LMFDB - Embedded newform 722.6.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	722.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$115.797117905$
Analytic rank:	$0$
Dimension:	$15$
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			1.4
Root			$-20.7673$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -22.6466 q^{3} +16.0000 q^{4} +79.6824 q^{5} +90.5866 q^{6} +191.779 q^{7} -64.0000 q^{8} +269.871 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -22.6466 q^{3} +16.0000 q^{4} +79.6824 q^{5} +90.5866 q^{6} +191.779 q^{7} -64.0000 q^{8} +269.871 q^{9} -318.730 q^{10} -358.282 q^{11} -362.346 q^{12} +443.782 q^{13} -767.114 q^{14} -1804.54 q^{15} +256.000 q^{16} +991.683 q^{17} -1079.48 q^{18} +1274.92 q^{20} -4343.14 q^{21} +1433.13 q^{22} +1339.07 q^{23} +1449.39 q^{24} +3224.28 q^{25} -1775.13 q^{26} -608.528 q^{27} +3068.46 q^{28} +5075.65 q^{29} +7218.16 q^{30} +6551.33 q^{31} -1024.00 q^{32} +8113.88 q^{33} -3966.73 q^{34} +15281.4 q^{35} +4317.93 q^{36} -13217.2 q^{37} -10050.2 q^{39} -5099.67 q^{40} +9883.49 q^{41} +17372.6 q^{42} +11277.0 q^{43} -5732.51 q^{44} +21503.9 q^{45} -5356.30 q^{46} +28164.4 q^{47} -5797.54 q^{48} +19972.0 q^{49} -12897.1 q^{50} -22458.3 q^{51} +7100.50 q^{52} -30630.6 q^{53} +2434.11 q^{54} -28548.7 q^{55} -12273.8 q^{56} -20302.6 q^{58} +41141.7 q^{59} -28872.6 q^{60} -16045.6 q^{61} -26205.3 q^{62} +51755.4 q^{63} +4096.00 q^{64} +35361.6 q^{65} -32455.5 q^{66} -22175.1 q^{67} +15866.9 q^{68} -30325.5 q^{69} -61125.5 q^{70} -16579.0 q^{71} -17271.7 q^{72} +6083.45 q^{73} +52868.9 q^{74} -73019.2 q^{75} -68710.7 q^{77} +40200.7 q^{78} +90542.9 q^{79} +20398.7 q^{80} -51797.4 q^{81} -39534.0 q^{82} -100994. q^{83} -69490.3 q^{84} +79019.7 q^{85} -45108.0 q^{86} -114946. q^{87} +22930.0 q^{88} -109943. q^{89} -86015.7 q^{90} +85107.8 q^{91} +21425.2 q^{92} -148366. q^{93} -112658. q^{94} +23190.2 q^{96} +81781.7 q^{97} -79888.0 q^{98} -96689.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−22.6466	−1.45278	−0.726391	−	0.687281i	$-0.758804\pi$
$3$	−22.6466	−1.45278	−0.726391	+	0.687281i	$0.758804\pi$
$4$	16.0000	0.500000
$5$	79.6824	1.42540	0.712701	−	0.701468i	$-0.247472\pi$
$5$	79.6824	1.42540	0.712701	+	0.701468i	$0.247472\pi$
$6$	90.5866	1.02727
$7$	191.779	1.47930	0.739648	−	0.672994i	$-0.234992\pi$
$7$	191.779	1.47930	0.739648	+	0.672994i	$0.234992\pi$
$8$	−64.0000	−0.353553
$9$	269.871	1.11058
$10$	−318.730	−1.00791
$11$	−358.282	−0.892777	−0.446388	−	0.894839i	$-0.647290\pi$
$11$	−358.282	−0.892777	−0.446388	+	0.894839i	$0.647290\pi$
$12$	−362.346	−0.726391
$13$	443.782	0.728301	0.364150	−	0.931340i	$-0.381359\pi$
$13$	443.782	0.728301	0.364150	+	0.931340i	$0.381359\pi$
$14$	−767.114	−1.04602
$15$	−1804.54	−2.07080
$16$	256.000	0.250000
$17$	991.683	0.832244	0.416122	−	0.909309i	$-0.363389\pi$
$17$	991.683	0.832244	0.416122	+	0.909309i	$0.363389\pi$
$18$	−1079.48	−0.785298
$19$	0	0
$19$	0	0
$20$	1274.92	0.712701
$21$	−4343.14	−2.14910
$22$	1433.13	0.631289
$23$	1339.07	0.527819	0.263910	−	0.964547i	$-0.414988\pi$
$23$	1339.07	0.527819	0.263910	+	0.964547i	$0.414988\pi$
$24$	1449.39	0.513636
$25$	3224.28	1.03177
$26$	−1775.13	−0.514986
$27$	−608.528	−0.160646
$28$	3068.46	0.739648
$29$	5075.65	1.12072	0.560359	−	0.828250i	$-0.310663\pi$
$29$	5075.65	1.12072	0.560359	+	0.828250i	$0.310663\pi$
$30$	7218.16	1.46428
$31$	6551.33	1.22440	0.612202	−	0.790701i	$-0.290284\pi$
$31$	6551.33	1.22440	0.612202	+	0.790701i	$0.290284\pi$
$32$	−1024.00	−0.176777
$33$	8113.88	1.29701
$34$	−3966.73	−0.588485
$35$	15281.4	2.10859
$36$	4317.93	0.555289
$37$	−13217.2	−1.58721	−0.793607	−	0.608430i	$-0.791799\pi$
$37$	−13217.2	−1.58721	−0.793607	+	0.608430i	$0.791799\pi$
$38$	0	0
$39$	−10050.2	−1.05806
$40$	−5099.67	−0.503956
$41$	9883.49	0.918228	0.459114	−	0.888377i	$-0.348167\pi$
$41$	9883.49	0.918228	0.459114	+	0.888377i	$0.348167\pi$
$42$	17372.6	1.51964
$43$	11277.0	0.930084	0.465042	−	0.885289i	$-0.346039\pi$
$43$	11277.0	0.930084	0.465042	+	0.885289i	$0.346039\pi$
$44$	−5732.51	−0.446388
$45$	21503.9	1.58302
$46$	−5356.30	−0.373224
$47$	28164.4	1.85976	0.929879	−	0.367865i	$-0.119911\pi$
$47$	28164.4	1.85976	0.929879	+	0.367865i	$0.119911\pi$
$48$	−5797.54	−0.363196
$49$	19972.0	1.18831
$50$	−12897.1	−0.729572
$51$	−22458.3	−1.20907
$52$	7100.50	0.364150
$53$	−30630.6	−1.49784	−0.748922	−	0.662658i	$-0.769428\pi$
$53$	−30630.6	−1.49784	−0.748922	+	0.662658i	$0.769428\pi$
$54$	2434.11	0.113594
$55$	−28548.7	−1.27257
$56$	−12273.8	−0.523010
$57$	0	0
$58$	−20302.6	−0.792468
$59$	41141.7	1.53869	0.769347	−	0.638831i	$-0.220582\pi$
$59$	41141.7	1.53869	0.769347	+	0.638831i	$0.220582\pi$
$60$	−28872.6	−1.03540
$61$	−16045.6	−0.552119	−0.276059	−	0.961141i	$-0.589029\pi$
$61$	−16045.6	−0.552119	−0.276059	+	0.961141i	$0.589029\pi$
