134
$405$	97765.5	0.0296175
$406$	4.57137e6	1.37636
$407$	−1.18662e6	−0.355079
$408$	−995037.	−0.295930
$409$	−2.89180e6	−0.854791	−0.427396	−	0.904065i	$-0.640569\pi$
$409$	−2.89180e6	−0.854791	−0.427396	+	0.904065i	$0.640569\pi$
$410$	210920.	0.0619667
$411$	1.25883e6	0.367589
$412$	−2.93016e6	−0.850448
$413$	−4.52055e6	−1.30412
$414$	6.11170e6	1.75251
$415$	153435.	0.0437324
$416$	563240.	0.159573
$417$	7.10396e6	2.00060
$418$	0	0
$419$	3.02091e6	0.840625	0.420313	−	0.907379i	$-0.361920\pi$
$419$	3.02091e6	0.840625	0.420313	+	0.907379i	$0.361920\pi$
$420$	−1.78765e6	−0.494492
$421$	1.04848e6	0.288307	0.144154	−	0.989555i	$-0.453954\pi$
$421$	1.04848e6	0.288307	0.144154	+	0.989555i	$0.453954\pi$
$422$	−1.65325e6	−0.451917
$423$	−1.49897e6	−0.407327
$424$	2.47508e6	0.668612
$425$	−1.71491e6	−0.460542
$426$	4.97326e6	1.32775
$427$	1.05276e7	2.79422
$428$	28465.8	0.00751128
$429$	−7.47363e6	−1.96060
$430$	375481.	0.0979303
$431$	2.77121e6	0.718583	0.359291	−	0.933225i	$-0.383018\pi$
$431$	2.77121e6	0.718583	0.359291	+	0.933225i	$0.383018\pi$
$432$	1.04135e6	0.268464
$433$	36221.2	0.00928416	0.00464208	−	0.999989i	$-0.498522\pi$
$433$	36221.2	0.00928416	0.00464208	+	0.999989i	$0.498522\pi$
$434$	8.38147e6	2.13597
$435$	2.12407e6	0.538202
$436$	1.73501e6	0.437105
$437$	0	0
$438$	42401.3	0.0105607
$439$	2.52413e6	0.625101	0.312551	−	0.949901i	$-0.398817\pi$
$439$	2.52413e6	0.625101	0.312551	+	0.949901i	$0.398817\pi$
$440$	−613383.	−0.151043
$441$	1.74547e7	4.27381
$442$	1.34581e6	0.327663
$443$	1.08546e6	0.262786	0.131393	−	0.991330i	$-0.458055\pi$
$443$	1.08546e6	0.262786	0.131393	+	0.991330i	$0.458055\pi$
$444$	−902718.	−0.217317
$445$	−1.24750e6	−0.298634
$446$	3.33738e6	0.794454
$447$	−6.60820e6	−1.56428
$448$	−1.00427e6	−0.236404
$449$	−42051.5	−0.00984387	−0.00492194	−	0.999988i	$-0.501567\pi$
$449$	−42051.5	−0.00984387	−0.00492194	+	0.999988i	$0.501567\pi$
$450$	4.51980e6	1.05217
$451$	−1.57226e6	−0.363984
$452$	−2.56016e6	−0.589414
$453$	−9.98905e6	−2.28707
$454$	2.87094e6	0.653708
$455$	2.41783e6	0.547517
$456$	0	0
$457$	487219.	0.109127	0.0545637	−	0.998510i	$-0.482623\pi$
$457$	487219.	0.109127	0.0545637	+	0.998510i	$0.482623\pi$
$458$	−3.49007e6	−0.777447
$459$	2.48820e6	0.551257
$460$	−1.08747e6	−0.239620
$461$	8.01979e6	1.75756	0.878781	−	0.477224i	$-0.158357\pi$
$461$	8.01979e6	1.75756	0.878781	+	0.477224i	$0.158357\pi$
$462$	1.33256e7	2.90458
$463$	−7.48341e6	−1.62236	−0.811180	−	0.584797i	$-0.801174\pi$
$463$	−7.48341e6	−1.62236	−0.811180	+	0.584797i	$0.801174\pi$
$464$	1.19326e6	0.257301
$465$	3.89442e6	0.835237
$466$	−5.71985e6	−1.22017
$467$	2.48701e6	0.527697	0.263849	−	0.964564i	$-0.415008\pi$
$467$	2.48701e6	0.527697	0.263849	+	0.964564i	$0.415008\pi$
$468$	−3.54700e6	−0.748594
$469$	5.98656e6	1.25674
$470$	266716.	0.0556935
$471$	7.63923e6	1.58671
$472$	−1.18000e6	−0.243796
$473$	−2.79895e6	−0.575230
$474$	−4.64423e6	−0.949441
$475$	0	0
$476$	−2.39961e6	−0.485425
$477$	−1.55868e7	−3.13661
$478$	1.18539e6	0.237297
$479$	−212402.	−0.0422981	−0.0211490	−	0.999776i	$-0.506732\pi$
$479$	−212402.	−0.0422981	−0.0211490	+	0.999776i	$0.506732\pi$
$480$	−466629.	−0.0924419
$481$	1.22095e6	0.240621
$482$	−6.54055e6	−1.28232
$483$	2.36251e7	4.60793
$484$	1.99551e6	0.387205
$485$	−1.95567e6	−0.377522
$486$	3.39946e6	0.652858
$487$	−7.47512e6	−1.42822	−0.714111	−	0.700032i	$-0.753169\pi$
$487$	−7.47512e6	−1.42822	−0.714111	+	0.700032i	$0.753169\pi$
$488$	2.74802e6	0.522361
$489$	−4.80951e6	−0.909555
$490$	−3.10575e6	−0.584355
$491$	−1.12513e6	−0.210620	−0.105310	−	0.994439i	$-0.533583\pi$
