LMFDB - Embedded newform 722.6.a.q.1.2

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2871 x^{13} - 4674 x^{12} + 3170019 x^{11} + 9081402 x^{10} - 1680307373 x^{9} + \cdots - 34\!\cdots\!72 $ x^15 - 2871x^13 - 4674x^12 + 3170019x^11 + 9081402x^10 - 1680307373x^9 - 6060225486x^8 + 437045334939x^7 + 1625551725606x^6 - 51993847360191x^5 - 166593470925336x^4 + 2435236025483701x^3 + 5743342864926480x^2 - 19853455953893436*x - 34308015556724472
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 19^{6} $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-26.2549$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -25.9076 q^{3} +16.0000 q^{4} -18.4597 q^{5} +103.630 q^{6} -122.093 q^{7} -64.0000 q^{8} +428.205 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -25.9076 q^{3} +16.0000 q^{4} -18.4597 q^{5} +103.630 q^{6} -122.093 q^{7} -64.0000 q^{8} +428.205 q^{9} +73.8387 q^{10} -71.1774 q^{11} -414.522 q^{12} -540.332 q^{13} +488.374 q^{14} +478.246 q^{15} +256.000 q^{16} +221.223 q^{17} -1712.82 q^{18} -295.355 q^{20} +3163.15 q^{21} +284.709 q^{22} +4117.82 q^{23} +1658.09 q^{24} -2784.24 q^{25} +2161.33 q^{26} -4798.21 q^{27} -1953.49 q^{28} -5552.53 q^{29} -1912.99 q^{30} -7551.01 q^{31} -1024.00 q^{32} +1844.04 q^{33} -884.893 q^{34} +2253.81 q^{35} +6851.27 q^{36} -6113.82 q^{37} +13998.7 q^{39} +1181.42 q^{40} +20366.8 q^{41} -12652.6 q^{42} +5103.37 q^{43} -1138.84 q^{44} -7904.52 q^{45} -16471.3 q^{46} +5256.30 q^{47} -6632.35 q^{48} -1900.20 q^{49} +11137.0 q^{50} -5731.37 q^{51} -8645.31 q^{52} +3445.20 q^{53} +19192.8 q^{54} +1313.91 q^{55} +7813.98 q^{56} +22210.1 q^{58} -52328.0 q^{59} +7651.94 q^{60} -44232.5 q^{61} +30204.0 q^{62} -52280.9 q^{63} +4096.00 q^{64} +9974.35 q^{65} -7376.14 q^{66} -65083.8 q^{67} +3539.57 q^{68} -106683. q^{69} -9015.22 q^{70} -39444.9 q^{71} -27405.1 q^{72} -7606.02 q^{73} +24455.3 q^{74} +72133.0 q^{75} +8690.29 q^{77} -55994.8 q^{78} -41667.2 q^{79} -4725.68 q^{80} +20256.4 q^{81} -81467.0 q^{82} -35753.5 q^{83} +50610.4 q^{84} -4083.71 q^{85} -20413.5 q^{86} +143853. q^{87} +4555.35 q^{88} -89085.2 q^{89} +31618.1 q^{90} +65970.9 q^{91} +65885.1 q^{92} +195629. q^{93} -21025.2 q^{94} +26529.4 q^{96} +16739.3 q^{97} +7600.80 q^{98} -30478.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) $ 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9} - 432 q^{10} + 126 q^{11} + 114 q^{13} - 336 q^{14} + 3840 q^{16} + 4119 q^{17} - 8508 q^{18} + 1728 q^{20} - 3408 q^{21} - 504 q^{22} + 3936 q^{23} + 26895 q^{25} - 456 q^{26} + 13017 q^{27} + 1344 q^{28} - 14658 q^{29} - 6840 q^{31} - 15360 q^{32} + 3945 q^{33} - 16476 q^{34} + 12636 q^{35} + 34032 q^{36} + 4278 q^{37} + 4956 q^{39} - 6912 q^{40} - 5112 q^{41} + 13632 q^{42} + 94191 q^{43} + 2016 q^{44} + 31770 q^{45} - 15744 q^{46} + 702 q^{47} + 63777 q^{49} - 107580 q^{50} + 108 q^{51} + 1824 q^{52} - 47544 q^{53} - 52068 q^{54} + 16848 q^{55} - 5376 q^{56} + 58632 q^{58} + 8832 q^{59} + 119196 q^{61} + 27360 q^{62} - 88068 q^{63} + 61440 q^{64} - 80646 q^{65} - 15780 q^{66} - 64248 q^{67} + 65904 q^{68} - 124224 q^{69} - 50544 q^{70} + 53364 q^{71} - 136128 q^{72} - 4908 q^{73} - 17112 q^{74} + 87480 q^{75} + 121218 q^{77} - 19824 q^{78} + 115500 q^{79} + 27648 q^{80} + 481659 q^{81} + 20448 q^{82} + 201630 q^{83} - 54528 q^{84} - 150282 q^{85} - 376764 q^{86} + 376512 q^{87} - 8064 q^{88} + 101505 q^{89} - 127080 q^{90} - 414918 q^{91} + 62976 q^{92} + 165960 q^{93} - 2808 q^{94} - 297114 q^{97} - 255108 q^{98} - 149895 q^{99}+O(q^{100}) \) 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9 - 432 * q^10 + 126 * q^11 + 114 * q^13 - 336 * q^14 + 3840 * q^16 + 4119 * q^17 - 8508 * q^18 + 1728 * q^20 - 3408 * q^21 - 504 * q^22 + 3936 * q^23 + 26895 * q^25 - 456 * q^26 + 13017 * q^27 + 1344 * q^28 - 14658 * q^29 - 6840 * q^31 - 15360 * q^32 + 3945 * q^33 - 16476 * q^34 + 12636 * q^35 + 34032 * q^36 + 4278 * q^37 + 4956 * q^39 - 6912 * q^40 - 5112 * q^41 + 13632 * q^42 + 94191 * q^43 + 2016 * q^44 + 31770 * q^45 - 15744 * q^46 + 702 * q^47 + 63777 * q^49 - 107580 * q^50 + 108 * q^51 + 1824 * q^52 - 47544 * q^53 - 52068 * q^54 + 16848 * q^55 - 5376 * q^56 + 58632 * q^58 + 8832 * q^59 + 119196 * q^61 + 27360 * q^62 - 88068 * q^63 + 61440 * q^64 - 80646 * q^65 - 15780 * q^66 - 64248 * q^67 + 65904 * q^68 - 124224 * q^69 - 50544 * q^70 + 53364 * q^71 - 136128 * q^72 - 4908 * q^73 - 17112 * q^74 + 87480 * q^75 + 121218 * q^77 - 19824 * q^78 + 115500 * q^79 + 27648 * q^80 + 481659 * q^81 + 20448 * q^82 + 201630 * q^83 - 54528 * q^84 - 150282 * q^85 - 376764 * q^86 + 376512 * q^87 - 8064 * q^88 + 101505 * q^89 - 127080 * q^90 - 414918 * q^91 + 62976 * q^92 + 165960 * q^93 - 2808 * q^94 - 297114 * q^97 - 255108 * q^98 - 149895 * 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
$3$	−25.9076	−1.66197	−0.830987	−	0.556292i	$-0.812224\pi$
$3$	−25.9076	−1.66197	−0.830987	+	0.556292i	$0.812224\pi$
$4$	16.0000	0.500000
$5$	−18.4597	−0.330217	−0.165108	−	0.986275i	$-0.552797\pi$
$5$	−18.4597	−0.330217	−0.165108	+	0.986275i	$0.552797\pi$
$6$	103.630	1.17519
$7$	−122.093	−0.941775	−0.470887	−	0.882193i	$-0.656066\pi$
$7$	−122.093	−0.941775	−0.470887	+	0.882193i	$0.656066\pi$
$8$	−64.0000	−0.353553
$9$	428.205	1.76216
$10$	73.8387	0.233499
$11$	−71.1774	−0.177362	−0.0886809	−	0.996060i	$-0.528265\pi$
$11$	−71.1774	−0.177362	−0.0886809	+	0.996060i	$0.528265\pi$
$12$	−414.522	−0.830987
$13$	−540.332	−0.886752	−0.443376	−	0.896336i	$-0.646219\pi$
$13$	−540.332	−0.886752	−0.443376	+	0.896336i	$0.646219\pi$
$14$	488.374	0.665935
$15$	478.246	0.548812
$16$	256.000	0.250000
$17$	221.223	0.185656	0.0928279	−	0.995682i	$-0.470409\pi$
$17$	221.223	0.185656	0.0928279	+	0.995682i	$0.470409\pi$
$18$	−1712.82	−1.24603
$19$	0	0
$19$	0	0
$20$	−295.355	−0.165108
$21$	3163.15	1.56521
$22$	284.709	0.125414
$23$	4117.82	1.62311	0.811554	−	0.584278i	$-0.198622\pi$
$23$	4117.82	1.62311	0.811554	+	0.584278i	$0.198622\pi$
$24$	1658.09	0.587597
$25$	−2784.24	−0.890957
$26$	2161.33	0.627028
$27$	−4798.21	−1.26669
$28$	−1953.49	−0.470887
$29$	−5552.53	−1.22602	−0.613008	−	0.790077i	$-0.710041\pi$
$29$	−5552.53	−1.22602	−0.613008	+	0.790077i	$0.710041\pi$
$30$	−1912.99	−0.388069