$62$	−26205.3	−0.865785
$63$	51755.4	1.64287
$64$	4096.00	0.125000
$65$	35361.6	1.03812
$66$	−32455.5	−0.917125
$67$	−22175.1	−0.603501	−0.301750	−	0.953387i	$-0.597571\pi$
$67$	−22175.1	−0.603501	−0.301750	+	0.953387i	$0.597571\pi$
$68$	15866.9	0.416122
$69$	−30325.5	−0.766807
$70$	−61125.5	−1.49100
$71$	−16579.0	−0.390312	−0.195156	−	0.980772i	$-0.562521\pi$
$71$	−16579.0	−0.390312	−0.195156	+	0.980772i	$0.562521\pi$
$72$	−17271.7	−0.392649
$73$	6083.45	0.133611	0.0668055	−	0.997766i	$-0.478719\pi$
$73$	6083.45	0.133611	0.0668055	+	0.997766i	$0.478719\pi$
$74$	52868.9	1.12233
$75$	−73019.2	−1.49894
$76$	0	0
$77$	−68710.7	−1.32068
$78$	40200.7	0.748164
$79$	90542.9	1.63225	0.816125	−	0.577876i	$-0.196118\pi$
$79$	90542.9	1.63225	0.816125	+	0.577876i	$0.196118\pi$
$80$	20398.7	0.356350
$81$	−51797.4	−0.877194
$82$	−39534.0	−0.649286
$83$	−100994.	−1.60916	−0.804582	−	0.593842i	$-0.797610\pi$
$83$	−100994.	−1.60916	−0.804582	+	0.593842i	$0.797610\pi$
$84$	−69490.3	−1.07455
$85$	79019.7	1.18628
$86$	−45108.0	−0.657668
$87$	−114946.	−1.62816
$88$	22930.0	0.315644
$89$	−109943.	−1.47127	−0.735636	−	0.677377i	$-0.763116\pi$
$89$	−109943.	−1.47127	−0.735636	+	0.677377i	$0.763116\pi$
$90$	−86015.7	−1.11936
$91$	85107.8	1.07737
$92$	21425.2	0.263910
$93$	−148366.	−1.77879
$94$	−112658.	−1.31505
$95$	0	0
$96$	23190.2	0.256818
$97$	81781.7	0.882525	0.441262	−	0.897378i	$-0.354531\pi$
$97$	81781.7	0.882525	0.441262	+	0.897378i	$0.354531\pi$
$98$	−79888.0	−0.840266
$99$	−96689.7	−0.991499
$100$	51588.5	0.515885
$101$	−120671.	−1.17706	−0.588531	−	0.808475i	$-0.700294\pi$
$101$	−120671.	−1.17706	−0.588531	+	0.808475i	$0.700294\pi$
$102$	89833.2	0.854941
$103$	−62072.2	−0.576506	−0.288253	−	0.957554i	$-0.593074\pi$
$103$	−62072.2	−0.576506	−0.288253	+	0.957554i	$0.593074\pi$
$104$	−28402.0	−0.257493
$105$	−346072.	−3.06332
$106$	122523.	1.05914
$107$	−17422.5	−0.147113	−0.0735565	−	0.997291i	$-0.523435\pi$
$107$	−17422.5	−0.147113	−0.0735565	+	0.997291i	$0.523435\pi$
$108$	−9736.45	−0.0803232
$109$	87033.0	0.701645	0.350823	−	0.936442i	$-0.385902\pi$
$109$	87033.0	0.701645	0.350823	+	0.936442i	$0.385902\pi$
$110$	114195.	0.899840
$111$	299326.	2.30588
$112$	49095.3	0.369824
$113$	−3534.27	−0.0260378	−0.0130189	−	0.999915i	$-0.504144\pi$
$113$	−3534.27	−0.0260378	−0.0130189	+	0.999915i	$0.504144\pi$
$114$	0	0
$115$	106701.	0.752354
$116$	81210.4	0.560359
$117$	119764.	0.808835
$118$	−164567.	−1.08802
$119$	190184.	1.23113
$120$	115490.	0.732138
$121$	−32685.2	−0.202949
$122$	64182.6	0.390407
$123$	−223828.	−1.33399
$124$	104821.	0.612202
$125$	7911.08	0.0452857
$126$	−207022.	−1.16169
$127$	228868.	1.25914	0.629572	−	0.776942i	$-0.283230\pi$
$127$	228868.	1.25914	0.629572	+	0.776942i	$0.283230\pi$
$128$	−16384.0	−0.0883883
$129$	−255386.	−1.35121
$130$	−141446.	−0.734063
$131$	21885.7	0.111425	0.0557125	−	0.998447i	$-0.482257\pi$
$131$	21885.7	0.111425	0.0557125	+	0.998447i	$0.482257\pi$
$132$	129822.	0.648506
$133$	0	0
$134$	88700.2	0.426739
$135$	−48489.0	−0.228986
$136$	−63467.7	−0.294243
$137$	−34032.4	−0.154914	−0.0774571	−	0.996996i	$-0.524680\pi$
$137$	−34032.4	−0.154914	−0.0774571	+	0.996996i	$0.524680\pi$
$138$	121302.	0.542214
$139$	56195.7	0.246698	0.123349	−	0.992363i	$-0.460636\pi$
$139$	56195.7	0.246698	0.123349	+	0.992363i	$0.460636\pi$
$140$	244502.	1.05430
$141$	−637830.	−2.70183
$142$	66315.9	0.275992
$143$	−158999.	−0.650210
$144$	69086.9	0.277645
$145$	404440.	1.59747
$146$	−24333.8	−0.0944773
$147$	−452299.	−1.72636
$148$	−211475.	−0.793607
$149$	38644.7	0.142602	0.0713009	−	0.997455i	$-0.477285\pi$
$149$	38644.7	0.142602	0.0713009	+	0.997455i	$0.477285\pi$
$150$	292077.	1.05991
$151$	177062.	0.631949	0.315974	−	0.948768i	$-0.397669\pi$
$151$	177062.	0.631949	0.315974	+	0.948768i	$0.397669\pi$
$152$	0	0
$153$	267626.	0.924272
$154$	274843.	0.933862
$155$	522025.	1.74527
$156$	−160803.	−0.529032
$157$	34176.2	0.110656	0.0553280	−	0.998468i	$-0.482380\pi$
$157$	34176.2	0.110656	0.0553280	+	0.998468i	$0.482380\pi$
$158$	−362171.	−1.15417
$159$	693681.	2.17604
$160$	−81594.8	−0.251978
$161$	256806.	0.780800
$162$	207190.	0.620270
$163$	−151256.	−0.445907	−0.222953	−	0.974829i	$-0.571570\pi$
$163$	−151256.	−0.445907	−0.222953	+	0.974829i	$0.571570\pi$
$164$	158136.	0.459114
$165$	646533.	1.84876
$166$	403976.	1.13785
$167$	247523.	0.686791	0.343396	−	0.939191i	$-0.388423\pi$
$167$	247523.	0.686791	0.343396	+	0.939191i	$0.388423\pi$
$168$	277961.	0.759820
$169$	−174351.	−0.469578
$170$	−316079.	−0.838828
$171$	0	0
$172$	180432.	0.465042
$173$	110496.	0.280692	0.140346	−	0.990103i	$-0.455178\pi$
$173$	110496.	0.280692	0.140346	+	0.990103i	$0.455178\pi$
$174$	459786.	1.15128
$175$	618348.	1.52629
$176$	−91720.1	−0.223194
$177$	−931722.	−2.23539
$178$	439772.	1.04035