$491$	−1.12513e6	−0.210620	−0.105310	+	0.994439i	$0.533583\pi$
$492$	−1.19609e6	−0.222768
$493$	2.85119e6	0.528334
$494$	0	0
$495$	3.86277e6	0.708575
$496$	2.18781e6	0.399306
$497$	1.19934e7	2.17796
$498$	−870103.	−0.157216
$499$	7.73965e6	1.39146	0.695729	−	0.718304i	$-0.255081\pi$
$499$	7.73965e6	1.39146	0.695729	+	0.718304i	$0.255081\pi$
$500$	−1.70064e6	−0.304220
$501$	−9.82290e6	−1.74842
$502$	−222605.	−0.0394253
$503$	6.20039e6	1.09270	0.546348	−	0.837558i	$-0.316018\pi$
$503$	6.20039e6	1.09270	0.546348	+	0.837558i	$0.316018\pi$
$504$	6.32437e6	1.10902
$505$	−252958.	−0.0441388
$506$	8.10631e6	1.40750
$507$	−1.74744e6	−0.301913
$508$	2.83582e6	0.487551
$509$	3.21592e6	0.550187	0.275094	−	0.961417i	$-0.411291\pi$
$509$	3.21592e6	0.550187	0.275094	+	0.961417i	$0.411291\pi$
$510$	−1.11497e6	−0.189818
$511$	102254.	0.0173232
$512$	−262144.	−0.0441942
$513$	0	0
$514$	4.14821e6	0.692552
$515$	−3.28332e6	−0.545501
$516$	−2.12929e6	−0.352055
$517$	−1.98818e6	−0.327136
$518$	−2.17697e6	−0.356474
$519$	−556914.	−0.0907548
$520$	631126.	0.102355
$521$	−1.50572e6	−0.243025	−0.121512	−	0.992590i	$-0.538774\pi$
$521$	−1.50572e6	−0.243025	−0.121512	+	0.992590i	$0.538774\pi$
$522$	−7.51455e6	−1.20705
$523$	7.54051e6	1.20544	0.602721	−	0.797952i	$-0.294083\pi$
$523$	7.54051e6	1.20544	0.602721	+	0.797952i	$0.294083\pi$
$524$	−3.10189e6	−0.493512
$525$	1.74715e7	2.76651
$526$	−3.88192e6	−0.611761
$527$	5.22757e6	0.819924
$528$	3.47839e6	0.542992
$529$	7.93540e6	1.23290
$530$	2.77340e6	0.428867
$531$	7.43103e6	1.14370
$532$	0	0
$533$	1.61774e6	0.246656
$534$	7.07433e6	1.07358
$535$	31896.7	0.00481794
$536$	1.56267e6	0.234939
$537$	−5.38136e6	−0.805298
$538$	4.95405e6	0.737912
$539$	2.31512e7	3.43243
$540$	1.16686e6	0.172200
$541$	561441.	0.0824729	0.0412364	−	0.999149i	$-0.486870\pi$
$541$	561441.	0.0824729	0.0412364	+	0.999149i	$0.486870\pi$
$542$	232033.	0.0339275
$543$	−4.28643e6	−0.623873
$544$	−626368.	−0.0907471
$545$	1.94413e6	0.280371
$546$	−1.37111e7	−1.96830
$547$	2.83477e6	0.405088	0.202544	−	0.979273i	$-0.435079\pi$
$547$	2.83477e6	0.405088	0.202544	+	0.979273i	$0.435079\pi$
$548$	792424.	0.112721
$549$	−1.73057e7	−2.45051
$550$	5.99488e6	0.845033
$551$	0	0
$552$	6.16686e6	0.861423
$553$	−1.11999e7	−1.55741
$554$	−250499.	−0.0346761
$555$	−1.01152e6	−0.139393
$556$	4.47189e6	0.613485
$557$	−8.38673e6	−1.14539	−0.572697	−	0.819767i	$-0.694103\pi$
$557$	−8.38673e6	−1.14539	−0.572697	+	0.819767i	$0.694103\pi$
$558$	−1.37777e7	−1.87323
$559$	2.87991e6	0.389807
$560$	−1.12531e6	−0.151636
$561$	8.31128e6	1.11496
$562$	8.27418e6	1.10506
$563$	−7.41426e6	−0.985819	−0.492909	−	0.870081i	$-0.664067\pi$
$563$	−7.41426e6	−0.985819	−0.492909	+	0.870081i	$0.664067\pi$
$564$	−1.51250e6	−0.200216
$565$	−2.86873e6	−0.378067
$566$	1.89959e6	0.249241
$567$	−1.33700e6	−0.174653
$568$	3.13063e6	0.407156
$569$	−1.00345e7	−1.29931	−0.649657	−	0.760227i	$-0.725088\pi$
$569$	−1.00345e7	−1.29931	−0.649657	+	0.760227i	$0.725088\pi$
$570$	0	0
$571$	−2.31523e6	−0.297169	−0.148584	−	0.988900i	$-0.547472\pi$
$571$	−2.31523e6	−0.297169	−0.148584	+	0.988900i	$0.547472\pi$
$572$	−4.70460e6	−0.601219
$573$	1.48558e7	1.89021
$574$	−2.88447e6	−0.365414
$575$	1.06284e7	1.34059
$576$	1.65085e6	0.207325
$577$	1.92639e6	0.240882	0.120441	−	0.992720i	$-0.461569\pi$
$577$	1.92639e6	0.240882	0.120441	+	0.992720i	$0.461569\pi$
$578$	4.18278e6	0.520769
$579$	1.24734e7	1.54629
$580$	1.33708e6	0.165040
$581$	−2.09832e6	−0.257888
$582$	1.10903e7	1.35717
$583$	−2.06737e7	−2.51911
$584$	26691.3	0.00323845