$31$	−7551.01	−1.41124	−0.705620	−	0.708591i	$-0.749331\pi$
$31$	−7551.01	−1.41124	−0.705620	+	0.708591i	$0.749331\pi$
$32$	−1024.00	−0.176777
$33$	1844.04	0.294771
$34$	−884.893	−0.131278
$35$	2253.81	0.310990
$36$	6851.27	0.881079
$37$	−6113.82	−0.734190	−0.367095	−	0.930184i	$-0.619648\pi$
$37$	−6113.82	−0.734190	−0.367095	+	0.930184i	$0.619648\pi$
$38$	0	0
$39$	13998.7	1.47376
$40$	1181.42	0.116749
$41$	20366.8	1.89218	0.946090	−	0.323905i	$-0.104996\pi$
$41$	20366.8	1.89218	0.946090	+	0.323905i	$0.104996\pi$
$42$	−12652.6	−1.10677
$43$	5103.37	0.420907	0.210453	−	0.977604i	$-0.432506\pi$
$43$	5103.37	0.420907	0.210453	+	0.977604i	$0.432506\pi$
$44$	−1138.84	−0.0886809
$45$	−7904.52	−0.581894
$46$	−16471.3	−1.14771
$47$	5256.30	0.347085	0.173542	−	0.984826i	$-0.444479\pi$
$47$	5256.30	0.347085	0.173542	+	0.984826i	$0.444479\pi$
$48$	−6632.35	−0.415494
$49$	−1900.20	−0.113060
$50$	11137.0	0.630002
$51$	−5731.37	−0.308555
$52$	−8645.31	−0.443376
$53$	3445.20	0.168471	0.0842355	−	0.996446i	$-0.473155\pi$
$53$	3445.20	0.168471	0.0842355	+	0.996446i	$0.473155\pi$
$54$	19192.8	0.895684
$55$	1313.91	0.0585679
$56$	7813.98	0.332968
$57$	0	0
$58$	22210.1	0.866924
$59$	−52328.0	−1.95706	−0.978529	−	0.206107i	$-0.933920\pi$
$59$	−52328.0	−1.95706	−0.978529	+	0.206107i	$0.933920\pi$
$60$	7651.94	0.274406
$61$	−44232.5	−1.52201	−0.761004	−	0.648747i	$-0.775293\pi$
$61$	−44232.5	−1.52201	−0.761004	+	0.648747i	$0.775293\pi$
$62$	30204.0	0.997897
$63$	−52280.9	−1.65956
$64$	4096.00	0.125000
$65$	9974.35	0.292820
$66$	−7376.14	−0.208434
$67$	−65083.8	−1.77127	−0.885637	−	0.464378i	$-0.846278\pi$
$67$	−65083.8	−1.77127	−0.885637	+	0.464378i	$0.846278\pi$
$68$	3539.57	0.0928279
$69$	−106683.	−2.69756
$70$	−9015.22	−0.219903
$71$	−39444.9	−0.928634	−0.464317	−	0.885669i	$-0.653700\pi$
$71$	−39444.9	−0.928634	−0.464317	+	0.885669i	$0.653700\pi$
$72$	−27405.1	−0.623017
$73$	−7606.02	−0.167052	−0.0835258	−	0.996506i	$-0.526618\pi$
$73$	−7606.02	−0.167052	−0.0835258	+	0.996506i	$0.526618\pi$
$74$	24455.3	0.519150
$75$	72133.0	1.48075
$76$	0	0
$77$	8690.29	0.167035
$78$	−55994.8	−1.04210
$79$	−41667.2	−0.751150	−0.375575	−	0.926792i	$-0.622555\pi$
$79$	−41667.2	−0.751150	−0.375575	+	0.926792i	$0.622555\pi$
$80$	−4725.68	−0.0825542
$81$	20256.4	0.343044
$82$	−81467.0	−1.33797
$83$	−35753.5	−0.569669	−0.284835	−	0.958577i	$-0.591939\pi$
$83$	−35753.5	−0.569669	−0.284835	+	0.958577i	$0.591939\pi$
$84$	50610.4	0.782603
$85$	−4083.71	−0.0613066
$86$	−20413.5	−0.297626
$87$	143853.	2.03761
$88$	4555.35	0.0627069
$89$	−89085.2	−1.19215	−0.596075	−	0.802929i	$-0.703274\pi$
$89$	−89085.2	−1.19215	−0.596075	+	0.802929i	$0.703274\pi$
$90$	31618.1	0.411461
$91$	65970.9	0.835121
$92$	65885.1	0.811554
$93$	195629.	2.34544
$94$	−21025.2	−0.245426
$95$	0	0
$96$	26529.4	0.293798
$97$	16739.3	0.180637	0.0903187	−	0.995913i	$-0.471211\pi$
$97$	16739.3	0.180637	0.0903187	+	0.995913i	$0.471211\pi$
$98$	7600.80	0.0799455
$99$	−30478.5	−0.312540
$100$	−44547.8	−0.445478
$101$	−87630.3	−0.854773	−0.427387	−	0.904069i	$-0.640566\pi$
$101$	−87630.3	−0.854773	−0.427387	+	0.904069i	$0.640566\pi$
$102$	22925.5	0.218181
$103$	−150197.	−1.39498	−0.697489	−	0.716595i	$-0.745699\pi$
$103$	−150197.	−1.39498	−0.697489	+	0.716595i	$0.745699\pi$
$104$	34581.2	0.313514
$105$	−58390.7	−0.516857
$106$	−13780.8	−0.119127
$107$	−54570.4	−0.460784	−0.230392	−	0.973098i	$-0.574001\pi$
$107$	−54570.4	−0.460784	−0.230392	+	0.973098i	$0.574001\pi$
$108$	−76771.3	−0.633344
$109$	4813.40	0.0388049	0.0194024	−	0.999812i	$-0.493824\pi$
$109$	4813.40	0.0388049	0.0194024	+	0.999812i	$0.493824\pi$
$110$	−5255.65	−0.0414137
$111$	158394.	1.22020
$112$	−31255.9	−0.235444
$113$	−116554.	−0.858676	−0.429338	−	0.903144i	$-0.641253\pi$
$113$	−116554.	−0.858676	−0.429338	+	0.903144i	$0.641253\pi$
$114$	0	0
$115$	−76013.6	−0.535977
$116$	−88840.5	−0.613008
$117$	−231372.	−1.56260
$118$	209312.	1.38385
$119$	−27009.9	−0.174846
$120$	−30607.8	−0.194034
$121$	−155985.	−0.968543
$122$	176930.	1.07622
$123$	−527654.	−3.14475
$124$	−120816.	−0.705620
$125$	109083.	0.624426
$126$	209124.	1.17348
$127$	245406.	1.35013	0.675066	−	0.737757i	$-0.264115\pi$
$127$	245406.	1.35013	0.675066	+	0.737757i	$0.264115\pi$
$128$	−16384.0	−0.0883883
$129$	−132216.	−0.699536
$130$	−39897.4	−0.207055
$131$	113196.	0.576305	0.288152	−	0.957585i	$-0.406959\pi$
$131$	113196.	0.576305	0.288152	+	0.957585i	$0.406959\pi$
$132$	29504.6	0.147385
$133$	0	0
$134$	260335.	1.25248
$135$	88573.4	0.418282
$136$	−14158.3	−0.0656392
$137$	197146.	0.897402	0.448701	−	0.893682i	$-0.351887\pi$
$137$	197146.	0.897402	0.448701	+	0.893682i	$0.351887\pi$
$138$	426731.	1.90747
$139$	175932.	0.772339	0.386170	−	0.922428i	$-0.373798\pi$
$139$	175932.	0.772339	0.386170	+	0.922428i	$0.373798\pi$
$140$	36060.9	0.155495
$141$	−136178.	−0.576846
$142$	157779.	0.656643
$143$	38459.4	0.157276
$144$	109620.	0.440540
$145$	102498.	0.404851
$146$	30424.1	0.118123
$147$	49229.7	0.187903
$148$	−97821.1	−0.367095
$149$	−457772.	−1.68921	−0.844606	−	0.535389i	$-0.820165\pi$
$149$	−457772.	−1.68921	−0.844606	+	0.535389i	$0.820165\pi$
$150$	−288532.	−1.04705
$151$	309788.	1.10566	0.552830	−	0.833294i	$-0.313548\pi$
$151$	309788.	1.10566	0.552830	+	0.833294i	$0.313548\pi$
$152$	0	0
$153$	94728.8	0.327155
$154$	−34761.1	−0.118112
$155$	139389.	0.466015
$156$	223979.	0.736879
$157$	71080.3	0.230144	0.115072	−	0.993357i	$-0.463290\pi$
$157$	71080.3	0.230144	0.115072	+	0.993357i	$0.463290\pi$
$158$	166669.	0.531143
$159$	−89257.0	−0.279994
$160$	18902.7	0.0583746
$161$	−502758.	−1.52860
$162$	−81025.6	−0.242569
$163$	−326839.	−0.963530	−0.481765	−	0.876301i	$-0.660004\pi$
$163$	−326839.	−0.963530	−0.481765	+	0.876301i	$0.660004\pi$
$164$	325868.	0.946090
$165$	−34040.3	−0.0973383
$166$	143014.	0.402817
$167$	227032.	0.629937	0.314968	−	0.949102i	$-0.398006\pi$
$167$	227032.	0.629937	0.314968	+	0.949102i	$0.398006\pi$
$168$	−202442.	−0.553384
$169$	−79334.6	−0.213671
$170$	16334.8	0.0433503
$171$	0	0
$172$	81653.9	0.210453
$173$	351351.	0.892536	0.446268	−	0.894899i	$-0.352753\pi$
$173$	351351.	0.892536	0.446268	+	0.894899i	$0.352753\pi$
$174$	−575411.	−1.44081
$175$	339937.	0.839081
$176$	−18221.4	−0.0443405
$177$	1.35569e6	3.25258
$178$	356341.	0.842977