$179$	218130.	0.508842	0.254421	−	0.967094i	$-0.418115\pi$
$179$	218130.	0.508842	0.254421	+	0.967094i	$0.418115\pi$
$180$	344063.	0.791510
$181$	−296875.	−0.673561	−0.336780	−	0.941583i	$-0.609338\pi$
$181$	−296875.	−0.673561	−0.336780	+	0.941583i	$0.609338\pi$
$182$	−340431.	−0.761817
$183$	363380.	0.802109
$184$	−85700.8	−0.186612
$185$	−1.05318e6	−2.26242
$186$	593462.	1.25780
$187$	−355302.	−0.743008
$188$	450631.	0.929879
$189$	−116703.	−0.237644
$190$	0	0
$191$	108735.	0.215668	0.107834	−	0.994169i	$-0.465609\pi$
$191$	108735.	0.215668	0.107834	+	0.994169i	$0.465609\pi$
$192$	−92760.7	−0.181598
$193$	−433570.	−0.837849	−0.418925	−	0.908021i	$-0.637593\pi$
$193$	−433570.	−0.837849	−0.418925	+	0.908021i	$0.637593\pi$
$194$	−327127.	−0.624039
$195$	−800821.	−1.50817
$196$	319552.	0.594157
$197$	−228260.	−0.419049	−0.209524	−	0.977803i	$-0.567192\pi$
$197$	−228260.	−0.419049	−0.209524	+	0.977803i	$0.567192\pi$
$198$	386759.	0.701096
$199$	914820.	1.63758	0.818791	−	0.574092i	$-0.194645\pi$
$199$	914820.	1.63758	0.818791	+	0.574092i	$0.194645\pi$
$200$	−206354.	−0.364786
$201$	502191.	0.876756
$202$	482684.	0.832309
$203$	973401.	1.65787
$204$	−359333.	−0.604535
$205$	787540.	1.30884
$206$	248289.	0.407651
$207$	361377.	0.586185
$208$	113608.	0.182075
$209$	0	0
$210$	1.38429e6	2.16610
$211$	−399878.	−0.618332	−0.309166	−	0.951008i	$-0.600050\pi$
$211$	−399878.	−0.618332	−0.309166	+	0.951008i	$0.600050\pi$
$212$	−490090.	−0.748922
$213$	375458.	0.567038
$214$	69690.0	0.104025
$215$	898577.	1.32574
$216$	38945.8	0.0567971
$217$	1.25640e6	1.81126
$218$	−348132.	−0.496138
$219$	−137770.	−0.194108
$220$	−456780.	−0.636283
$221$	440091.	0.606124
$222$	−1.19730e6	−1.63050
$223$	−1.20223e6	−1.61892	−0.809459	−	0.587177i	$-0.800239\pi$
$223$	−1.20223e6	−1.61892	−0.809459	+	0.587177i	$0.800239\pi$
$224$	−196381.	−0.261505
$225$	870139.	1.14586
$226$	14137.1	0.0184115
$227$	−172708.	−0.222458	−0.111229	−	0.993795i	$-0.535479\pi$
$227$	−172708.	−0.222458	−0.111229	+	0.993795i	$0.535479\pi$
$228$	0	0
$229$	106292.	0.133941	0.0669704	−	0.997755i	$-0.478667\pi$
$229$	106292.	0.133941	0.0669704	+	0.997755i	$0.478667\pi$
$230$	−426803.	−0.531995
$231$	1.55607e6	1.91866
$232$	−324842.	−0.396234
$233$	506211.	0.610860	0.305430	−	0.952215i	$-0.401200\pi$
$233$	506211.	0.610860	0.305430	+	0.952215i	$0.401200\pi$
$234$	−479054.	−0.571933
$235$	2.24421e6	2.65090
$236$	658267.	0.769347
$237$	−2.05049e6	−2.37130
$238$	−760734.	−0.870544
$239$	−762857.	−0.863871	−0.431935	−	0.901905i	$-0.642169\pi$
$239$	−762857.	−0.863871	−0.431935	+	0.901905i	$0.642169\pi$
$240$	−461962.	−0.517700
$241$	−226268.	−0.250947	−0.125473	−	0.992097i	$-0.540045\pi$
$241$	−226268.	−0.250947	−0.125473	+	0.992097i	$0.540045\pi$
$242$	130741.	0.143507
$243$	1.32091e6	1.43502
$244$	−256730.	−0.276059
$245$	1.59142e6	1.69383
$246$	895312.	0.943271
$247$	0	0
$248$	−419285.	−0.432892
$249$	2.28717e6	2.33777
$250$	−31644.3	−0.0320218
$251$	−1.07704e6	−1.07906	−0.539532	−	0.841965i	$-0.681399\pi$
$251$	−1.07704e6	−1.07906	−0.539532	+	0.841965i	$0.681399\pi$
$252$	828086.	0.821437
$253$	−479766.	−0.471225
$254$	−915471.	−0.890349
$255$	−1.78953e6	−1.72341
$256$	65536.0	0.0625000
$257$	−464815.	−0.438983	−0.219491	−	0.975614i	$-0.570440\pi$
$257$	−464815.	−0.438983	−0.219491	+	0.975614i	$0.570440\pi$
$258$	1.02154e6	0.955449
$259$	−2.53478e6	−2.34796
$260$	565785.	0.519061
$261$	1.36977e6	1.24465
$262$	−87543.0	−0.0787894
$263$	1.47729e6	1.31697	0.658484	−	0.752594i	$-0.271198\pi$
$263$	1.47729e6	1.31697	0.658484	+	0.752594i	$0.271198\pi$
$264$	−519288.	−0.458563
$265$	−2.44072e6	−2.13503
$266$	0	0
$267$	2.48984e6	2.13744
$268$	−354801.	−0.301750
$269$	620419.	0.522762	0.261381	−	0.965236i	$-0.415822\pi$
$269$	620419.	0.522762	0.261381	+	0.965236i	$0.415822\pi$
$270$	193956.	0.161917
$271$	−1.51293e6	−1.25139	−0.625697	−	0.780066i	$-0.715186\pi$
$271$	−1.51293e6	−1.25139	−0.625697	+	0.780066i	$0.715186\pi$
$272$	253871.	0.208061
$273$	−1.92741e6	−1.56519
$274$	136130.	0.109541
$275$	−1.15520e6	−0.921141
$276$	−485209.	−0.383403
$277$	2.23980e6	1.75392	0.876961	−	0.480562i	$-0.159567\pi$
$277$	2.23980e6	1.75392	0.876961	+	0.480562i	$0.159567\pi$
$278$	−224783.	−0.174442
$279$	1.76801e6	1.35980
$280$	−978008.	−0.745499
$281$	419780.	0.317144	0.158572	−	0.987347i	$-0.449311\pi$
$281$	419780.	0.317144	0.158572	+	0.987347i	$0.449311\pi$
$282$	2.55132e6	1.91048
$283$	−1.21876e6	−0.904587	−0.452294	−	0.891869i	$-0.649394\pi$
$283$	−1.21876e6	−0.904587	−0.452294	+	0.891869i	$0.649394\pi$
$284$	−265264.	−0.195156
$285$	0	0
$286$	635995.	0.459768
$287$	1.89544e6	1.35833
$288$	−276347.	−0.196324
$289$	−436422.	−0.307370
$290$	−1.61776e6	−1.12959
$291$	−1.85208e6	−1.28212
$292$	97335.1	0.0668055
$293$	−714114.	−0.485957	−0.242979	−	0.970032i	$-0.578125\pi$