$585$	−3.97451e6	−0.480169
$586$	−216523.	−0.0260471
$587$	1.36991e7	1.64096	0.820479	−	0.571676i	$-0.193707\pi$
$587$	1.36991e7	1.64096	0.820479	+	0.571676i	$0.193707\pi$
$588$	1.76122e7	2.10073
$589$	0	0
$590$	−1.32222e6	−0.156377
$591$	1.11236e7	1.31001
$592$	−568254.	−0.0666405
$593$	7.54267e6	0.880823	0.440411	−	0.897796i	$-0.354833\pi$
$593$	7.54267e6	0.880823	0.440411	+	0.897796i	$0.354833\pi$
$594$	−8.69811e6	−1.01148
$595$	−2.68883e6	−0.311365
$596$	−4.15981e6	−0.479687
$597$	−1.61901e7	−1.85914
$598$	−8.34081e6	−0.953796
$599$	1.43965e7	1.63942	0.819710	−	0.572778i	$-0.194134\pi$
$599$	1.43965e7	1.63942	0.819710	+	0.572778i	$0.194134\pi$
$600$	4.56059e6	0.517181
$601$	−3.89102e6	−0.439417	−0.219708	−	0.975566i	$-0.570511\pi$
$601$	−3.89102e6	−0.439417	−0.219708	+	0.975566i	$0.570511\pi$
$602$	−5.13494e6	−0.577490
$603$	−9.84089e6	−1.10215
$604$	−6.28803e6	−0.701330
$605$	2.23603e6	0.248364
$606$	1.43448e6	0.158677
$607$	−3.32505e6	−0.366291	−0.183145	−	0.983086i	$-0.558628\pi$
$607$	−3.32505e6	−0.366291	−0.183145	+	0.983086i	$0.558628\pi$
$608$	0	0
$609$	−2.90479e7	−3.17375
$610$	3.07924e6	0.335057
$611$	2.04569e6	0.221685
$612$	3.94455e6	0.425715
$613$	2.50851e6	0.269628	0.134814	−	0.990871i	$-0.456956\pi$
$613$	2.50851e6	0.269628	0.134814	+	0.990871i	$0.456956\pi$
$614$	−1.11171e7	−1.19007
$615$	−1.34026e6	−0.142889
$616$	8.38839e6	0.890691
$617$	−2.17108e6	−0.229596	−0.114798	−	0.993389i	$-0.536622\pi$
$617$	−2.17108e6	−0.229596	−0.114798	+	0.993389i	$0.536622\pi$
$618$	1.86192e7	1.96105
$619$	5.56819e6	0.584100	0.292050	−	0.956403i	$-0.405663\pi$
$619$	5.56819e6	0.584100	0.292050	+	0.956403i	$0.405663\pi$
$620$	2.45151e6	0.256126
$621$	−1.54209e7	−1.60465
$622$	−9.29278e6	−0.963096
$623$	1.70603e7	1.76103
$624$	−3.57901e6	−0.367961
$625$	6.85554e6	0.702008
$626$	−976183.	−0.0995624
$627$	0	0
$628$	4.80884e6	0.486565
$629$	−1.35779e6	−0.136838
$630$	7.08663e6	0.711359
$631$	−3.55773e6	−0.355712	−0.177856	−	0.984056i	$-0.556916\pi$
$631$	−3.55773e6	−0.355712	−0.177856	+	0.984056i	$0.556916\pi$
$632$	−2.92351e6	−0.291147
$633$	1.05053e7	1.04208
$634$	8.28542e6	0.818637
$635$	3.17762e6	0.312728
$636$	−1.57275e7	−1.54176
$637$	−2.38209e7	−2.32600
$638$	−9.96700e6	−0.969422
$639$	−1.97151e7	−1.91006
$640$	−293740.	−0.0283474
$641$	−8.21280e6	−0.789489	−0.394745	−	0.918791i	$-0.629167\pi$
$641$	−8.21280e6	−0.789489	−0.394745	+	0.918791i	$0.629167\pi$
$642$	−180881.	−0.0173203
$643$	−3.67001e6	−0.350058	−0.175029	−	0.984563i	$-0.556002\pi$
$643$	−3.67001e6	−0.350058	−0.175029	+	0.984563i	$0.556002\pi$
$644$	1.48718e7	1.41303
$645$	−2.38593e6	−0.225818
$646$	0	0
$647$	−7.40045e6	−0.695020	−0.347510	−	0.937676i	$-0.612973\pi$
$647$	−7.40045e6	−0.695020	−0.347510	+	0.937676i	$0.612973\pi$
$648$	−348998.	−0.0326502
$649$	9.85622e6	0.918541
$650$	−6.16830e6	−0.572640
$651$	−5.32586e7	−4.92535
$652$	−3.02755e6	−0.278916
$653$	1.88045e7	1.72575	0.862877	−	0.505414i	$-0.168660\pi$
$653$	1.88045e7	1.72575	0.862877	+	0.505414i	$0.168660\pi$
$654$	−1.10248e7	−1.00792
$655$	−3.47575e6	−0.316552
$656$	−752931.	−0.0683118
$657$	−168088.	−0.0151923
$658$	−3.64751e6	−0.328422
$659$	7.60736e6	0.682371	0.341186	−	0.939996i	$-0.389172\pi$
$659$	7.60736e6	0.682371	0.341186	+	0.939996i	$0.389172\pi$
$660$	3.89763e6	0.348290
$661$	−1.11165e7	−0.989609	−0.494804	−	0.869004i	$-0.664760\pi$
$661$	−1.11165e7	−0.989609	−0.494804	+	0.869004i	$0.664760\pi$
$662$	−554492.	−0.0491756
$663$	−8.55171e6	−0.755560
$664$	−547723.	−0.0482104
$665$	0	0
$666$	3.57857e6	0.312625
$667$	−1.76706e7	−1.53793