$179$	−196138.	−0.457539	−0.228770	−	0.973481i	$-0.573470\pi$
$179$	−196138.	−0.457539	−0.228770	+	0.973481i	$0.573470\pi$
$180$	−126472.	−0.290947
$181$	−315725.	−0.716329	−0.358164	−	0.933659i	$-0.616597\pi$
$181$	−315725.	−0.716329	−0.358164	+	0.933659i	$0.616597\pi$
$182$	−263884.	−0.590519
$183$	1.14596e6	2.52954
$184$	−263540.	−0.573855
$185$	112859.	0.242442
$186$	−782515.	−1.65848
$187$	−15746.1	−0.0329282
$188$	84100.8	0.173542
$189$	585829.	1.19293
$190$	0	0
$191$	−489237.	−0.970367	−0.485184	−	0.874412i	$-0.661247\pi$
$191$	−489237.	−0.970367	−0.485184	+	0.874412i	$0.661247\pi$
$192$	−106118.	−0.207747
$193$	−325338.	−0.628697	−0.314348	−	0.949308i	$-0.601786\pi$
$193$	−325338.	−0.628697	−0.314348	+	0.949308i	$0.601786\pi$
$194$	−66957.2	−0.127730
$195$	−258412.	−0.486660
$196$	−30403.2	−0.0565300
$197$	−797050.	−1.46325	−0.731627	−	0.681705i	$-0.761239\pi$
$197$	−797050.	−1.46325	−0.731627	+	0.681705i	$0.761239\pi$
$198$	121914.	0.220999
$199$	32381.2	0.0579643	0.0289822	−	0.999580i	$-0.490773\pi$
$199$	32381.2	0.0579643	0.0289822	+	0.999580i	$0.490773\pi$
$200$	178191.	0.315001
$201$	1.68617e6	2.94381
$202$	350521.	0.604416
$203$	677927.	1.15463
$204$	−91701.9	−0.154278
$205$	−375964.	−0.624829
$206$	600787.	0.986398
$207$	1.76327e6	2.86017
$208$	−138325.	−0.221688
$209$	0	0
$210$	233563.	0.365473
$211$	516580.	0.798788	0.399394	−	0.916779i	$-0.369220\pi$
$211$	516580.	0.798788	0.399394	+	0.916779i	$0.369220\pi$
$212$	55123.3	0.0842355
$213$	1.02192e6	1.54337
$214$	218282.	0.325824
$215$	−94206.6	−0.138991
$216$	307085.	0.447842
$217$	921929.	1.32907
$218$	−19253.6	−0.0274392
$219$	197054.	0.277635
$220$	21022.6	0.0292839
$221$	−119534.	−0.164631
$222$	−633578.	−0.862815
$223$	1.30708e6	1.76012	0.880058	−	0.474866i	$-0.157503\pi$
$223$	1.30708e6	1.76012	0.880058	+	0.474866i	$0.157503\pi$
$224$	125024.	0.166484
$225$	−1.19222e6	−1.57001
$226$	466214.	0.607176
$227$	1.11112e6	1.43119	0.715593	−	0.698517i	$-0.246156\pi$
$227$	1.11112e6	1.43119	0.715593	+	0.698517i	$0.246156\pi$
$228$	0	0
$229$	−824.381	−0.00103882	−0.000519409	−	1.00000i	$-0.500165\pi$
$229$	−824.381	−0.00103882	−0.000519409		1.00000i	$0.500165\pi$
$230$	304054.	0.378993
$231$	−225145.	−0.277608
$232$	355362.	0.433462
$233$	176542.	0.213039	0.106519	−	0.994311i	$-0.466029\pi$
$233$	176542.	0.213039	0.106519	+	0.994311i	$0.466029\pi$
$234$	925490.	1.10492
$235$	−97029.6	−0.114613
$236$	−837248.	−0.978529
$237$	1.07950e6	1.24839
$238$	108040.	0.123635
$239$	623861.	0.706469	0.353235	−	0.935535i	$-0.385082\pi$
$239$	623861.	0.706469	0.353235	+	0.935535i	$0.385082\pi$
$240$	122431.	0.137203
$241$	−695351.	−0.771190	−0.385595	−	0.922668i	$-0.626004\pi$
$241$	−695351.	−0.771190	−0.385595	+	0.922668i	$0.626004\pi$
$242$	623939.	0.684863
$243$	641169.	0.696557
$244$	−707720.	−0.761004
$245$	35077.1	0.0373343
$246$	2.11062e6	2.22368
$247$	0	0
$248$	483265.	0.498949
$249$	926287.	0.946776
$250$	−436331.	−0.441536
$251$	105883.	0.106082	0.0530408	−	0.998592i	$-0.483109\pi$
$251$	105883.	0.106082	0.0530408	+	0.998592i	$0.483109\pi$
$252$	−836495.	−0.829778
$253$	−293095.	−0.287877
$254$	−981625.	−0.954688
$255$	105799.	0.101890
$256$	65536.0	0.0625000
$257$	−235591.	−0.222498	−0.111249	−	0.993793i	$-0.535485\pi$
$257$	−235591.	−0.222498	−0.111249	+	0.993793i	$0.535485\pi$
$258$	528865.	0.494647
$259$	746457.	0.691441
$260$	159590.	0.146410
$261$	−2.37762e6	−2.16043
$262$	−452783.	−0.407509
$263$	−175828.	−0.156747	−0.0783734	−	0.996924i	$-0.524973\pi$
$263$	−175828.	−0.156747	−0.0783734	+	0.996924i	$0.524973\pi$
$264$	−118018.	−0.104217
$265$	−63597.4	−0.0556320
$266$	0	0
$267$	2.30799e6	1.98132
$268$	−1.04134e6	−0.885637
$269$	−212351.	−0.178926	−0.0894628	−	0.995990i	$-0.528515\pi$
$269$	−212351.	−0.178926	−0.0894628	+	0.995990i	$0.528515\pi$
$270$	−354293.	−0.295770
$271$	391655.	0.323952	0.161976	−	0.986795i	$-0.448213\pi$
$271$	391655.	0.323952	0.161976	+	0.986795i	$0.448213\pi$
$272$	56633.1	0.0464139
$273$	−1.70915e6	−1.38795
$274$	−788585.	−0.634559
$275$	198175.	0.158022
$276$	−1.70692e6	−1.34878
$277$	−2.04552e6	−1.60179	−0.800894	−	0.598807i	$-0.795642\pi$
$277$	−2.04552e6	−1.60179	−0.800894	+	0.598807i	$0.795642\pi$
$278$	−703728.	−0.546126
$279$	−3.23338e6	−2.48683
$280$	−144244.	−0.109952
$281$	1.62227e6	1.22562	0.612811	−	0.790230i	$-0.290039\pi$
$281$	1.62227e6	1.22562	0.612811	+	0.790230i	$0.290039\pi$
$282$	544713.	0.407891
$283$	1.76197e6	1.30777	0.653887	−	0.756592i	$-0.273137\pi$
$283$	1.76197e6	1.30777	0.653887	+	0.756592i	$0.273137\pi$
$284$	−631118.	−0.464317
$285$	0	0
$286$	−153838.	−0.111211
$287$	−2.48665e6	−1.78201
$288$	−438481.	−0.311509
$289$	−1.37092e6	−0.965532
$290$	−409992.	−0.286273
$291$	−433675.	−0.300215
$292$	−121696.	−0.0835258
$293$	−1.34969e6	−0.918471	−0.459236	−	0.888314i	$-0.651877\pi$
$293$	−1.34969e6	−0.918471	−0.459236	+	0.888314i	$0.651877\pi$
$294$	−196919.	−0.132867
$295$	965958.	0.646254
$296$	391284.	0.259575
$297$	341524.	0.224662
$298$	1.83109e6	1.19445
$299$	−2.22499e6	−1.43929
$300$	1.15413e6	0.740374
$301$	−623088.	−0.396399
$302$	−1.23915e6	−0.781820
$303$	2.27029e6	1.42061
$304$	0	0
$305$	816518.	0.502593
$306$	−378915.	−0.231333
$307$	1.95897e6	1.18627	0.593134	−	0.805104i	$-0.297891\pi$
$307$	1.95897e6	1.18627	0.593134	+	0.805104i	$0.297891\pi$
$308$	139045.	0.0835175
$309$	3.89124e6	2.31842
$310$	−557557.	−0.329522
$311$	759335.	0.445177	0.222588	−	0.974912i	$-0.428549\pi$
$311$	759335.	0.445177	0.222588	+	0.974912i	$0.428549\pi$
$312$	−895917.	−0.521052
$313$	−1.43385e6	−0.827260	−0.413630	−	0.910445i	$-0.635739\pi$
$313$	−1.43385e6	−0.827260	−0.413630	+	0.910445i	$0.635739\pi$
$314$	−284321.	−0.162737
$315$	965090.	0.548013
$316$	−666675.	−0.375575
$317$	−2.59644e6	−1.45121	−0.725605	−	0.688111i	$-0.758440\pi$
$317$	−2.59644e6	−1.45121	−0.725605	+	0.688111i	$0.758440\pi$
$318$	357028.	0.197986
$319$	395214.	0.217448
$320$	−75610.9	−0.0412771
$321$	1.41379e6	0.765812
$322$	2.01103e6	1.08088
$323$	0	0
$324$	324102.	0.171522
$325$	1.50441e6	0.790058
$326$	1.30736e6	0.681318
$327$	−124704.	−0.0644927
$328$	−1.30347e6	−0.668986
$329$	−641759.	−0.326876
$330$	136161.	0.0688286
$331$	−2.77156e6	−1.39044	−0.695222	−	0.718795i	$-0.744694\pi$