$293$	−714114.	−0.485957	−0.242979	+	0.970032i	$0.578125\pi$
$294$	1.80920e6	1.22072
$295$	3.27827e6	2.19326
$296$	845902.	0.561165
$297$	218024.	0.143421
$298$	−154579.	−0.100835
$299$	594256.	0.384411
$300$	−1.16831e6	−0.749469
$301$	2.16268e6	1.37587
$302$	−708246.	−0.446855
$303$	2.73279e6	1.71002
$304$	0	0
$305$	−1.27856e6	−0.786991
$306$	−1.07050e6	−0.653559
$307$	−254547.	−0.154143	−0.0770713	−	0.997026i	$-0.524557\pi$
$307$	−254547.	−0.154143	−0.0770713	+	0.997026i	$0.524557\pi$
$308$	−1.09937e6	−0.660340
$309$	1.40573e6	0.837538
$310$	−2.08810e6	−1.23409
$311$	−2.39467e6	−1.40392	−0.701962	−	0.712214i	$-0.747693\pi$
$311$	−2.39467e6	−1.40392	−0.701962	+	0.712214i	$0.747693\pi$
$312$	643210.	0.374082
$313$	567326.	0.327320	0.163660	−	0.986517i	$-0.447670\pi$
$313$	567326.	0.327320	0.163660	+	0.986517i	$0.447670\pi$
$314$	−136705.	−0.0782456
$315$	4.12399e6	2.34176
$316$	1.44869e6	0.816125
$317$	−1.17888e6	−0.658900	−0.329450	−	0.944173i	$-0.606863\pi$
$317$	−1.17888e6	−0.658900	−0.329450	+	0.944173i	$0.606863\pi$
$318$	−2.77473e6	−1.53869
$319$	−1.81851e6	−1.00055
$320$	326379.	0.178175
$321$	394561.	0.213723
$322$	−1.02722e6	−0.552109
$323$	0	0
$324$	−828759.	−0.438597
$325$	1.43088e6	0.751439
$326$	605025.	0.315304
$327$	−1.97101e6	−1.01934
$328$	−632543.	−0.324643
$329$	5.40134e6	2.75113
$330$	−2.58613e6	−1.30727
$331$	668070.	0.335160	0.167580	−	0.985859i	$-0.446405\pi$
$331$	668070.	0.335160	0.167580	+	0.985859i	$0.446405\pi$
$332$	−1.61590e6	−0.804582
$333$	−3.56694e6	−1.76273
$334$	−990093.	−0.485635
$335$	−1.76696e6	−0.860231
$336$	−1.11184e6	−0.537274
$337$	2.79679e6	1.34148	0.670742	−	0.741691i	$-0.265976\pi$
$337$	2.79679e6	1.34148	0.670742	+	0.741691i	$0.265976\pi$
$338$	697404.	0.332042
$339$	80039.4	0.0378272
$340$	1.26431e6	0.593141
$341$	−2.34722e6	−1.09312
$342$	0	0
$343$	606981.	0.278574
$344$	−721727.	−0.328834
$345$	−2.41641e6	−1.09301
$346$	−441983.	−0.198479
$347$	1.46987e6	0.655321	0.327661	−	0.944795i	$-0.393740\pi$
$347$	1.46987e6	0.655321	0.327661	+	0.944795i	$0.393740\pi$
$348$	−1.83914e6	−0.814081
$349$	2.93939e6	1.29179	0.645897	−	0.763424i	$-0.276483\pi$
$349$	2.93939e6	1.29179	0.645897	+	0.763424i	$0.276483\pi$
$350$	−2.47339e6	−1.07925
$351$	−270054.	−0.116999
$352$	366880.	0.157822
$353$	−2.44075e6	−1.04253	−0.521263	−	0.853396i	$-0.674539\pi$
$353$	−2.44075e6	−1.04253	−0.521263	+	0.853396i	$0.674539\pi$
$354$	3.72689e6	1.58066
$355$	−1.32105e6	−0.556351
$356$	−1.75909e6	−0.735636
$357$	−4.30702e6	−1.78857
$358$	−872521.	−0.359806
$359$	548005.	0.224413	0.112207	−	0.993685i	$-0.464208\pi$
$359$	548005.	0.224413	0.112207	+	0.993685i	$0.464208\pi$
$360$	−1.37625e6	−0.559682
$361$	0	0
$362$	1.18750e6	0.476279
$363$	740210.	0.294841
$364$	1.36172e6	0.538686
$365$	484743.	0.190449
$366$	−1.45352e6	−0.567177
$367$	3.61119e6	1.39954	0.699771	−	0.714368i	$-0.253286\pi$
$367$	3.61119e6	1.39954	0.699771	+	0.714368i	$0.253286\pi$
$368$	342803.	0.131955
$369$	2.66726e6	1.01976
$370$	4.21272e6	1.59977
$371$	−5.87430e6	−2.21575
$372$	−2.37385e6	−0.889397
$373$	502139.	0.186875	0.0934377	−	0.995625i	$-0.470214\pi$
$373$	502139.	0.186875	0.0934377	+	0.995625i	$0.470214\pi$
$374$	1.42121e6	0.525386
$375$	−179159.	−0.0657902
$376$	−1.80252e6	−0.657524
$377$	2.25248e6	0.816220
$378$	466811.	0.168039
$379$	−240568.	−0.0860278	−0.0430139	−	0.999074i	$-0.513696\pi$
$379$	−240568.	−0.0860278	−0.0430139	+	0.999074i	$0.513696\pi$
$380$	0	0
$381$	−5.18309e6	−1.82926
$382$	−434939.	−0.152500
$383$	−2.57949e6	−0.898540	−0.449270	−	0.893396i	$-0.648316\pi$
$383$	−2.57949e6	−0.898540	−0.449270	+	0.893396i	$0.648316\pi$
$384$	371043.	0.128409
$385$	−5.47504e6	−1.88250
$386$	1.73428e6	0.592449
$387$	3.04333e6	1.03293
$388$	1.30851e6	0.441262
$389$	263297.	0.0882209	0.0441104	−	0.999027i	$-0.485955\pi$
$389$	263297.	0.0882209	0.0441104	+	0.999027i	$0.485955\pi$
$390$	3.20328e6	1.06643
$391$	1.32794e6	0.439274
$392$	−1.27821e6	−0.420133
$393$	−495639.	−0.161876
$394$	913041.	0.296312
$395$	7.21467e6	2.32661
$396$	−1.54704e6	−0.495749
$397$	3.08689e6	0.982981	0.491491	−	0.870883i	$-0.336452\pi$
$397$	3.08689e6	0.982981	0.491491	+	0.870883i	$0.336452\pi$
$398$	−3.65928e6	−1.15794
$399$	0	0
$400$	825416.	0.257943
$401$	1.67059e6	0.518809	0.259405	−	0.965769i	$-0.416474\pi$
$401$	1.67059e6	0.518809	0.259405	+	0.965769i	$0.416474\pi$
$402$	−2.00876e6	−0.619960
$403$	2.90736e6	0.891735
$404$	−1.93074e6	−0.588531
$405$	−4.12734e6	−1.25035
$406$	−3.89360e6	−1.17229
$407$	4.73549e6	1.41703
$408$	1.43733e6	0.427471
$409$	6.11240e6	1.80677	0.903386	−	0.428829i	$-0.141074\pi$
$409$	6.11240e6	1.80677	0.903386	+	0.428829i	$0.141074\pi$
$410$	−3.15016e6	−0.925493
$411$	770720.	0.225057
$412$	−993155.	−0.288253
$413$	7.89010e6	2.27618
$414$	−1.44551e6	−0.414495
$415$	−8.04744e6	−2.29370