$668$	−6.18344e6	−0.536153
$669$	−2.12068e7	−1.83194
$670$	1.75102e6	0.150696
$671$	−2.29535e7	−1.96808
$672$	6.38145e6	0.545125
$673$	1.37169e7	1.16740	0.583699	−	0.811970i	$-0.301605\pi$
$673$	1.37169e7	1.16740	0.583699	+	0.811970i	$0.301605\pi$
$674$	2.88382e6	0.244522
$675$	−1.14043e7	−0.963403
$676$	−1.10000e6	−0.0925817
$677$	2.24075e6	0.187898	0.0939488	−	0.995577i	$-0.470051\pi$
$677$	2.24075e6	0.187898	0.0939488	+	0.995577i	$0.470051\pi$
$678$	1.62681e7	1.35913
$679$	2.67451e7	2.22622
$680$	−701863.	−0.0582077
$681$	−1.82429e7	−1.50739
$682$	−1.82742e7	−1.50445
$683$	1.33781e6	0.109734	0.0548672	−	0.998494i	$-0.482526\pi$
$683$	1.33781e6	0.109734	0.0548672	+	0.998494i	$0.482526\pi$
$684$	0	0
$685$	887933.	0.0723026
$686$	2.59900e7	2.10861
$687$	2.21770e7	1.79272
$688$	−1.34037e6	−0.107958
$689$	2.12717e7	1.70708
$690$	6.91014e6	0.552540
$691$	1.76420e7	1.40557	0.702787	−	0.711401i	$-0.251939\pi$
$691$	1.76420e7	1.40557	0.702787	+	0.711401i	$0.251939\pi$
$692$	−350573.	−0.0278300
$693$	−5.28258e7	−4.17843
$694$	−3.49959e6	−0.275815
$695$	5.01088e6	0.393506
$696$	−7.58238e6	−0.593311
$697$	−1.79906e6	−0.140270
$698$	647357.	0.0502928
$699$	3.63458e7	2.81359
$700$	1.09982e7	0.848353
$701$	−1.74716e7	−1.34288	−0.671439	−	0.741060i	$-0.734324\pi$
$701$	−1.74716e7	−1.34288	−0.671439	+	0.741060i	$0.734324\pi$
$702$	8.94972e6	0.685436
$703$	0	0
$704$	2.18962e6	0.166509
$705$	−1.69480e6	−0.128424
$706$	−1.27187e7	−0.960350
$707$	3.45937e6	0.260284
$708$	7.49810e6	0.562170
$709$	−1.93045e7	−1.44226	−0.721128	−	0.692802i	$-0.756376\pi$
$709$	−1.93045e7	−1.44226	−0.721128	+	0.692802i	$0.756376\pi$
$710$	3.50796e6	0.261161
$711$	1.84108e7	1.36583
$712$	4.45324e6	0.329212
$713$	−3.23985e7	−2.38672
$714$	1.52479e7	1.11934
$715$	−5.27163e6	−0.385638
$716$	−3.38753e6	−0.246945
$717$	−7.53238e6	−0.547185
$718$	7.90579e6	0.572314
$719$	4.07001e6	0.293611	0.146806	−	0.989165i	$-0.453101\pi$
$719$	4.07001e6	0.293611	0.146806	+	0.989165i	$0.453101\pi$
$720$	1.84982e6	0.132984
$721$	4.49015e7	3.21679
$722$	0	0
$723$	4.15608e7	2.95691
$724$	−2.69827e6	−0.191311
$725$	−1.30679e7	−0.923342
$726$	−1.26801e7	−0.892858
$727$	−7.26292e6	−0.509654	−0.254827	−	0.966987i	$-0.582018\pi$
$727$	−7.26292e6	−0.509654	−0.254827	+	0.966987i	$0.582018\pi$
$728$	−8.63105e6	−0.603581
$729$	−2.29264e7	−1.59778
$730$	29908.3	0.00207723
$731$	−3.20269e6	−0.221678
$732$	−1.74618e7	−1.20452
$733$	1.25623e7	0.863595	0.431797	−	0.901971i	$-0.357880\pi$
$733$	1.25623e7	0.863595	0.431797	+	0.901971i	$0.357880\pi$
$734$	1.25672e7	0.860991
$735$	1.97350e7	1.34747
$736$	3.88199e6	0.264156
$737$	−1.30526e7	−0.885171
$738$	4.74158e6	0.320466
$739$	8.74340e6	0.588937	0.294469	−	0.955661i	$-0.404857\pi$
$739$	8.74340e6	0.588937	0.294469	+	0.955661i	$0.404857\pi$
$740$	−636744.	−0.0427451
$741$	0	0
$742$	−3.79279e7	−2.52900
$743$	1.63290e6	0.108515	0.0542573	−	0.998527i	$-0.482721\pi$
$743$	1.63290e6	0.108515	0.0542573	+	0.998527i	$0.482721\pi$
$744$	−1.39021e7	−0.920762
$745$	−4.66119e6	−0.307685
$746$	−5.51482e6	−0.362814
$747$	3.44928e6	0.226166
$748$	5.23189e6	0.341904
$749$	−436208.	−0.0284111
$750$	1.08064e7	0.701502
$751$	1.62875e7	1.05379	0.526896	−	0.849930i	$-0.323356\pi$
$751$	1.62875e7	1.05379	0.526896	+	0.849930i	$0.323356\pi$
$752$	−952108.	−0.0613962
$753$	1.41450e6	0.0909109
$754$	1.02553e7	0.656933
$755$	−7.04592e6	−0.449852
$756$	−1.59575e7	−1.01546
$757$	1.01122e7	0.641363	0.320681	−	0.947187i	$-0.396088\pi$
$757$	1.01122e7	0.641363	0.320681	+	0.947187i	$0.396088\pi$
$758$	1.52799e7	0.965933