$331$	−2.77156e6	−1.39044	−0.695222	+	0.718795i	$0.744694\pi$
$332$	−572055.	−0.284835
$333$	−2.61796e6	−1.29376
$334$	−908130.	−0.445432
$335$	1.20143e6	0.584905
$336$	809766.	0.391301
$337$	−438916.	−0.210527	−0.105263	−	0.994444i	$-0.533569\pi$
$337$	−438916.	−0.210527	−0.105263	+	0.994444i	$0.533569\pi$
$338$	317339.	0.151088
$339$	3.01963e6	1.42710
$340$	−65339.4	−0.0306533
$341$	537461.	0.250300
$342$	0	0
$343$	2.28403e6	1.04825
$344$	−326616.	−0.148813
$345$	1.96933e6	0.890781
$346$	−1.40540e6	−0.631118
$347$	1.33693e6	0.596053	0.298027	−	0.954558i	$-0.403672\pi$
$347$	1.33693e6	0.596053	0.298027	+	0.954558i	$0.403672\pi$
$348$	2.30164e6	1.01880
$349$	1.62135e6	0.712546	0.356273	−	0.934382i	$-0.384047\pi$
$349$	1.62135e6	0.712546	0.356273	+	0.934382i	$0.384047\pi$
$350$	−1.35975e6	−0.593320
$351$	2.59262e6	1.12324
$352$	72885.6	0.0313534
$353$	−2.21858e6	−0.947627	−0.473813	−	0.880625i	$-0.657123\pi$
$353$	−2.21858e6	−0.947627	−0.473813	+	0.880625i	$0.657123\pi$
$354$	−5.42277e6	−2.29992
$355$	728140.	0.306651
$356$	−1.42536e6	−0.596075
$357$	699762.	0.290589
$358$	784551.	0.323529
$359$	1.20336e6	0.492785	0.246393	−	0.969170i	$-0.420755\pi$
$359$	1.20336e6	0.492785	0.246393	+	0.969170i	$0.420755\pi$
$360$	505889.	0.205731
$361$	0	0
$362$	1.26290e6	0.506521
$363$	4.04119e6	1.60969
$364$	1.05554e6	0.417560
$365$	140405.	0.0551632
$366$	−4.58384e6	−1.78865
$367$	−4.58889e6	−1.77845	−0.889226	−	0.457468i	$-0.848756\pi$
$367$	−4.58889e6	−1.77845	−0.889226	+	0.457468i	$0.848756\pi$
$368$	1.05416e6	0.405777
$369$	8.72114e6	3.33432
$370$	−451437.	−0.171432
$371$	−420637.	−0.158662
$372$	3.13006e6	1.17272
$373$	4.88969e6	1.81974	0.909870	−	0.414894i	$-0.136181\pi$
$373$	4.88969e6	1.81974	0.909870	+	0.414894i	$0.136181\pi$
$374$	62984.3	0.0232838
$375$	−2.82607e6	−1.03778
$376$	−336403.	−0.122713
$377$	3.00021e6	1.08717
$378$	−2.34332e6	−0.843532
$379$	−4.54801e6	−1.62639	−0.813193	−	0.581995i	$-0.802272\pi$
$379$	−4.54801e6	−1.62639	−0.813193	+	0.581995i	$0.802272\pi$
$380$	0	0
$381$	−6.35789e6	−2.24389
$382$	1.95695e6	0.686153
$383$	−1.45394e6	−0.506465	−0.253232	−	0.967405i	$-0.581494\pi$
$383$	−1.45394e6	−0.506465	−0.253232	+	0.967405i	$0.581494\pi$
$384$	424470.	0.146899
$385$	−160420.	−0.0551577
$386$	1.30135e6	0.444556
$387$	2.18529e6	0.741705
$388$	267829.	0.0903187
$389$	−1.46176e6	−0.489782	−0.244891	−	0.969551i	$-0.578752\pi$
$389$	−1.46176e6	−0.489782	−0.244891	+	0.969551i	$0.578752\pi$
$390$	1.03365e6	0.344121
$391$	910956.	0.301339
$392$	121613.	0.0399728
$393$	−2.93263e6	−0.957803
$394$	3.18820e6	1.03468
$395$	769163.	0.248042
$396$	−487656.	−0.156270
$397$	1.58654e6	0.505215	0.252607	−	0.967569i	$-0.418712\pi$
$397$	1.58654e6	0.505215	0.252607	+	0.967569i	$0.418712\pi$
$398$	−129525.	−0.0409870
$399$	0	0
$400$	−712765.	−0.222739
$401$	−3.79092e6	−1.17729	−0.588645	−	0.808392i	$-0.700338\pi$
$401$	−3.79092e6	−1.17729	−0.588645	+	0.808392i	$0.700338\pi$
$402$	−6.74466e6	−2.08159
$403$	4.08005e6	1.25142
$404$	−1.40208e6	−0.427387
$405$	−373927.	−0.113279
$406$	−2.71171e6	−0.816447
$407$	435165.	0.130217
$408$	366807.	0.109091
$409$	−2.71940e6	−0.803830	−0.401915	−	0.915677i	$-0.631655\pi$
$409$	−2.71940e6	−0.803830	−0.401915	+	0.915677i	$0.631655\pi$
$410$	1.50386e6	0.441821
$411$	−5.10759e6	−1.49146
$412$	−2.40315e6	−0.697489
$413$	6.38890e6	1.84311
$414$	−7.05307e6	−2.02245
$415$	659998.	0.188114
$416$	553300.	0.156757
$417$	−4.55798e6	−1.28361
$418$	0	0
$419$	−1.05626e6	−0.293924	−0.146962	−	0.989142i	$-0.546950\pi$
$419$	−1.05626e6	−0.293924	−0.146962	+	0.989142i	$0.546950\pi$
$420$	−934252.	−0.258429
$421$	526136.	0.144675	0.0723374	−	0.997380i	$-0.476954\pi$
$421$	526136.	0.144675	0.0723374	+	0.997380i	$0.476954\pi$
$422$	−2.06632e6	−0.564829
$423$	2.25077e6	0.611618
$424$	−220493.	−0.0595635
$425$	−615939.	−0.165411
$426$	−4.08769e6	−1.09132
$427$	5.40050e6	1.43339
$428$	−873126.	−0.230392
$429$	−996391.	−0.261389
$430$	376826.	0.0982811
$431$	6.54813e6	1.69795	0.848973	−	0.528436i	$-0.177222\pi$
$431$	6.54813e6	1.69795	0.848973	+	0.528436i	$0.177222\pi$
$432$	−1.22834e6	−0.316672
$433$	−61048.2	−0.0156478	−0.00782390	−	0.999969i	$-0.502490\pi$
$433$	−61048.2	−0.0156478	−0.00782390	+	0.999969i	$0.502490\pi$
$434$	−3.68771e6	−0.939795
$435$	−2.65548e6	−0.672852
$436$	77014.5	0.0194024
$437$	0	0
$438$	−788216.	−0.196318
$439$	−3.76181e6	−0.931614	−0.465807	−	0.884886i	$-0.654236\pi$
$439$	−3.76181e6	−0.931614	−0.465807	+	0.884886i	$0.654236\pi$
$440$	−84090.3	−0.0207069
$441$	−813674.	−0.199230
$442$	478136.	0.116411
$443$	−1.10697e6	−0.267995	−0.133997	−	0.990982i	$-0.542781\pi$
$443$	−1.10697e6	−0.267995	−0.133997	+	0.990982i	$0.542781\pi$
$444$	2.53431e6	0.610102
$445$	1.64448e6	0.393668
$446$	−5.22834e6	−1.24459
$447$	1.18598e7	2.80743
$448$	−500095.	−0.117722
$449$	3.95879e6	0.926717	0.463358	−	0.886171i	$-0.346644\pi$
$449$	3.95879e6	0.926717	0.463358	+	0.886171i	$0.346644\pi$
$450$	4.76890e6	1.11016
$451$	−1.44965e6	−0.335600
$452$	−1.86486e6	−0.429338
$453$	−8.02586e6	−1.83758
$454$	−4.44448e6	−1.01200
$455$	−1.21780e6	−0.275771
$456$	0	0
$457$	−4.54409e6	−1.01779	−0.508893	−	0.860830i	$-0.669945\pi$
$457$	−4.54409e6	−1.01779	−0.508893	+	0.860830i	$0.669945\pi$
$458$	3297.52	0.000734555 0
$459$	−1.06147e6	−0.235168
$460$	−1.21622e6	−0.267989
$461$	−758874.	−0.166310	−0.0831549	−	0.996537i	$-0.526500\pi$
$461$	−758874.	−0.166310	−0.0831549	+	0.996537i	$0.526500\pi$
$462$	900578.	0.196298
$463$	−2.57443e6	−0.558122	−0.279061	−	0.960273i	$-0.590023\pi$
$463$	−2.57443e6	−0.558122	−0.279061	+	0.960273i	$0.590023\pi$
$464$	−1.42145e6	−0.306504
$465$	−3.61124e6	−0.774505
$466$	−706169.	−0.150641
$467$	−8.06727e6	−1.71173	−0.855864	−	0.517201i	$-0.826974\pi$
$467$	−8.06727e6	−1.71173	−0.855864	+	0.517201i	$0.826974\pi$
$468$	−3.70196e6	−0.781299
$469$	7.94630e6	1.66814
$470$	388118.	0.0810437
$471$	−1.84152e6	−0.382494
$472$	3.34899e6	0.691925
$473$	−363244.	−0.0746528
$474$	−4.31799e6	−0.882746
$475$	0	0
$476$	−432158.	−0.0874230
$477$	1.47525e6	0.296873
$478$	−2.49545e6	−0.499549
$479$	1.33280e6	0.265416	0.132708	−	0.991155i	$-0.457633\pi$
$479$	1.33280e6	0.265416	0.132708	+	0.991155i	$0.457633\pi$
$480$	−489724.	−0.0970171
$481$	3.30349e6	0.651044