$416$	−454432.	−0.128747
$417$	−1.27264e6	−0.358399
$418$	0	0
$419$	1.09637e6	0.305087	0.152543	−	0.988297i	$-0.451254\pi$
$419$	1.09637e6	0.305087	0.152543	+	0.988297i	$0.451254\pi$
$420$	−5.53715e6	−1.53166
$421$	5.42330e6	1.49128	0.745638	−	0.666351i	$-0.232145\pi$
$421$	5.42330e6	1.49128	0.745638	+	0.666351i	$0.232145\pi$
$422$	1.59951e6	0.437227
$423$	7.60075e6	2.06541
$424$	1.96036e6	0.529568
$425$	3.19747e6	0.858685
$426$	−1.50183e6	−0.400957
$427$	−3.07721e6	−0.816747
$428$	−278760.	−0.0735565
$429$	3.60079e6	0.944614
$430$	−3.59431e6	−0.937442
$431$	5.46122e6	1.41611	0.708054	−	0.706158i	$-0.249573\pi$
$431$	5.46122e6	1.41611	0.708054	+	0.706158i	$0.249573\pi$
$432$	−155783.	−0.0401616
$433$	5.18650e6	1.32940	0.664699	−	0.747112i	$-0.268560\pi$
$433$	5.18650e6	1.32940	0.664699	+	0.747112i	$0.268560\pi$
$434$	−5.02562e6	−1.28075
$435$	−9.15921e6	−2.32078
$436$	1.39253e6	0.350823
$437$	0	0
$438$	551079.	0.137255
$439$	429040.	0.106252	0.0531259	−	0.998588i	$-0.483082\pi$
$439$	429040.	0.106252	0.0531259	+	0.998588i	$0.483082\pi$
$440$	1.82712e6	0.449920
$441$	5.38986e6	1.31972
$442$	−1.76036e6	−0.428594
$443$	3.49738e6	0.846708	0.423354	−	0.905964i	$-0.360853\pi$
$443$	3.49738e6	0.846708	0.423354	+	0.905964i	$0.360853\pi$
$444$	4.78921e6	1.15294
$445$	−8.76052e6	−2.09715
$446$	4.80891e6	1.14475
$447$	−875174.	−0.207169
$448$	785525.	0.184912
$449$	2.86674e6	0.671076	0.335538	−	0.942027i	$-0.391082\pi$
$449$	2.86674e6	0.671076	0.335538	+	0.942027i	$0.391082\pi$
$450$	−3.48056e6	−0.810247
$451$	−3.54107e6	−0.819773
$452$	−56548.3	−0.0130189
$453$	−4.00985e6	−0.918085
$454$	690831.	0.157301
$455$	6.78159e6	1.53569
$456$	0	0
$457$	−6.29130e6	−1.40913	−0.704563	−	0.709642i	$-0.748857\pi$
$457$	−6.29130e6	−1.40913	−0.704563	+	0.709642i	$0.748857\pi$
$458$	−425169.	−0.0947105
$459$	−603467.	−0.133697
$460$	1.70721e6	0.376177
$461$	4.49087e6	0.984188	0.492094	−	0.870542i	$-0.336232\pi$
$461$	4.49087e6	0.984188	0.492094	+	0.870542i	$0.336232\pi$
$462$	−6.22427e6	−1.35670
$463$	6.06753e6	1.31541	0.657703	−	0.753277i	$-0.271528\pi$
$463$	6.06753e6	1.31541	0.657703	+	0.753277i	$0.271528\pi$
$464$	1.29937e6	0.280180
$465$	−1.18221e7	−2.53550
$466$	−2.02484e6	−0.431943
$467$	−6.88549e6	−1.46097	−0.730487	−	0.682927i	$-0.760707\pi$
$467$	−6.88549e6	−1.46097	−0.730487	+	0.682927i	$0.760707\pi$
$468$	1.91622e6	0.404418
$469$	−4.25270e6	−0.892756
$470$	−8.97684e6	−1.87447
$471$	−773977.	−0.160759
$472$	−2.63307e6	−0.544011
$473$	−4.04034e6	−0.830357
$474$	8.20197e6	1.67677
$475$	0	0
$476$	3.04294e6	0.615567
$477$	−8.26631e6	−1.66347
$478$	3.05143e6	0.610849
$479$	6.11464e6	1.21768	0.608839	−	0.793294i	$-0.291636\pi$
$479$	6.11464e6	1.21768	0.608839	+	0.793294i	$0.291636\pi$
$480$	1.84785e6	0.366069
$481$	−5.86556e6	−1.15597
$482$	905074.	0.177446
$483$	−5.81579e6	−1.13433
$484$	−522963.	−0.101475
$485$	6.51656e6	1.25795
$486$	−5.28364e6	−1.01471
$487$	1.92140e6	0.367109	0.183554	−	0.983010i	$-0.441240\pi$
$487$	1.92140e6	0.367109	0.183554	+	0.983010i	$0.441240\pi$
$488$	1.02692e6	0.195204
$489$	3.42545e6	0.647806
$490$	−6.36567e6	−1.19772
$491$	−4.28233e6	−0.801634	−0.400817	−	0.916158i	$-0.631274\pi$
$491$	−4.28233e6	−0.801634	−0.400817	+	0.916158i	$0.631274\pi$
$492$	−3.58125e6	−0.666993
$493$	5.03344e6	0.932711
$494$	0	0
$495$	−7.70447e6	−1.41328
$496$	1.67714e6	0.306101
$497$	−3.17949e6	−0.577387
$498$	−9.14870e6	−1.65305
$499$	7.37167e6	1.32530	0.662650	−	0.748929i	$-0.269432\pi$
$499$	7.37167e6	1.32530	0.662650	+	0.748929i	$0.269432\pi$
$500$	126577.	0.0226428
$501$	−5.60557e6	−0.997759
$502$	4.30816e6	0.763014
$503$	7.06701e6	1.24542	0.622710	−	0.782453i	$-0.286032\pi$
$503$	7.06701e6	1.24542	0.622710	+	0.782453i	$0.286032\pi$
$504$	−3.31234e6	−0.580844
$505$	−9.61535e6	−1.67779
$506$	1.91906e6	0.333206
$507$	3.94846e6	0.682195
$508$	3.66188e6	0.629572
$509$	−8.87828e6	−1.51892	−0.759459	−	0.650555i	$-0.774536\pi$
$509$	−8.87828e6	−1.51892	−0.759459	+	0.650555i	$0.774536\pi$
$510$	7.15812e6	1.21864
$511$	1.16667e6	0.197650
$512$	−262144.	−0.0441942
$513$	0	0
$514$	1.85926e6	0.310408
$515$	−4.94606e6	−0.821753
$516$	−4.08618e6	−0.675605
$517$	−1.00908e7	−1.66035
$518$	1.01391e7	1.66026
$519$	−2.50236e6	−0.407785
$520$	−2.26314e6	−0.367031
$521$	−4.73223e6	−0.763786	−0.381893	−	0.924207i	$-0.624728\pi$
$521$	−4.73223e6	−0.763786	−0.381893	+	0.924207i	$0.624728\pi$
$522$	−5.47907e6	−0.880098
$523$	1.80814e6	0.289053	0.144526	−	0.989501i	$-0.453834\pi$
$523$	1.80814e6	0.289053	0.144526	+	0.989501i	$0.453834\pi$
$524$	350172.	0.0557125
$525$	−1.40035e7	−2.21737
$526$	−5.90915e6	−0.931238
$527$	6.49684e6	1.01900
$528$	2.07715e6	0.324253
$529$	−4.64322e6	−0.721407
$530$	9.76289e6	1.50969
$531$	1.11029e7	1.70884
$532$	0	0
$533$	4.38611e6	0.668747
$534$	−9.95937e6	−1.51140
$535$	−1.38827e6	−0.209695