$759$	−5.15102e7	−3.24555
$760$	0	0
$761$	−1.69173e7	−1.05894	−0.529469	−	0.848329i	$-0.677609\pi$
$761$	−1.69173e7	−1.05894	−0.529469	+	0.848329i	$0.677609\pi$
$762$	−1.80197e7	−1.12425
$763$	−2.65872e7	−1.65333
$764$	9.35162e6	0.579633
$765$	4.41998e6	0.273065
$766$	1.82816e7	1.12575
$767$	−1.01413e7	−0.622453
$768$	1.66575e6	0.101908
$769$	2.23870e7	1.36515	0.682575	−	0.730816i	$-0.260860\pi$
$769$	2.23870e7	1.36515	0.682575	+	0.730816i	$0.260860\pi$
$770$	9.39943e6	0.571314
$771$	−2.63591e7	−1.59696
$772$	7.85194e6	0.474170
$773$	6.93749e6	0.417594	0.208797	−	0.977959i	$-0.433045\pi$
$773$	6.93749e6	0.417594	0.208797	+	0.977959i	$0.433045\pi$
$774$	8.44098e6	0.506455
$775$	−2.39597e7	−1.43294
$776$	6.98125e6	0.416178
$777$	1.38332e7	0.821995
$778$	−2.13707e6	−0.126581
$779$	0	0
$780$	−4.01038e6	−0.236020
$781$	−2.61493e7	−1.53403
$782$	9.27565e6	0.542410
$783$	1.89606e7	1.10522
$784$	1.10867e7	0.644190
$785$	5.38844e6	0.312096
$786$	1.97104e7	1.13799
$787$	−2.66033e7	−1.53108	−0.765540	−	0.643388i	$-0.777528\pi$
$787$	−2.66033e7	−1.53108	−0.765540	+	0.643388i	$0.777528\pi$
$788$	7.00220e6	0.401716
$789$	2.46670e7	1.41066
$790$	−3.27587e6	−0.186750
$791$	3.92317e7	2.22944
$792$	−1.37891e7	−0.781130
$793$	2.36175e7	1.33368
$794$	1.39271e7	0.783986
$795$	−1.76231e7	−0.988925
$796$	−1.01915e7	−0.570107
$797$	6.74803e6	0.376297	0.188149	−	0.982141i	$-0.439751\pi$
$797$	6.74803e6	0.376297	0.188149	+	0.982141i	$0.439751\pi$
$798$	0	0
$799$	−2.27497e6	−0.126069
$800$	2.87086e6	0.158594
$801$	−2.80442e7	−1.54441
$802$	−6.44036e6	−0.353569
$803$	−222945.	−0.0122014
$804$	−9.92971e6	−0.541747
$805$	1.66643e7	0.906354
$806$	1.88029e7	1.01950
$807$	−3.14796e7	−1.70156
$808$	902997.	0.0486584
$809$	−6.90081e6	−0.370705	−0.185353	−	0.982672i	$-0.559343\pi$
$809$	−6.90081e6	−0.370705	−0.185353	+	0.982672i	$0.559343\pi$
$810$	−391062.	−0.0209427
$811$	1.01870e7	0.543871	0.271935	−	0.962316i	$-0.412336\pi$
$811$	1.01870e7	0.543871	0.271935	+	0.962316i	$0.412336\pi$
$812$	−1.82855e7	−0.973231
$813$	−1.47441e6	−0.0782336
$814$	4.74648e6	0.251079
$815$	−3.39246e6	−0.178904
$816$	3.98015e6	0.209254
$817$	0	0
$818$	1.15672e7	0.604429
$819$	5.43539e7	2.83153
$820$	−843681.	−0.0438171
$821$	−1.35551e7	−0.701851	−0.350926	−	0.936403i	$-0.614133\pi$
$821$	−1.35551e7	−0.701851	−0.350926	+	0.936403i	$0.614133\pi$
$822$	−5.03532e6	−0.259925
$823$	1.87926e7	0.967135	0.483567	−	0.875307i	$-0.339341\pi$
$823$	1.87926e7	0.967135	0.483567	+	0.875307i	$0.339341\pi$
$824$	1.17206e7	0.601358
$825$	−3.80934e7	−1.94856
$826$	1.80822e7	0.922150
$827$	6.92315e6	0.351998	0.175999	−	0.984390i	$-0.443684\pi$
$827$	6.92315e6	0.351998	0.175999	+	0.984390i	$0.443684\pi$
$828$	−2.44468e7	−1.23921
$829$	−7.65376e6	−0.386802	−0.193401	−	0.981120i	$-0.561952\pi$
$829$	−7.65376e6	−0.386802	−0.193401	+	0.981120i	$0.561952\pi$
$830$	−613739.	−0.0309235
$831$	1.59175e6	0.0799599
$832$	−2.25296e6	−0.112835
$833$	2.64907e7	1.32276
$834$	−2.84158e7	−1.41464
$835$	−6.92872e6	−0.343904
$836$	0	0
$837$	3.47637e7	1.71519
$838$	−1.20836e7	−0.594412
$839$	−2.39733e7	−1.17577	−0.587885	−	0.808945i	$-0.700039\pi$
$839$	−2.39733e7	−1.17577	−0.587885	+	0.808945i	$0.700039\pi$
$840$	7.15059e6	0.349658
$841$	1.21545e6	0.0592582
$842$	−4.19393e6	−0.203864
$843$	−5.25768e7	−2.54815
$844$	6.61302e6	0.319554
$845$	−1.23258e6	−0.0593844
$846$	5.99589e6	0.288023
$847$	−3.05791e7	−1.46459
$848$	−9.90032e6	−0.472780
$849$	−1.20706e7	−0.574726
$850$	6.85964e6	0.325652
$851$	8.41506e6	0.398321
$852$	−1.98930e7	−0.938862