$482$	2.78141e6	0.545314
$483$	1.30253e7	2.54050
$484$	−2.49576e6	−0.484271
$485$	−309002.	−0.0596495
$486$	−2.56468e6	−0.492541
$487$	8.10239e6	1.54807	0.774035	−	0.633142i	$-0.218235\pi$
$487$	8.10239e6	1.54807	0.774035	+	0.633142i	$0.218235\pi$
$488$	2.83088e6	0.538111
$489$	8.46762e6	1.60136
$490$	−140308.	−0.0263994
$491$	−6.47606e6	−1.21229	−0.606146	−	0.795354i	$-0.707285\pi$
$491$	−6.47606e6	−1.21229	−0.606146	+	0.795354i	$0.707285\pi$
$492$	−8.44247e6	−1.57238
$493$	−1.22835e6	−0.227617
$494$	0	0
$495$	562623.	0.103206
$496$	−1.93306e6	−0.352810
$497$	4.81596e6	0.874564
$498$	−3.70515e6	−0.669472
$499$	2.05069e6	0.368680	0.184340	−	0.982863i	$-0.440985\pi$
$499$	2.05069e6	0.368680	0.184340	+	0.982863i	$0.440985\pi$
$500$	1.74532e6	0.312213
$501$	−5.88187e6	−1.04694
$502$	−423530.	−0.0750111
$503$	−2.64774e6	−0.466611	−0.233305	−	0.972404i	$-0.574954\pi$
$503$	−2.64774e6	−0.466611	−0.233305	+	0.972404i	$0.574954\pi$
$504$	3.34598e6	0.586742
$505$	1.61763e6	0.282260
$506$	1.17238e6	0.203560
$507$	2.05537e6	0.355116
$508$	3.92650e6	0.675066
$509$	6.89163e6	1.17904	0.589519	−	0.807755i	$-0.299318\pi$
$509$	6.89163e6	1.17904	0.589519	+	0.807755i	$0.299318\pi$
$510$	−423197.	−0.0720472
$511$	928645.	0.157325
$512$	−262144.	−0.0441942
$513$	0	0
$514$	942366.	0.157330
$515$	2.77258e6	0.460645
$516$	−2.11546e6	−0.349768
$517$	−374129.	−0.0615596
$518$	−2.98583e6	−0.488923
$519$	−9.10266e6	−1.48337
$520$	−638358.	−0.103528
$521$	−7.60601e6	−1.22762	−0.613808	−	0.789456i	$-0.710363\pi$
$521$	−7.60601e6	−1.22762	−0.613808	+	0.789456i	$0.710363\pi$
$522$	9.51047e6	1.52766
$523$	8.18896e6	1.30911	0.654553	−	0.756016i	$-0.272857\pi$
$523$	8.18896e6	1.30911	0.654553	+	0.756016i	$0.272857\pi$
$524$	1.81113e6	0.288152
$525$	−8.80697e6	−1.39453
$526$	703312.	0.110837
$527$	−1.67046e6	−0.262005
$528$	472073.	0.0736927
$529$	1.05201e7	1.63448
$530$	254389.	0.0393377
$531$	−2.24071e7	−3.44865
$532$	0	0
$533$	−1.10048e7	−1.67789
$534$	−9.23194e6	−1.40101
$535$	1.00735e6	0.152159
$536$	4.16536e6	0.626240
$537$	5.08146e6	0.760419
$538$	849402.	0.126520
$539$	135251.	0.0200525
$540$	1.41717e6	0.209141
$541$	−6.30982e6	−0.926881	−0.463441	−	0.886128i	$-0.653385\pi$
$541$	−6.30982e6	−0.926881	−0.463441	+	0.886128i	$0.653385\pi$
$542$	−1.56662e6	−0.229068
$543$	8.17968e6	1.19052
$544$	−226533.	−0.0328196
$545$	−88853.9	−0.0128140
$546$	6.83660e6	0.981428
$547$	−7.15032e6	−1.02178	−0.510889	−	0.859646i	$-0.670684\pi$
$547$	−7.15032e6	−1.02178	−0.510889	+	0.859646i	$0.670684\pi$
$548$	3.15434e6	0.448701
$549$	−1.89406e7	−2.68202
$550$	−792700.	−0.111738
$551$	0	0
$552$	6.82770e6	0.953733
$553$	5.08729e6	0.707414
$554$	8.18209e6	1.13263
$555$	−2.92391e6	−0.402932
$556$	2.81491e6	0.386170
$557$	5.92866e6	0.809690	0.404845	−	0.914385i	$-0.367325\pi$
$557$	5.92866e6	0.809690	0.404845	+	0.914385i	$0.367325\pi$
$558$	1.29335e7	1.75845
$559$	−2.75751e6	−0.373240
$560$	576974.	0.0777475
$561$	407944.	0.0547259
$562$	−6.48906e6	−0.866645
$563$	−8.71198e6	−1.15837	−0.579183	−	0.815197i	$-0.696628\pi$
$563$	−8.71198e6	−1.15837	−0.579183	+	0.815197i	$0.696628\pi$
$564$	−2.17885e6	−0.288423
$565$	2.15154e6	0.283549
$566$	−7.04789e6	−0.924736
$567$	−2.47317e6	−0.323070
$568$	2.52447e6	0.328322
$569$	−8.64609e6	−1.11954	−0.559769	−	0.828648i	$-0.689110\pi$
$569$	−8.64609e6	−1.11954	−0.559769	+	0.828648i	$0.689110\pi$
$570$	0	0
$571$	4.32709e6	0.555399	0.277700	−	0.960668i	$-0.410428\pi$
$571$	4.32709e6	0.555399	0.277700	+	0.960668i	$0.410428\pi$
$572$	615350.	0.0786380
$573$	1.26750e7	1.61273
$574$	9.94659e6	1.26007
$575$	−1.14650e7	−1.44612
$576$	1.75393e6	0.220270
$577$	1.18236e7	1.47846	0.739232	−	0.673451i	$-0.235189\pi$
$577$	1.18236e7	1.47846	0.739232	+	0.673451i	$0.235189\pi$
$578$	5.48367e6	0.682734
$579$	8.42873e6	1.04488
$580$	1.63997e6	0.202425
$581$	4.36526e6	0.536500
$582$	1.73470e6	0.212284
$583$	−245221.	−0.0298803
$584$	486786.	0.0590617
$585$	4.27106e6	0.515996
$586$	5.39877e6	0.649457
$587$	1.30732e7	1.56599	0.782994	−	0.622030i	$-0.213692\pi$
$587$	1.30732e7	1.56599	0.782994	+	0.622030i	$0.213692\pi$
$588$	787675.	0.0939515
$589$	0	0
$590$	−3.86383e6	−0.456970
$591$	2.06497e7	2.43189
$592$	−1.56514e6	−0.183547
$593$	−9.12173e6	−1.06522	−0.532612	−	0.846360i	$-0.678789\pi$
$593$	−9.12173e6	−1.06522	−0.532612	+	0.846360i	$0.678789\pi$
$594$	−1.36610e6	−0.158860
$595$	498594.	0.0577371
$596$	−7.32436e6	−0.844606
$597$	−838921.	−0.0963352
$598$	8.89995e6	1.01773
$599$	−1.30345e6	−0.148432	−0.0742161	−	0.997242i	$-0.523645\pi$
$599$	−1.30345e6	−0.148432	−0.0742161	+	0.997242i	$0.523645\pi$
$600$	−4.61651e6	−0.523523
$601$	−1.63545e7	−1.84693	−0.923465	−	0.383682i	$-0.874656\pi$
$601$	−1.63545e7	−1.84693	−0.923465	+	0.383682i	$0.874656\pi$
$602$	2.49235e6	0.280297
$603$	−2.78692e7	−3.12127
$604$	4.95660e6	0.552830
$605$	2.87943e6	0.319829
$606$	−9.08117e6	−1.00452
$607$	7.38027e6	0.813019	0.406509	−	0.913647i	$-0.366746\pi$
$607$	7.38027e6	0.813019	0.406509	+	0.913647i	$0.366746\pi$
$608$	0	0
$609$	−1.75635e7	−1.91897
$610$	−3.26607e6	−0.355387
$611$	−2.84014e6	−0.307778
$612$	1.51566e6	0.163577
$613$	9.34721e6	1.00469	0.502344	−	0.864668i	$-0.332471\pi$
$613$	9.34721e6	1.00469	0.502344	+	0.864668i	$0.332471\pi$
$614$	−7.83589e6	−0.838818
$615$	9.74033e6	1.03845
$616$	−556178.	−0.0590558
$617$	3.60578e6	0.381317	0.190659	−	0.981656i	$-0.438938\pi$
$617$	3.60578e6	0.381317	0.190659	+	0.981656i	$0.438938\pi$
$618$	−1.55650e7	−1.63937
$619$	−1.50621e7	−1.58001	−0.790004	−	0.613102i	$-0.789922\pi$
$619$	−1.50621e7	−1.58001	−0.790004	+	0.613102i	$0.789922\pi$
$620$	2.23023e6	0.233008
$621$	−1.97581e7	−2.05597
$622$	−3.03734e6	−0.314788
$623$	1.08767e7	1.12274
$624$	3.58367e6	0.368440
$625$	6.68712e6	0.684761
$626$	5.73539e6	0.584961
$627$	0	0
$628$	1.13729e6	0.115072
$629$	−1.35252e6	−0.136307
$630$	−3.86036e6	−0.387504
$631$	−1.16729e7	−1.16710	−0.583548	−	0.812079i	$-0.698336\pi$
$631$	−1.16729e7	−1.16710	−0.583548	+	0.812079i	$0.698336\pi$
$632$	2.66670e6	0.265572
$633$	−1.33834e7	−1.32757
$634$	1.03858e7	1.02616
$635$	−4.53012e6	−0.445837
$636$	−1.42811e6	−0.139997
$637$	1.02674e6	0.100256
$638$	−1.58086e6	−0.153759
$639$	−1.68905e7	−1.63640
$640$	302443.	0.0291873