$536$	1.41920e6	0.213370
$537$	−4.93992e6	−0.739237
$538$	−2.48168e6	−0.369649
$539$	−7.15561e6	−1.06090
$540$	−775824.	−0.114493
$541$	1.16521e6	0.171163	0.0855817	−	0.996331i	$-0.472725\pi$
$541$	1.16521e6	0.171163	0.0855817	+	0.996331i	$0.472725\pi$
$542$	6.05170e6	0.884870
$543$	6.72321e6	0.978537
$544$	−1.01548e6	−0.147121
$545$	6.93500e6	1.00013
$546$	7.70962e6	1.10675
$547$	4.11534e6	0.588081	0.294040	−	0.955793i	$-0.405000\pi$
$547$	4.11534e6	0.588081	0.294040	+	0.955793i	$0.405000\pi$
$548$	−544519.	−0.0774571
$549$	−4.33025e6	−0.613171
$550$	4.62081e6	0.651345
$551$	0	0
$552$	1.94083e6	0.271107
$553$	1.73642e7	2.41458
$554$	−8.95921e6	−1.24021
$555$	2.38510e7	3.28680
$556$	899131.	0.123349
$557$	8.90734e6	1.21649	0.608247	−	0.793748i	$-0.291873\pi$
$557$	8.90734e6	1.21649	0.608247	+	0.793748i	$0.291873\pi$
$558$	−7.07204e6	−0.961522
$559$	5.00452e6	0.677381
$560$	3.91203e6	0.527148
$561$	8.04640e6	1.07943
$562$	−1.67912e6	−0.224255
$563$	−4.55469e6	−0.605603	−0.302801	−	0.953054i	$-0.597922\pi$
$563$	−4.55469e6	−0.605603	−0.302801	+	0.953054i	$0.597922\pi$
$564$	−1.02053e7	−1.35091
$565$	−281619.	−0.0371143
$566$	4.87502e6	0.639640
$567$	−9.93364e6	−1.29763
$568$	1.06105e6	0.137996
$569$	−6.90310e6	−0.893848	−0.446924	−	0.894572i	$-0.647481\pi$
$569$	−6.90310e6	−0.893848	−0.446924	+	0.894572i	$0.647481\pi$
$570$	0	0
$571$	−3.20907e6	−0.411897	−0.205949	−	0.978563i	$-0.566028\pi$
$571$	−3.20907e6	−0.411897	−0.205949	+	0.978563i	$0.566028\pi$
$572$	−2.54398e6	−0.325105
$573$	−2.46248e6	−0.313318
$574$	−7.58177e6	−0.960485
$575$	4.31755e6	0.544588
$576$	1.10539e6	0.138822
$577$	−6.19764e6	−0.774973	−0.387487	−	0.921875i	$-0.626657\pi$
$577$	−6.19764e6	−0.774973	−0.387487	+	0.921875i	$0.626657\pi$
$578$	1.74569e6	0.217344
$579$	9.81890e6	1.21721
$580$	6.47104e6	0.798737
$581$	−1.93685e7	−2.38043
$582$	7.40832e6	0.906593
$583$	1.09744e7	1.33724
$584$	−389341.	−0.0472387
$585$	9.54305e6	1.15292
$586$	2.85645e6	0.343624
$587$	1.05771e7	1.26698	0.633492	−	0.773749i	$-0.281621\pi$
$587$	1.05771e7	1.26698	0.633492	+	0.773749i	$0.281621\pi$
$588$	−7.23678e6	−0.863182
$589$	0	0
$590$	−1.31131e7	−1.55087
$591$	5.16933e6	0.608787
$592$	−3.38361e6	−0.396804
$593$	−9.74395e6	−1.13788	−0.568942	−	0.822377i	$-0.692647\pi$
$593$	−9.74395e6	−1.13788	−0.568942	+	0.822377i	$0.692647\pi$
$594$	−872098.	−0.101414
$595$	1.51543e7	1.75486
$596$	618316.	0.0713009
$597$	−2.07176e7	−2.37905
$598$	−2.37703e6	−0.271820
$599$	−9.74002e6	−1.10916	−0.554578	−	0.832131i	$-0.687120\pi$
$599$	−9.74002e6	−1.10916	−0.554578	+	0.832131i	$0.687120\pi$
$600$	4.67323e6	0.529955
$601$	3.60512e6	0.407131	0.203565	−	0.979061i	$-0.434747\pi$
$601$	3.60512e6	0.407131	0.203565	+	0.979061i	$0.434747\pi$
$602$	−8.65074e6	−0.972886
$603$	−5.98440e6	−0.670235
$604$	2.83299e6	0.315974
$605$	−2.60444e6	−0.289284
$606$	−1.09312e7	−1.20916
$607$	1.80180e6	0.198488	0.0992441	−	0.995063i	$-0.468358\pi$
$607$	1.80180e6	0.198488	0.0992441	+	0.995063i	$0.468358\pi$
$608$	0	0
$609$	−2.20443e7	−2.40853
$610$	5.11422e6	0.556487
$611$	1.24989e7	1.35446
$612$	4.28202e6	0.462136
$613$	−7.30558e6	−0.785241	−0.392621	−	0.919700i	$-0.628431\pi$
$613$	−7.30558e6	−0.785241	−0.392621	+	0.919700i	$0.628431\pi$
$614$	1.01819e6	0.108995
$615$	−1.78351e7	−1.90147
$616$	4.39749e6	0.466931
$617$	−1.34101e7	−1.41814	−0.709072	−	0.705136i	$-0.750886\pi$
$617$	−1.34101e7	−1.41814	−0.709072	+	0.705136i	$0.750886\pi$
$618$	−5.62290e6	−0.592229
$619$	1.77599e7	1.86300	0.931500	−	0.363741i	$-0.118501\pi$
$619$	1.77599e7	1.86300	0.931500	+	0.363741i	$0.118501\pi$
$620$	8.35240e6	0.872634
$621$	−814864.	−0.0847923
$622$	9.57866e6	0.992725
$623$	−2.10847e7	−2.17644
$624$	−2.57284e6	−0.264516
$625$	−9.44551e6	−0.967220
$626$	−2.26931e6	−0.231450
$627$	0	0
$628$	546820.	0.0553280
$629$	−1.31073e7	−1.32095
$630$	−1.64960e7	−1.65587
$631$	−3.04664e6	−0.304612	−0.152306	−	0.988333i	$-0.548670\pi$
$631$	−3.04664e6	−0.304612	−0.152306	+	0.988333i	$0.548670\pi$
$632$	−5.79474e6	−0.577087
$633$	9.05590e6	0.898302
$634$	4.71550e6	0.465913
$635$	1.82367e7	1.79479
$636$	1.10989e7	1.08802
$637$	8.86321e6	0.865451
$638$	7.27405e6	0.707497
$639$	−4.47418e6	−0.433472
$640$	−1.30552e6	−0.125989
$641$	−6.41199e6	−0.616379	−0.308189	−	0.951325i	$-0.599723\pi$
$641$	−6.41199e6	−0.616379	−0.308189	+	0.951325i	$0.599723\pi$
$642$	−1.57824e6	−0.151125
$643$	7.29876e6	0.696180	0.348090	−	0.937461i	$-0.386830\pi$
$643$	7.29876e6	0.696180	0.348090	+	0.937461i	$0.386830\pi$
$644$	4.10889e6	0.390400
$645$	−2.03498e7	−1.92602
$646$	0	0
$647$	−9.74699e6	−0.915397	−0.457699	−	0.889107i	$-0.651326\pi$
$647$	−9.74699e6	−0.915397	−0.457699	+	0.889107i	$0.651326\pi$
$648$	3.31504e6	0.310135
$649$	−1.47403e7	−1.37371
$650$	−5.72351e6	−0.531348
$651$	−2.84533e7	−2.63136
$652$	−2.42010e6	−0.222953