$853$	−1.80106e7	−0.847533	−0.423767	−	0.905771i	$-0.639292\pi$
$853$	−1.80106e7	−0.847533	−0.423767	+	0.905771i	$0.639292\pi$
$854$	−4.21105e7	−1.97581
$855$	0	0
$856$	−113863.	−0.00531127
$857$	7.91294e6	0.368032	0.184016	−	0.982923i	$-0.441090\pi$
$857$	7.91294e6	0.368032	0.184016	+	0.982923i	$0.441090\pi$
$858$	2.98945e7	1.38635
$859$	−2.43601e7	−1.12641	−0.563205	−	0.826317i	$-0.690432\pi$
$859$	−2.43601e7	−1.12641	−0.563205	+	0.826317i	$0.690432\pi$
$860$	−1.50193e6	−0.0692472
$861$	1.83288e7	0.842611
$862$	−1.10849e7	−0.508115
$863$	6.37643e6	0.291441	0.145720	−	0.989326i	$-0.453450\pi$
$863$	6.37643e6	0.291441	0.145720	+	0.989326i	$0.453450\pi$
$864$	−4.16539e6	−0.189833
$865$	−392827.	−0.0178509
$866$	−144885.	−0.00656489
$867$	−2.65787e7	−1.20084
$868$	−3.35259e7	−1.51036
$869$	2.44193e7	1.09694
$870$	−8.49626e6	−0.380566
$871$	1.34302e7	0.599840
$872$	−6.94004e6	−0.309080
$873$	−4.39644e7	−1.95238
$874$	0	0
$875$	2.60605e7	1.15070
$876$	−169605.	−0.00746756
$877$	2.76270e7	1.21293	0.606464	−	0.795111i	$-0.292588\pi$
$877$	2.76270e7	1.21293	0.606464	+	0.795111i	$0.292588\pi$
$878$	−1.00965e7	−0.442013
$879$	1.37586e6	0.0600621
$880$	2.45353e6	0.106803
$881$	6.76021e6	0.293441	0.146720	−	0.989178i	$-0.453128\pi$
$881$	6.76021e6	0.293441	0.146720	+	0.989178i	$0.453128\pi$
$882$	−6.98187e7	−3.02204
$883$	4.04565e7	1.74617	0.873086	−	0.487566i	$-0.162115\pi$
$883$	4.04565e7	1.74617	0.873086	+	0.487566i	$0.162115\pi$
$884$	−5.38324e6	−0.231693
$885$	8.40183e6	0.360591
$886$	−4.34183e6	−0.185818
$887$	478166.	0.0204066	0.0102033	−	0.999948i	$-0.496752\pi$
$887$	478166.	0.0204066	0.0102033	+	0.999948i	$0.496752\pi$
$888$	3.61087e6	0.153667
$889$	−4.34559e7	−1.84414
$890$	4.98998e6	0.211166
$891$	2.91509e6	0.123015
$892$	−1.33495e7	−0.561764
$893$	0	0
$894$	2.64328e7	1.10611
$895$	−3.79582e6	−0.158397
$896$	4.01708e6	0.167163
$897$	5.30002e7	2.19936
$898$	168206.	0.00696067
$899$	3.98351e7	1.64387
$900$	−1.80792e7	−0.743999
$901$	−2.36559e7	−0.970794
$902$	6.28904e6	0.257376
$903$	3.26291e7	1.33164
$904$	1.02406e7	0.416779
$905$	−3.02349e6	−0.122712
$906$	3.99562e7	1.61720
$907$	−2.64563e7	−1.06785	−0.533925	−	0.845532i	$-0.679284\pi$
$907$	−2.64563e7	−1.06785	−0.533925	+	0.845532i	$0.679284\pi$
$908$	−1.14837e7	−0.462242
$909$	−5.68661e6	−0.228268
$910$	−9.67133e6	−0.387153
$911$	943321.	0.0376585	0.0188293	−	0.999823i	$-0.494006\pi$
$911$	943321.	0.0376585	0.0188293	+	0.999823i	$0.494006\pi$
$912$	0	0
$913$	4.57499e6	0.181641
$914$	−1.94888e6	−0.0771647
$915$	−1.95665e7	−0.772610
$916$	1.39603e7	0.549738
$917$	4.75331e7	1.86669
$918$	−9.95281e6	−0.389797
$919$	−4.58125e7	−1.78935	−0.894675	−	0.446718i	$-0.852593\pi$
$919$	−4.58125e7	−1.78935	−0.894675	+	0.446718i	$0.852593\pi$
$920$	4.34988e6	0.169437
$921$	7.06417e7	2.74418
$922$	−3.20792e7	−1.24278
$923$	2.69058e7	1.03954
$924$	−5.33026e7	−2.05385
$925$	6.22320e6	0.239144
$926$	2.99336e7	1.14718
$927$	−7.38105e7	−2.82110
$928$	−4.77305e6	−0.181939
$929$	3.90147e7	1.48316	0.741582	−	0.670862i	$-0.234076\pi$
$929$	3.90147e7	1.48316	0.741582	+	0.670862i	$0.234076\pi$
$930$	−1.55777e7	−0.590602
$931$	0	0
$932$	2.28794e7	0.862790
$933$	5.90494e7	2.22081
$934$	−9.94803e6	−0.373138
$935$	5.86248e6	0.219307
$936$	1.41880e7	0.529336
$937$	9.10163e6	0.338665	0.169332	−	0.985559i	$-0.445839\pi$
$937$	9.10163e6	0.338665	0.169332	+	0.985559i	$0.445839\pi$
$938$	−2.39462e7	−0.888649
$939$	6.20299e6	0.229581
$940$	−1.06686e6	−0.0393812
$941$	5.84337e6	0.215124	0.107562	−	0.994198i	$-0.465696\pi$
$941$	5.84337e6	0.215124	0.107562	+	0.994198i	$0.465696\pi$