$641$	3.49062e6	0.335551	0.167775	−	0.985825i	$-0.446342\pi$
$641$	3.49062e6	0.335551	0.167775	+	0.985825i	$0.446342\pi$
$642$	−5.65516e6	−0.541511
$643$	1.66826e7	1.59124	0.795622	−	0.605793i	$-0.207144\pi$
$643$	1.66826e7	1.59124	0.795622	+	0.605793i	$0.207144\pi$
$644$	−8.04413e6	−0.764301
$645$	2.44067e6	0.230999
$646$	0	0
$647$	6.00141e6	0.563628	0.281814	−	0.959469i	$-0.409064\pi$
$647$	6.00141e6	0.563628	0.281814	+	0.959469i	$0.409064\pi$
$648$	−1.29641e6	−0.121284
$649$	3.72457e6	0.347108
$650$	−6.01765e6	−0.558655
$651$	−2.38850e7	−2.20888
$652$	−5.22943e6	−0.481765
$653$	−7.27603e6	−0.667746	−0.333873	−	0.942618i	$-0.608356\pi$
$653$	−7.27603e6	−0.667746	−0.333873	+	0.942618i	$0.608356\pi$
$654$	498815.	0.0456032
$655$	−2.08956e6	−0.190305
$656$	5.21389e6	0.473045
$657$	−3.25693e6	−0.294371
$658$	2.56704e6	0.231136
$659$	1.88665e7	1.69230	0.846151	−	0.532943i	$-0.178914\pi$
$659$	1.88665e7	1.69230	0.846151	+	0.532943i	$0.178914\pi$
$660$	−544645.	−0.0486691
$661$	1.74053e7	1.54945	0.774725	−	0.632299i	$-0.217889\pi$
$661$	1.74053e7	1.54945	0.774725	+	0.632299i	$0.217889\pi$
$662$	1.10862e7	0.983193
$663$	3.09684e6	0.273612
$664$	2.28822e6	0.201409
$665$	0	0
$666$	1.04719e7	0.914825
$667$	−2.28643e7	−1.98995
$668$	3.63252e6	0.314968
$669$	−3.38634e7	−2.92527
$670$	−4.80570e6	−0.413590
$671$	3.14835e6	0.269946
$672$	−3.23906e6	−0.276692
$673$	7.04986e6	0.599988	0.299994	−	0.953941i	$-0.403015\pi$
$673$	7.04986e6	0.599988	0.299994	+	0.953941i	$0.403015\pi$
$674$	1.75567e6	0.148865
$675$	1.33594e7	1.12856
$676$	−1.26935e6	−0.106836
$677$	1.14595e7	0.960934	0.480467	−	0.877013i	$-0.340467\pi$
$677$	1.14595e7	0.960934	0.480467	+	0.877013i	$0.340467\pi$
$678$	−1.20785e7	−1.00911
$679$	−2.04376e6	−0.170120
$680$	261357.	0.0216752
$681$	−2.87865e7	−2.37860
$682$	−2.14984e6	−0.176989
$683$	6.01391e6	0.493294	0.246647	−	0.969105i	$-0.420671\pi$
$683$	6.01391e6	0.493294	0.246647	+	0.969105i	$0.420671\pi$
$684$	0	0
$685$	−3.63926e6	−0.296337
$686$	−9.13610e6	−0.741226
$687$	21357.7	0.00172649
$688$	1.30646e6	0.105227
$689$	−1.86155e6	−0.149392
$690$	−7.87732e6	−0.629877
$691$	−2.04132e7	−1.62636	−0.813180	−	0.582012i	$-0.802266\pi$
$691$	−2.04132e7	−1.62636	−0.813180	+	0.582012i	$0.802266\pi$
$692$	5.62161e6	0.446268
$693$	3.72122e6	0.294342
$694$	−5.34772e6	−0.421473
$695$	−3.24765e6	−0.255039
$696$	−9.20658e6	−0.720403
$697$	4.50560e6	0.351294
$698$	−6.48539e6	−0.503846
$699$	−4.57379e6	−0.354065
$700$	5.43900e6	0.419540
$701$	1.12414e6	0.0864024	0.0432012	−	0.999066i	$-0.486244\pi$
$701$	1.12414e6	0.0864024	0.0432012	+	0.999066i	$0.486244\pi$
$702$	−1.03705e7	−0.794249
$703$	0	0
$704$	−291543.	−0.0221702
$705$	2.51380e6	0.190484
$706$	8.87430e6	0.670073
$707$	1.06991e7	0.805004
$708$	2.16911e7	1.62629
$709$	−6.99935e6	−0.522928	−0.261464	−	0.965213i	$-0.584205\pi$
$709$	−6.99935e6	−0.522928	−0.261464	+	0.965213i	$0.584205\pi$
$710$	−2.91256e6	−0.216835
$711$	−1.78421e7	−1.32365
$712$	5.70145e6	0.421488
$713$	−3.10937e7	−2.29059
$714$	−2.79905e6	−0.205478
$715$	−709948.	−0.0519352
$716$	−3.13820e6	−0.228770
$717$	−1.61628e7	−1.17413
$718$	−4.81342e6	−0.348452
$719$	5.91241e6	0.426523	0.213261	−	0.976995i	$-0.431591\pi$
$719$	5.91241e6	0.426523	0.213261	+	0.976995i	$0.431591\pi$
$720$	−2.02356e6	−0.145474
$721$	1.83380e7	1.31376
$722$	0	0
$723$	1.80149e7	1.28170
$724$	−5.05160e6	−0.358164
$725$	1.54596e7	1.09233
$726$	−1.61648e7	−1.13822
$727$	−4.72221e6	−0.331367	−0.165684	−	0.986179i	$-0.552983\pi$
$727$	−4.72221e6	−0.331367	−0.165684	+	0.986179i	$0.552983\pi$
$728$	−4.22214e6	−0.295260
$729$	−2.15335e7	−1.50070
$730$	−561619.	−0.0390063
$731$	1.12898e6	0.0781438
$732$	1.83353e7	1.26477
$733$	−140043.	−0.00962721	−0.00481360	−	0.999988i	$-0.501532\pi$
$733$	−140043.	−0.00962721	−0.00481360	+	0.999988i	$0.501532\pi$
$734$	1.83555e7	1.25756
$735$	−908764.	−0.0620487
$736$	−4.21664e6	−0.286928
$737$	4.63249e6	0.314156
$738$	−3.48846e7	−2.35772
$739$	6.33856e6	0.426953	0.213476	−	0.976948i	$-0.431521\pi$
$739$	6.33856e6	0.426953	0.213476	+	0.976948i	$0.431521\pi$
$740$	1.80575e6	0.121221
$741$	0	0
$742$	1.68255e6	0.112191
$743$	−5.14618e6	−0.341990	−0.170995	−	0.985272i	$-0.554698\pi$
$743$	−5.14618e6	−0.341990	−0.170995	+	0.985272i	$0.554698\pi$
$744$	−1.25202e7	−0.829240
$745$	8.45033e6	0.557806
$746$	−1.95588e7	−1.28675
$747$	−1.53098e7	−1.00385
$748$	−251937.	−0.0164641
$749$	6.66269e6	0.433955
$750$	1.13043e7	0.733821
$751$	2.29378e7	1.48406	0.742032	−	0.670365i	$-0.233862\pi$
$751$	2.29378e7	1.48406	0.742032	+	0.670365i	$0.233862\pi$
$752$	1.34561e6	0.0867711
$753$	−2.74317e6	−0.176305
$754$	−1.20008e7	−0.768746
$755$	−5.71858e6	−0.365108
$756$	9.37327e6	0.596467
$757$	−2.64001e6	−0.167442	−0.0837211	−	0.996489i	$-0.526680\pi$
$757$	−2.64001e6	−0.167442	−0.0837211	+	0.996489i	$0.526680\pi$
$758$	1.81920e7	1.15003
$759$	7.59340e6	0.478445
$760$	0	0
$761$	−2.07364e7	−1.29799	−0.648997	−	0.760791i	$-0.724811\pi$
$761$	−2.07364e7	−1.29799	−0.648997	+	0.760791i	$0.724811\pi$
$762$	2.54316e7	1.58667
$763$	−587685.	−0.0365454
$764$	−7.82780e6	−0.485184
$765$	−1.74866e6	−0.108032
$766$	5.81576e6	0.358125
$767$	2.82745e7	1.73543
$768$	−1.69788e6	−0.103873
$769$	6.34499e6	0.386915	0.193457	−	0.981109i	$-0.438030\pi$
$769$	6.34499e6	0.386915	0.193457	+	0.981109i	$0.438030\pi$
$770$	641680.	0.0390024
$771$	6.10361e6	0.369787
$772$	−5.20541e6	−0.314348
$773$	−2.63780e7	−1.58779	−0.793896	−	0.608054i	$-0.791950\pi$
$773$	−2.63780e7	−1.58779	−0.793896	+	0.608054i	$0.791950\pi$
$774$	−8.74115e6	−0.524464
$775$	2.10238e7	1.25735
$776$	−1.07131e6	−0.0638650
$777$	−1.93389e7	−1.14916
$778$	5.84705e6	0.346328
$779$	0	0
$780$	−4.13459e6	−0.243330
$781$	2.80758e6	0.164704
$782$	−3.64383e6	−0.213079
$783$	2.66422e7	1.55298
$784$	−486451.	−0.0282650
$785$	−1.31212e6	−0.0759975
$786$	1.17305e7	0.677269
$787$	−4.97864e6	−0.286533	−0.143266	−	0.989684i	$-0.545761\pi$
$787$	−4.97864e6	−0.286533	−0.143266	+	0.989684i	$0.545761\pi$
$788$	−1.27528e7	−0.731627
$789$	4.55528e6	0.260509
$790$	−3.07665e6	−0.175392
$791$	1.42304e7	0.808680
$792$	1.95062e6	0.110499
$793$	2.39002e7	1.34964
$794$	−6.34618e6	−0.357241
$795$	1.64766e6	0.0924589
$796$	518100.	0.0289822
$797$	7.99224e6	0.445680	0.222840	−	0.974855i	$-0.428467\pi$