$653$	1.24278e7	1.14054	0.570269	−	0.821458i	$-0.306839\pi$
$653$	1.24278e7	1.14054	0.570269	+	0.821458i	$0.306839\pi$
$654$	7.88402e6	0.720781
$655$	1.74391e6	0.158826
$656$	2.53017e6	0.229557
$657$	1.64174e6	0.148386
$658$	−2.16053e7	−1.94534
$659$	−7.62574e6	−0.684019	−0.342010	−	0.939696i	$-0.611108\pi$
$659$	−7.62574e6	−0.684019	−0.342010	+	0.939696i	$0.611108\pi$
$660$	1.03445e7	0.924381
$661$	−1.11061e7	−0.988681	−0.494340	−	0.869268i	$-0.664590\pi$
$661$	−1.11061e7	−0.988681	−0.494340	+	0.869268i	$0.664590\pi$
$662$	−2.67228e6	−0.236994
$663$	−9.96658e6	−0.880566
$664$	6.46361e6	0.568925
$665$	0	0
$666$	1.42677e7	1.24644
$667$	6.79667e6	0.591537
$668$	3.96037e6	0.343396
$669$	2.72264e7	2.35194
$670$	7.06785e6	0.608275
$671$	5.74886e6	0.492919
$672$	4.44738e6	0.379910
$673$	4.52106e6	0.384771	0.192386	−	0.981319i	$-0.438378\pi$
$673$	4.52106e6	0.384771	0.192386	+	0.981319i	$0.438378\pi$
$674$	−1.11872e7	−0.948573
$675$	−1.96207e6	−0.165750
$676$	−2.78962e6	−0.234789
$677$	1.32041e7	1.10723	0.553616	−	0.832772i	$-0.313248\pi$
$677$	1.32041e7	1.10723	0.553616	+	0.832772i	$0.313248\pi$
$678$	−320157.	−0.0267479
$679$	1.56840e7	1.30551
$680$	−5.05726e6	−0.419414
$681$	3.91125e6	0.323183
$682$	9.38888e6	0.772953
$683$	−889471.	−0.0729592	−0.0364796	−	0.999334i	$-0.511614\pi$
$683$	−889471.	−0.0729592	−0.0364796	+	0.999334i	$0.511614\pi$
$684$	0	0
$685$	−2.71178e6	−0.220815
$686$	−2.42792e6	−0.196981
$687$	−2.40716e6	−0.194587
$688$	2.88691e6	0.232521
$689$	−1.35933e7	−1.09088
$690$	9.66565e6	0.772873
$691$	−1.59304e7	−1.26921	−0.634604	−	0.772838i	$-0.718837\pi$
$691$	−1.59304e7	−1.26921	−0.634604	+	0.772838i	$0.718837\pi$
$692$	1.76793e6	0.140346
$693$	−1.85430e7	−1.46672
$694$	−5.87947e6	−0.463382
$695$	4.47781e6	0.351644
$696$	7.35657e6	0.575642
$697$	9.80129e6	0.764190
$698$	−1.17576e7	−0.913437
$699$	−1.14640e7	−0.887447
$700$	9.89357e6	0.763147
$701$	−1.65606e7	−1.27286	−0.636432	−	0.771333i	$-0.719590\pi$
$701$	−1.65606e7	−1.27286	−0.636432	+	0.771333i	$0.719590\pi$
$702$	1.08021e6	0.0827308
$703$	0	0
$704$	−1.46752e6	−0.111597
$705$	−5.08238e7	−3.85119
$706$	9.76301e6	0.737177
$707$	−2.31421e7	−1.74122
$708$	−1.49075e7	−1.11769
$709$	−1.24095e7	−0.927124	−0.463562	−	0.886064i	$-0.653429\pi$
$709$	−1.24095e7	−0.927124	−0.463562	+	0.886064i	$0.653429\pi$
$710$	5.28421e6	0.393400
$711$	2.44349e7	1.81274
$712$	7.03636e6	0.520173
$713$	8.77271e6	0.646264
$714$	1.72281e7	1.26471
$715$	−1.26694e7	−0.926811
$716$	3.49008e6	0.254421
$717$	1.72762e7	1.25502
$718$	−2.19202e6	−0.158684
$719$	−2.10450e7	−1.51819	−0.759096	−	0.650979i	$-0.774359\pi$
$719$	−2.10450e7	−1.51819	−0.759096	+	0.650979i	$0.774359\pi$
$720$	5.50501e6	0.395755
$721$	−1.19041e7	−0.852823
$722$	0	0
$723$	5.12422e6	0.364571
$724$	−4.74999e6	−0.336780
$725$	1.63653e7	1.15632
$726$	−2.96084e6	−0.208484
$727$	1.41438e7	0.992496	0.496248	−	0.868181i	$-0.334711\pi$
$727$	1.41438e7	0.992496	0.496248	+	0.868181i	$0.334711\pi$
$728$	−5.44690e6	−0.380909
$729$	−1.73274e7	−1.20758
$730$	−1.93897e6	−0.134668
$731$	1.11832e7	0.774056
$732$	5.81408e6	0.401055
$733$	1.46251e7	1.00540	0.502699	−	0.864462i	$-0.332340\pi$
$733$	1.46251e7	1.00540	0.502699	+	0.864462i	$0.332340\pi$
$734$	−1.44448e7	−0.989625
$735$	−3.60403e7	−2.46076
$736$	−1.37121e6	−0.0933061
$737$	7.94492e6	0.538792
$738$	−1.06691e7	−0.721083
$739$	−2.91473e7	−1.96330	−0.981650	−	0.190693i	$-0.938926\pi$
$739$	−2.91473e7	−1.96330	−0.981650	+	0.190693i	$0.938926\pi$
$740$	−1.68509e7	−1.13121
$741$	0	0
$742$	2.34972e7	1.56677
$743$	1.72429e7	1.14588	0.572939	−	0.819598i	$-0.305803\pi$
$743$	1.72429e7	1.14588	0.572939	+	0.819598i	$0.305803\pi$
$744$	9.49540e6	0.628899
$745$	3.07931e6	0.203265
$746$	−2.00856e6	−0.132141
$747$	−2.72553e7	−1.78710
$748$	−5.68483e6	−0.371504
$749$	−3.34126e6	−0.217623
$750$	716638.	0.0465207
$751$	−3.59549e6	−0.232626	−0.116313	−	0.993213i	$-0.537108\pi$
$751$	−3.59549e6	−0.232626	−0.116313	+	0.993213i	$0.537108\pi$
$752$	7.21010e6	0.464940
$753$	2.43913e7	1.56765
$754$	−9.00992e6	−0.577155
$755$	1.41087e7	0.900781
$756$	−1.86724e6	−0.118822
$757$	1.43218e7	0.908358	0.454179	−	0.890910i	$-0.349933\pi$
$757$	1.43218e7	0.908358	0.454179	+	0.890910i	$0.349933\pi$
$758$	962270.	0.0608309
$759$	1.08651e7	0.684587
$760$	0	0
$761$	2.54776e7	1.59477	0.797384	−	0.603473i	$-0.206217\pi$
$761$	2.54776e7	1.59477	0.797384	+	0.603473i	$0.206217\pi$
$762$	2.07323e7	1.29348
$763$	1.66911e7	1.03794
$764$	1.73976e6	0.107834
$765$	2.13251e7	1.31746
$766$	1.03180e7	0.635364
$767$	1.82579e7	1.12063
$768$	−1.48417e6	−0.0907989
$769$	1.84621e7	1.12581	0.562905	−	0.826522i	$-0.309684\pi$
$769$	1.84621e7	1.12581	0.562905	+	0.826522i	$0.309684\pi$
$770$	2.19001e7	1.33113
$771$	1.05265e7	0.637747
$772$	−6.93712e6	−0.418925
$773$	1.35477e7	0.815484	0.407742	−	0.913097i	$-0.366316\pi$