$942$	−3.05569e7	−1.12197
$943$	1.11499e7	0.408311
$944$	4.71999e6	0.172390
$945$	−1.78809e7	−0.651342
$946$	1.11958e7	0.406749
$947$	1.63421e7	0.592152	0.296076	−	0.955164i	$-0.404322\pi$
$947$	1.63421e7	0.592152	0.296076	+	0.955164i	$0.404322\pi$
$948$	1.85769e7	0.671356
$949$	229395.	0.00826833
$950$	0	0
$951$	−5.26483e7	−1.88770
$952$	9.59842e6	0.343248
$953$	3.78978e7	1.35170	0.675852	−	0.737037i	$-0.263776\pi$
$953$	3.78978e7	1.35170	0.675852	+	0.737037i	$0.263776\pi$
$954$	6.23471e7	2.21792
$955$	1.04788e7	0.371793
$956$	−4.74157e6	−0.167795
$957$	6.33336e7	2.23539
$958$	849609.	0.0299093
$959$	−1.21430e7	−0.426365
$960$	1.86652e6	0.0653663
$961$	4.44074e7	1.55113
$962$	−4.88378e6	−0.170145
$963$	717052.	0.0249164
$964$	2.61622e7	0.906738
$965$	8.79832e6	0.304145
$966$	−9.45005e7	−3.25830
$967$	−924233.	−0.0317845	−0.0158922	−	0.999874i	$-0.505059\pi$
$967$	−924233.	−0.0317845	−0.0158922	+	0.999874i	$0.505059\pi$
$968$	−7.98205e6	−0.273795
$969$	0	0
$970$	7.82269e6	0.266948
$971$	6.10860e6	0.207919	0.103959	−	0.994582i	$-0.466849\pi$
$971$	6.10860e6	0.207919	0.103959	+	0.994582i	$0.466849\pi$
$972$	−1.35978e7	−0.461640
$973$	−6.85269e7	−2.32049
$974$	2.99005e7	1.00991
$975$	3.91954e7	1.32045
$976$	−1.09921e7	−0.369365
$977$	1.99215e6	0.0667708	0.0333854	−	0.999443i	$-0.489371\pi$
$977$	1.99215e6	0.0667708	0.0333854	+	0.999443i	$0.489371\pi$
$978$	1.92381e7	0.643153
$979$	−3.71967e7	−1.24036
$980$	1.24230e7	0.413201
$981$	4.37048e7	1.44996
$982$	4.50053e6	0.148931
$983$	9.55237e6	0.315302	0.157651	−	0.987495i	$-0.449608\pi$
$983$	9.55237e6	0.315302	0.157651	+	0.987495i	$0.449608\pi$
$984$	4.78437e6	0.157521
$985$	7.84617e6	0.257672
$986$	−1.14047e7	−0.373588
$987$	2.31775e7	0.757309
$988$	0	0
$989$	1.98491e7	0.645282
$990$	−1.54511e7	−0.501038
$991$	−3.18868e7	−1.03140	−0.515700	−	0.856769i	$-0.672468\pi$
$991$	−3.18868e7	−1.03140	−0.515700	+	0.856769i	$0.672468\pi$
$992$	−8.75125e6	−0.282352
$993$	3.52342e6	0.113394
$994$	−4.79735e7	−1.54005
$995$	−1.14199e7	−0.365682
$996$	3.48041e6	0.111169
$997$	554628.	0.0176711	0.00883555	−	0.999961i	$-0.497188\pi$
$997$	554628.	0.0176711	0.00883555	+	0.999961i	$0.497188\pi$
$998$	−3.09586e7	−0.983909
$999$	−9.02939e6	−0.286249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.h.1.4	✓	4
19.18	odd	2		722.6.a.i.1.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.6.a.h.1.4	✓	4	1.1	even	1	trivial
722.6.a.i.1.1	yes	4	19.18	odd	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +25.4173 q^{3} +16.0000 q^{4} +17.9284 q^{5} -101.669 q^{6} -245.183 q^{7} -64.0000 q^{8} +403.039 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +25.4173 q^{3} +16.0000 q^{4} +17.9284 q^{5} -101.669 q^{6} -245.183 q^{7} -64.0000 q^{8} +403.039 q^{9} -71.7138 q^{10} +534.575 q^{11} +406.677 q^{12} -550.039 q^{13} +980.731 q^{14} +455.693 q^{15} +256.000 q^{16} +611.688 q^{17} -1612.16 q^{18} +286.855 q^{20} -6231.89 q^{21} -2138.30 q^{22} -3791.01 q^{23} -1626.71 q^{24} -2803.57 q^{25} +2200.16 q^{26} +4067.77 q^{27} -3922.93 q^{28} +4661.18 q^{29} -1822.77 q^{30} +8546.14 q^{31} -1024.00 q^{32} +13587.5 q^{33} -2446.75 q^{34} -4395.75 q^{35} +6448.63 q^{36} -2219.74 q^{37} -13980.5 q^{39} -1147.42 q^{40} -2941.14 q^{41} +24927.5 q^{42} -5235.83 q^{43} +8553.20 q^{44} +7225.87 q^{45} +15164.0 q^{46} -3719.17 q^{47} +6506.83 q^{48} +43307.6 q^{49} +11214.3 q^{50} +15547.5 q^{51} -8800.63 q^{52} -38673.1 q^{53} -16271.1 q^{54} +9584.10 q^{55} +15691.7 q^{56} -18644.7 q^{58} +18437.5 q^{59} +7291.08 q^{60} -42937.9 q^{61} -34184.6 q^{62} -98818.3 