$797$	7.99224e6	0.445680	0.222840	+	0.974855i	$0.428467\pi$
$798$	0	0
$799$	1.16282e6	0.0644382
$800$	2.85106e6	0.157500
$801$	−3.81467e7	−2.10076
$802$	1.51637e7	0.832470
$803$	541377.	0.0296286
$804$	2.69787e7	1.47191
$805$	9.28075e6	0.504770
$806$	−1.63202e7	−0.884887
$807$	5.50150e6	0.297370
$808$	5.60834e6	0.302208
$809$	1.16824e6	0.0627570	0.0313785	−	0.999508i	$-0.490010\pi$
$809$	1.16824e6	0.0627570	0.0313785	+	0.999508i	$0.490010\pi$
$810$	1.49571e6	0.0801003
$811$	3.38432e7	1.80684	0.903419	−	0.428759i	$-0.141049\pi$
$811$	3.38432e7	1.80684	0.903419	+	0.428759i	$0.141049\pi$
$812$	1.08468e7	0.577315
$813$	−1.01468e7	−0.538399
$814$	−1.74066e6	−0.0920775
$815$	6.03335e6	0.318174
$816$	−1.46723e6	−0.0771388
$817$	0	0
$818$	1.08776e7	0.568394
$819$	2.82491e7	1.47161
$820$	−6.01542e6	−0.312415
$821$	1.33014e7	0.688717	0.344358	−	0.938838i	$-0.388096\pi$
$821$	1.33014e7	0.688717	0.344358	+	0.938838i	$0.388096\pi$
$822$	2.04304e7	1.05462
$823$	2.19124e7	1.12769	0.563845	−	0.825881i	$-0.309322\pi$
$823$	2.19124e7	1.12769	0.563845	+	0.825881i	$0.309322\pi$
$824$	9.61259e6	0.493199
$825$	−5.13424e6	−0.262628
$826$	−2.55556e7	−1.30327
$827$	−2.56042e7	−1.30181	−0.650905	−	0.759159i	$-0.725610\pi$
$827$	−2.56042e7	−1.30181	−0.650905	+	0.759159i	$0.725610\pi$
$828$	2.82123e7	1.43009
$829$	−1.19693e6	−0.0604900	−0.0302450	−	0.999543i	$-0.509629\pi$
$829$	−1.19693e6	−0.0604900	−0.0302450	+	0.999543i	$0.509629\pi$
$830$	−2.63999e6	−0.133017
$831$	5.29946e7	2.66213
$832$	−2.21320e6	−0.110844
$833$	−420368.	−0.0209903
$834$	1.82319e7	0.907648
$835$	−4.19095e6	−0.208016
$836$	0	0
$837$	3.62313e7	1.78760
$838$	4.22504e6	0.207836
$839$	3.43410e7	1.68426	0.842129	−	0.539276i	$-0.181302\pi$
$839$	3.43410e7	1.68426	0.842129	+	0.539276i	$0.181302\pi$
$840$	3.73701e6	0.182737
$841$	1.03194e7	0.503114
$842$	−2.10454e6	−0.102301
$843$	−4.20290e7	−2.03695
$844$	8.26529e6	0.399394
$845$	1.46449e6	0.0705578
$846$	−9.00308e6	−0.432479
$847$	1.90447e7	0.912149
$848$	881972.	0.0421178
$849$	−4.56485e7	−2.17349
$850$	2.46375e6	0.116963
$851$	−2.51756e7	−1.19167
$852$	1.63508e7	0.771683
$853$	1.55326e7	0.730922	0.365461	−	0.930827i	$-0.380911\pi$
$853$	1.55326e7	0.730922	0.365461	+	0.930827i	$0.380911\pi$
$854$	−2.16020e7	−1.01356
$855$	0	0
$856$	3.49251e6	0.162912
$857$	−1.00267e7	−0.466342	−0.233171	−	0.972436i	$-0.574910\pi$
$857$	−1.00267e7	−0.466342	−0.233171	+	0.972436i	$0.574910\pi$
$858$	3.98556e6	0.184830
$859$	4.30238e6	0.198942	0.0994709	−	0.995040i	$-0.468285\pi$
$859$	4.30238e6	0.198942	0.0994709	+	0.995040i	$0.468285\pi$
$860$	−1.50731e6	−0.0694953
$861$	6.44231e7	2.96165
$862$	−2.61925e7	−1.20063
$863$	171879.	0.00785589	0.00392794	−	0.999992i	$-0.498750\pi$
$863$	171879.	0.00785589	0.00392794	+	0.999992i	$0.498750\pi$
$864$	4.91336e6	0.223921
$865$	−6.48582e6	−0.294730
$866$	244193.	0.0110647
$867$	3.55172e7	1.60469
$868$	1.47509e7	0.664535
$869$	2.96576e6	0.133225
$870$	1.06219e7	0.475778
$871$	3.51668e7	1.57068
$872$	−308058.	−0.0137196
$873$	7.16784e6	0.318312
$874$	0	0
$875$	−1.33183e7	−0.588068
$876$	3.15286e6	0.138818
$877$	−1.89873e7	−0.833610	−0.416805	−	0.908996i	$-0.636850\pi$
$877$	−1.89873e7	−0.833610	−0.416805	+	0.908996i	$0.636850\pi$
$878$	1.50473e7	0.658751
$879$	3.49673e7	1.52648
$880$	336361.	0.0146420
$881$	3.54928e7	1.54064	0.770320	−	0.637658i	$-0.220097\pi$
$881$	3.54928e7	1.54064	0.770320	+	0.637658i	$0.220097\pi$
$882$	3.25470e6	0.140877
$883$	4.40043e6	0.189930	0.0949649	−	0.995481i	$-0.469726\pi$
$883$	4.40043e6	0.189930	0.0949649	+	0.995481i	$0.469726\pi$
$884$	−1.91254e6	−0.0823153
$885$	−2.50257e7	−1.07406
$886$	4.42788e6	0.189501
$887$	2.12356e7	0.906265	0.453132	−	0.891443i	$-0.350306\pi$
$887$	2.12356e7	0.906265	0.453132	+	0.891443i	$0.350306\pi$
$888$	−1.01372e7	−0.431407
$889$	−2.99625e7	−1.27152
$890$	−6.57794e6	−0.278365
$891$	−1.44180e6	−0.0608429
$892$	2.09133e7	0.880058
$893$	0	0
$894$	−4.74392e7	−1.98515
$895$	3.62064e6	0.151087
$896$	2.00038e6	0.0832419
$897$	5.76441e7	2.39207
$898$	−1.58352e7	−0.655288
$899$	4.19272e7	1.73020
$900$	−1.90756e7	−0.785004
$901$	762159.	0.0312776
$902$	5.79861e6	0.237305
$903$	1.61427e7	0.658806
$904$	7.45943e6	0.303588
$905$	5.82818e6	0.236544
$906$	3.21034e7	1.29936
$907$	−2.06632e7	−0.834026	−0.417013	−	0.908901i	$-0.636923\pi$
$907$	−2.06632e7	−0.834026	−0.417013	+	0.908901i	$0.636923\pi$
$908$	1.77779e7	0.715593
$909$	−3.75237e7	−1.50625
$910$	4.87121e6	0.194999
$911$	2.41650e7	0.964695	0.482348	−	0.875980i	$-0.339784\pi$
$911$	2.41650e7	0.964695	0.482348	+	0.875980i	$0.339784\pi$
$912$	0	0
$913$	2.54484e6	0.101038
$914$	1.81763e7	0.719683
$915$	−2.11540e7	−0.835296
$916$	−13190.1	−0.000519409 0
$917$	−1.38205e7	−0.542749
$918$	4.24590e6	0.166289
$919$	3.18213e7	1.24288	0.621440	−	0.783462i	$-0.286548\pi$
$919$	3.18213e7	1.24288	0.621440	+	0.783462i	$0.286548\pi$
$920$	4.86487e6	0.189497
$921$	−5.07523e7	−1.97155
$922$	3.03550e6	0.117599
$923$	2.13133e7	0.823468
$924$	−3.60231e6	−0.138804
$925$	1.70223e7	0.654131
$926$	1.02977e7	0.394652
$927$	−6.43149e7	−2.45817
$928$	5.68579e6	0.216731
$929$	−2.24224e7	−0.852399	−0.426200	−	0.904629i	$-0.640148\pi$
$929$	−2.24224e7	−0.852399	−0.426200	+	0.904629i	$0.640148\pi$
$930$	1.44450e7	0.547658
$931$	0	0
$932$	2.82468e6	0.106519
$933$	−1.96726e7	−0.739873
$934$	3.22691e7	1.21037
$935$	290668.	0.0108735
$936$	1.48078e7	0.552462
$937$	1.88888e7	0.702840	0.351420	−	0.936218i	$-0.385699\pi$
$937$	1.88888e7	0.702840	0.351420	+	0.936218i	$0.385699\pi$
$938$	−3.17852e7	−1.17955
$939$	3.71476e7	1.37489
$940$	−1.55247e6	−0.0573066
$941$	−2.67683e7	−0.985479	−0.492739	−	0.870177i	$-0.664004\pi$
$941$	−2.67683e7	−0.985479	−0.492739	+	0.870177i	$0.664004\pi$
$942$	7.36609e6	0.270464
$943$	8.38666e7	3.07121
$944$	−1.33960e7	−0.489265
$945$	−1.08142e7	−0.393927
$946$	1.45298e6	0.0527875
$947$	−3.03008e7	−1.09794	−0.548970	−	0.835842i	$-0.684980\pi$
$947$	−3.03008e7	−1.09794	−0.548970	+	0.835842i	$0.684980\pi$
$948$	1.72720e7	0.624196
$949$	4.10978e6	0.148133
$950$	0	0
$951$	6.72676e7	2.41187
$952$	1.72863e6	0.0618174
$953$	−3.57788e7	−1.27612	−0.638062	−	0.769985i	$-0.720264\pi$
$953$	−3.57788e7	−1.27612	−0.638062	+	0.769985i	$0.720264\pi$
$954$	−5.90101e6	−0.209921
$955$	9.03117e6	0.320432
$956$	9.98178e6	0.353235
$957$	−1.02391e7	−0.361394
$958$	−5.33120e6	−0.187677
$959$	−2.40703e7	−0.845151
$960$	1.95890e6	0.0686015
$961$	2.83886e7	0.991598
$962$	−1.32140e7	−0.460358
$963$	−2.33673e7	−0.811975
$964$	−1.11256e7	−0.385595
$965$	6.00563e6	0.207606
$966$	−5.21011e7	−1.79640
$967$	1.82420e7	0.627344	0.313672	−	0.949531i	$-0.398441\pi$
$967$	1.82420e7	0.627344	0.313672	+	0.949531i	$0.398441\pi$
$968$	9.98303e6	0.342432
$969$	0	0
$970$	1.23601e6	0.0421786
$971$	−3.70969e7	−1.26267	−0.631335	−	0.775510i	$-0.717493\pi$
$971$	−3.70969e7	−1.26267	−0.631335	+	0.775510i	$0.717493\pi$
$972$	1.02587e7	0.348279
$973$	−2.14802e7	−0.727370
$974$	−3.24096e7	−1.09465
$975$	−3.89758e7	−1.31306
$976$	−1.13235e7	−0.380502
$977$	−1.04825e7	−0.351340	−0.175670	−	0.984449i	$-0.556209\pi$
$977$	−1.04825e7	−0.351340	−0.175670	+	0.984449i	$0.556209\pi$
$978$	−3.38705e7	−1.13233
$979$	6.34085e6	0.211442
$980$	561234.	0.0186672
$981$	2.06112e6	0.0683803
$982$	2.59042e7	0.857219
$983$	3.18862e6	0.105249	0.0526245	−	0.998614i	$-0.483241\pi$
$983$	3.18862e6	0.105249	0.0526245	+	0.998614i	$0.483241\pi$
$984$	3.37699e7	1.11184
$985$	1.47133e7	0.483191
$986$	4.91339e6	0.160949
$987$	1.66265e7	0.543259
$988$	0	0
$989$	2.10147e7	0.683177
$990$	−2.25049e6	−0.0729776
$991$	−4.23419e7	−1.36958	−0.684789	−	0.728742i	$-0.740106\pi$
$991$	−4.23419e7	−1.36958	−0.684789	+	0.728742i	$0.740106\pi$
$992$	7.73223e6	0.249474
$993$	7.18044e7	2.31088
$994$	−1.92638e7	−0.618410
$995$	−597747.	−0.0191408
$996$	1.48206e7	0.473388
$997$	1.52691e7	0.486492	0.243246	−	0.969965i	$-0.421788\pi$
$997$	1.52691e7	0.486492	0.243246	+	0.969965i	$0.421788\pi$
$998$	−8.20277e6	−0.260696
$999$	2.93354e7	0.929989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.q.1.2		15
19.3	odd	18		38.6.e.b.9.5	✓	30
19.13	odd	18		38.6.e.b.17.5	yes	30
19.18	odd	2		722.6.a.r.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.9.5	✓	30	19.3	odd	18
38.6.e.b.17.5	yes	30	19.13	odd	18
722.6.a.q.1.2		15	1.1	even	1	trivial
722.6.a.r.1.14		15	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -25.9076 q^{3} +16.0000 q^{4} -18.4597 q^{5} +103.630 q^{6} -122.093 q^{7} -64.0000 q^{8} +428.205 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -25.9076 q^{3} +16.0000 q^{4} -18.4597 q^{5} +103.630 q^{6} -122.093 q^{7} -64.0000 q^{8} +428.205 q^{9} +73.8387 q^{10} -71.1774 q^{11} -414.522 q^{12} -540.332 q^{13} +488.374 q^{14} +478.246 q^{15} +256.000 q^{16} +221.223 q^{17} -1712.82 q^{18} -295.355 q^{20} +3163.15 q^{21} +284.709 q^{22} +4117.82 q^{23} +1658.09 q^{24} -2784.24 q^{25} +2161.33 q^{26} -4798.21 q^{27} -1953.49 q^{28} -5552.53 q^{29} -1912.99 q^{30} -7551.01 q^{31} -1024.00 q^{32} +1844.04 q^{33} -884.893 q^{34} +2253.81 q^{35} +6851.27 q^{36} -6113.82 q^{37} +13998.7 q^{39} +1181.42 q^{40} +20366.8 q^{41} -12652.6 q^{42} +5103.37 q^{43} -1138.84 q^{44} -7904.52 q^{45} -16471.3 q^{46} +5256.30 q^{47} -6632.35 q^{48} -1900.20 q^{49} +11137.0 q^{50} -5731.37 q^{51} -8645.31 q^{52} +3445.20 q^{53} +19192.8 q^{54} +1313.91 q^{55} +7813.98 q^{56} +22210.1 q^{58} -52328.0 q^{59} +7651.94 q^{60} -44232.5 q^{61} +30204.0 q^{62} -52280.9 q^{63} +4096.00 q^{64} +9974.35 q^{65} -7376.14 q^{66} -65083.8 q^{67} +3539.57 q^{68} -106683. q^{69} -9015.22 q^{70} -39444.9 q^{71} -27405.1 q^{72} -7606.02 q^{73} +24455.3 q^{74} +72133.0 q^{75} +8690.29 q^{77} -55994.8 q^{78} -41667.2 q^{79} -4725.68 q^{80} +20256.4 q^{81} -81467.0 q^{82} -35753.5 q^{83} +50610.4 q^{84} -4083.71 q^{85} -20413.5 q^{86} +143853. q^{87} +4555.35 q^{88} -89085.2 q^{89} +31618.1 q^{90} +65970.9 q^{91} +65885.1 q^{92} +195629. q^{93} -21025.2 q^{94} +26529.4 q^{96} +16739.3 q^{97} +7600.80 q^{98} -30478.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9} - 432 q^{10} + 126 q^{11} + 114 q^{13} - 336 q^{14} + 3840 q^{16} + 4119 q^{17} - 8508 q^{18} + 1728 q^{20} - 3408 q^{21} - 504 q^{22} + 3936 q^{23} + 26895 q^{25} - 456 q^{26} + 13017 q^{27} + 1344 q^{28} - 14658 q^{29} - 6840 q^{31} - 15360 q^{32} + 3945 q^{33} - 16476 q^{34} + 12636 q^{35} + 34032 q^{36} + 4278 q^{37} + 4956 q^{39} - 6912 q^{40} - 5112 q^{41} + 13632 q^{42} + 94191 q^{43} + 2016 q^{44} + 31770 q^{45} - 15744 q^{46} + 702 q^{47} + 63777 q^{49} - 107580 q^{50} + 108 q^{51} + 1824 q^{52} - 47544 q^{53} - 52068 q^{54} + 16848 q^{55} - 5376 q^{56} + 58632 q^{58} + 8832 q^{59} + 119196 q^{61} + 27360 q^{62} - 88068 q^{63} + 61440 q^{64} - 80646 q^{65} - 15780 q^{66} - 64248 q^{67} + 65904 q^{68} - 124224 q^{69} - 50544 q^{70} + 53364 q^{71} - 136128 q^{72} - 4908 q^{73} - 17112 q^{74} + 87480 q^{75} + 121218 q^{77} - 19824 q^{78} + 115500 q^{79} + 27648 q^{80} + 481659 q^{81} + 20448 q^{82} + 201630 q^{83} - 54528 q^{84} - 150282 q^{85} - 376764 q^{86} + 376512 q^{87} - 8064 q^{88} + 101505 q^{89} - 127080 q^{90} - 414918 q^{91} + 62976 q^{92} + 165960 q^{93} - 2808 q^{94} - 297114 q^{97} - 255108 q^{98} - 149895 q^{99}+O(q^{100}) \) 15 * q - 60 * q^2 + 240 * q^4 + 108 * q^5 + 84 * q^7 - 960 * q^8 + 2127 * q^9 - 432 * q^10 + 126 * q^11 + 114 * q^13 - 336 * q^14 + 3840 * q^16 + 4119 * q^17 - 8508 * q^18 + 1728 * q^20 - 3408 * q^21 - 504 * q^22 + 3936 * q^23 + 26895 * q^25 - 456 * q^26 + 13017 * q^27 + 1344 * q^28 - 14658 * q^29 - 6840 * q^31 - 15360 * q^32 + 3945 * q^33 - 16476 * q^34 + 12636 * q^35 + 34032 * q^36 + 4278 * q^37 + 4956 * q^39 - 6912 * q^40 - 5112 * q^41 + 13632 * q^42 + 94191 * q^43 + 2016 * q^44 + 31770 * q^45 - 15744 * q^46 + 702 * q^47 + 63777 * q^49 - 107580 * q^50 + 108 * q^51 + 1824 * q^52 - 47544 * q^53 - 52068 * q^54 + 16848 * q^55 - 5376 * q^56 + 58632 * q^58 + 8832 * q^59 + 119196 * q^61 + 27360 * q^62 - 88068 * q^63 + 61440 * q^64 - 80646 * q^65 - 15780 * q^66 - 64248 * q^67 + 65904 * q^68 - 124224 * q^69 - 50544 * q^70 + 53364 * q^71 - 136128 * q^72 - 4908 * q^73 - 17112 * q^74 + 87480 * q^75 + 121218 * q^77 - 19824 * q^78 + 115500 * q^79 + 27648 * q^80 + 481659 * q^81 + 20448 * q^82 + 201630 * q^83 - 54528 * q^84 - 150282 * q^85 - 376764 * q^86 + 376512 * q^87 - 8064 * q^88 + 101505 * q^89 - 127080 * q^90 - 414918 * q^91 + 62976 * q^92 + 165960 * q^93 - 2808 * q^94 - 297114 * q^97 - 255108 * q^98 - 149895 * q^99

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