q^{63} +4096.00 q^{64} -9861.35 q^{65} -54349.8 q^{66} -24416.7 q^{67} +9787.01 q^{68} -96357.2 q^{69} +17583.0 q^{70} -48916.1 q^{71} -25794.5 q^{72} -417.051 q^{73} +8878.97 q^{74} -71259.2 q^{75} -131069. q^{77} +55922.1 q^{78} +45679.8 q^{79} +4589.68 q^{80} +5453.09 q^{81} +11764.6 q^{82} +8558.17 q^{83} -99710.2 q^{84} +10966.6 q^{85} +20943.3 q^{86} +118475. q^{87} -34212.8 q^{88} -69581.9 q^{89} -28903.5 q^{90} +134860. q^{91} -60656.1 q^{92} +217220. q^{93} +14876.7 q^{94} -26027.3 q^{96} -109082. q^{97} -173230. q^{98} +215455. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + q^{3} + 64 q^{4} - 14 q^{5} - 4 q^{6} + 97 q^{7} - 256 q^{8} + 877 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + q^3 + 64 * q^4 - 14 * q^5 - 4 * q^6 + 97 * q^7 - 256 * q^8 + 877 * q^9	\( 4 q - 16 q^{2} + q^{3} + 64 q^{4} - 14 q^{5} - 4 q^{6} + 97 q^{7} - 256 q^{8} + 877 q^{9} + 56 q^{10} + 758 q^{11} + 16 q^{12} - 1465 q^{13} - 388 q^{14} + 926 q^{15} + 1024 q^{16} + 599 q^{17} - 3508 q^{18} - 224 q^{20} - 7199 q^{21} - 3032 q^{22} - 3651 q^{23} - 64 q^{24} - 418 q^{25} + 5860 q^{26} - 7793 q^{27} + 1552 q^{28} + 12451 q^{29} - 3704 q^{30} - 3038 q^{31} - 4096 q^{32} - 9590 q^{33} - 2396 q^{34} - 20302 q^{35} + 14032 q^{36} - 10282 q^{37} + 7403 q^{39} + 896 q^{40} - 6520 q^{41} + 28796 q^{42} - 2330 q^{43} + 12128 q^{44} - 43708 q^{45} + 14604 q^{46} + 12760 q^{47} + 256 q^{48} + 49263 q^{49} + 1672 q^{50} + 72111 q^{51} - 23440 q^{52} - 78509 q^{53} + 31172 q^{54} - 4840 q^{55} - 6208 q^{56} - 49804 q^{58} + 20605 q^{59} + 14816 q^{60} + 36040 q^{61} + 12152 q^{62} - 22226 q^{63} + 16384 q^{64} + 45766 q^{65} + 38360 q^{66} - 42707 q^{67} + 9584 q^{68} - 42827 q^{69} + 81208 q^{70} + 24000 q^{71} - 56128 q^{72} - 55595 q^{73} + 41128 q^{74} - 140365 q^{75} - 135836 q^{77} - 29612 q^{78} - 81936 q^{79} - 3584 q^{80} + 143716 q^{81} + 26080 q^{82} - 173966 q^{83} - 115184 q^{84} + 188508 q^{85} + 9320 q^{86} + 190339 q^{87} - 48512 q^{88} - 35682 q^{89} + 174832 q^{90} + 7967 q^{91} - 58416 q^{92} + 278686 q^{93} - 51040 q^{94} - 1024 q^{96} - 44748 q^{97} - 197052 q^{98} + 575764 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + q^3 + 64 * q^4 - 14 * q^5 - 4 * q^6 + 97 * q^7 - 256 * q^8 + 877 * q^9 + 56 * q^10 + 758 * q^11 + 16 * q^12 - 1465 * q^13 - 388 * q^14 + 926 * q^15 + 1024 * q^16 + 599 * q^17 - 3508 * q^18 - 224 * q^20 - 7199 * q^21 - 3032 * q^22 - 3651 * q^23 - 64 * q^24 - 418 * q^25 + 5860 * q^26 - 7793 * q^27 + 1552 * q^28 + 12451 * q^29 - 3704 * q^30 - 3038 * q^31 - 4096 * q^32 - 9590 * q^33 - 2396 * q^34 - 20302 * q^35 + 14032 * q^36 - 10282 * q^37 + 7403 * q^39 + 896 * q^40 - 6520 * q^41 + 28796 * q^42 - 2330 * q^43 + 12128 * q^44 - 43708 * q^45 + 14604 * q^46 + 12760 * q^47 + 256 * q^48 + 49263 * q^49 + 1672 * q^50 + 72111 * q^51 - 23440 * q^52 - 78509 * q^53 + 31172 * q^54 - 4840 * q^55 - 6208 * q^56 - 49804 * q^58 + 20605 * q^59 + 14816 * q^60 + 36040 * q^61 + 12152 * q^62 - 22226 * q^63 + 16384 * q^64 + 45766 * q^65 + 38360 * q^66 - 42707 * q^67 + 9584 * q^68 - 42827 * q^69 + 81208 * q^70 + 24000 * q^71 - 56128 * q^72 - 55595 * q^73 + 41128 * q^74 - 140365 * q^75 - 135836 * q^77 - 29612 * q^78 - 81936 * q^79 - 3584 * q^80 + 143716 * q^81 + 26080 * q^82 - 173966 * q^83 - 115184 * q^84 + 188508 * q^85 + 9320 * q^86 + 190339 * q^87 - 48512 * q^88 - 35682 * q^89 + 174832 * q^90 + 7967 * q^91 - 58416 * q^92 + 278686 * q^93 - 51040 * q^94 - 1024 * q^96 - 44748 * q^97 - 197052 * q^98 + 575764 * q^99

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