$773$	1.35477e7	0.815484	0.407742	+	0.913097i	$0.366316\pi$
$774$	−1.21733e7	−0.730392
$775$	2.11233e7	1.26330
$776$	−5.23403e6	−0.312020
$777$	5.74042e7	3.41108
$778$	−1.05319e6	−0.0623816
$779$	0	0
$780$	−1.28131e7	−0.754083
$781$	5.93994e6	0.348461
$782$	−5.31175e6	−0.310614
$783$	−3.08868e6	−0.180040
$784$	5.11283e6	0.297079
$785$	2.72324e6	0.157729
$786$	1.98255e6	0.114464
$787$	−1.58174e7	−0.910330	−0.455165	−	0.890407i	$-0.650420\pi$
$787$	−1.58174e7	−0.910330	−0.455165	+	0.890407i	$0.650420\pi$
$788$	−3.65216e6	−0.209524
$789$	−3.34556e7	−1.91327
$790$	−2.88587e7	−1.64516
$791$	−677797.	−0.0385175
$792$	6.18814e6	0.350548
$793$	−7.12076e6	−0.402109
$794$	−1.23476e7	−0.695073
$795$	5.52742e7	3.10173
$796$	1.46371e7	0.818791
$797$	1.51049e7	0.842312	0.421156	−	0.906988i	$-0.361625\pi$
$797$	1.51049e7	0.842312	0.421156	+	0.906988i	$0.361625\pi$
$798$	0	0
$799$	2.79302e7	1.54777
$800$	−3.30167e6	−0.182393
$801$	−2.96704e7	−1.63396
$802$	−6.68234e6	−0.366854
$803$	−2.17959e6	−0.119285
$804$	8.03505e6	0.438378
$805$	2.04629e7	1.11295
$806$	−1.16294e7	−0.630552
$807$	−1.40504e7	−0.759460
$808$	7.72294e6	0.416154
$809$	1.01681e7	0.546220	0.273110	−	0.961983i	$-0.411948\pi$
$809$	1.01681e7	0.546220	0.273110	+	0.961983i	$0.411948\pi$
$810$	1.65094e7	0.884134
$811$	2.16511e7	1.15592	0.577961	−	0.816065i	$-0.303849\pi$
$811$	2.16511e7	1.15592	0.577961	+	0.816065i	$0.303849\pi$
$812$	1.55744e7	0.828937
$813$	3.42627e7	1.81801
$814$	−1.89419e7	−1.00199
$815$	−1.20525e7	−0.635597
$816$	−5.74932e6	−0.302267
$817$	0	0
$818$	−2.44496e7	−1.27758
$819$	2.29681e7	1.19651
$820$	1.26006e7	0.654422
$821$	−1.37109e6	−0.0709920	−0.0354960	−	0.999370i	$-0.511301\pi$
$821$	−1.37109e6	−0.0709920	−0.0354960	+	0.999370i	$0.511301\pi$
$822$	−3.08288e6	−0.159139
$823$	2.72302e7	1.40136	0.700682	−	0.713473i	$-0.252879\pi$
$823$	2.72302e7	1.40136	0.700682	+	0.713473i	$0.252879\pi$
$824$	3.97262e6	0.203826
$825$	2.61614e7	1.33822
$826$	−3.15604e7	−1.60950
$827$	1.63661e7	0.832113	0.416057	−	0.909339i	$-0.363412\pi$
$827$	1.63661e7	0.832113	0.416057	+	0.909339i	$0.363412\pi$
$828$	5.78203e6	0.293092
$829$	−4.82305e6	−0.243745	−0.121872	−	0.992546i	$-0.538890\pi$
$829$	−4.82305e6	−0.243745	−0.121872	+	0.992546i	$0.538890\pi$
$830$	3.21898e7	1.62189
$831$	−5.07240e7	−2.54807
$832$	1.81773e6	0.0910376
$833$	1.98059e7	0.988968
$834$	5.09058e6	0.253426
$835$	1.97232e7	0.978953
$836$	0	0
$837$	−3.98667e6	−0.196696
$838$	−4.38549e6	−0.215729
$839$	−9.95403e6	−0.488196	−0.244098	−	0.969751i	$-0.578492\pi$
$839$	−9.95403e6	−0.488196	−0.244098	+	0.969751i	$0.578492\pi$
$840$	2.21486e7	1.08305
$841$	5.25107e6	0.256010
$842$	−2.16932e7	−1.05449
$843$	−9.50662e6	−0.460741
$844$	−6.39805e6	−0.309166
$845$	−1.38927e7	−0.669337
$846$	−3.04030e7	−1.46046
$847$	−6.26832e6	−0.300222
$848$	−7.84144e6	−0.374461
$849$	2.76007e7	1.31417
$850$	−1.27899e7	−0.607182
$851$	−1.76988e7	−0.837762
$852$	6.00733e6	0.283519
$853$	1.72788e7	0.813094	0.406547	−	0.913630i	$-0.366733\pi$
$853$	1.72788e7	0.813094	0.406547	+	0.913630i	$0.366733\pi$
$854$	1.23088e7	0.577527
$855$	0	0
$856$	1.11504e6	0.0520123
$857$	−7.03868e6	−0.327370	−0.163685	−	0.986513i	$-0.552338\pi$
$857$	−7.03868e6	−0.327370	−0.163685	+	0.986513i	$0.552338\pi$
$858$	−1.44032e7	−0.667943
$859$	−2.23544e7	−1.03366	−0.516832	−	0.856087i	$-0.672889\pi$
$859$	−2.23544e7	−1.03366	−0.516832	+	0.856087i	$0.672889\pi$
$860$	1.43772e7	0.662871
$861$	−4.29254e7	−1.97336
$862$	−2.18449e7	−1.00134
$863$	5.27273e6	0.240995	0.120498	−	0.992714i	$-0.461551\pi$
$863$	5.27273e6	0.240995	0.120498	+	0.992714i	$0.461551\pi$
$864$	623133.	0.0283986
$865$	8.80457e6	0.400099
$866$	−2.07460e7	−0.940026
$867$	9.88349e6	0.446542
$868$	2.01025e7	0.905628
$869$	−3.24399e7	−1.45723
$870$	3.66368e7	1.64104
$871$	−9.84088e6	−0.439530
$872$	−5.57011e6	−0.248069
$873$	2.20705e7	0.980113
$874$	0	0
$875$	1.51718e6	0.0669909
$876$	−2.20431e6	−0.0970540
$877$	−5.66757e6	−0.248827	−0.124414	−	0.992230i	$-0.539705\pi$
$877$	−5.66757e6	−0.248827	−0.124414	+	0.992230i	$0.539705\pi$
$878$	−1.71616e6	−0.0751313
$879$	1.61723e7	0.705991
$880$	−7.30848e6	−0.318141
$881$	1.22064e7	0.529842	0.264921	−	0.964270i	$-0.414654\pi$
$881$	1.22064e7	0.529842	0.264921	+	0.964270i	$0.414654\pi$
$882$	−2.15594e7	−0.933181
$883$	3.45683e7	1.49203	0.746013	−	0.665931i	$-0.231965\pi$
$883$	3.45683e7	1.49203	0.746013	+	0.665931i	$0.231965\pi$
$884$	7.04145e6	0.303062
$885$	−7.42418e7	−3.18633
$886$	−1.39895e7	−0.598713
$887$	−2.33388e7	−0.996021	−0.498011	−	0.867171i	$-0.665936\pi$
$887$	−2.33388e7	−0.996021	−0.498011	+	0.867171i	$0.665936\pi$
$888$	−1.91568e7	−0.815251
$889$	4.38919e7	1.86265
$890$	3.50421e7	1.48291
$891$	1.85581e7	0.783139
$892$	−1.92356e7	−0.809459
$893$	0	0
$894$	3.50070e6	0.146491
$895$	1.73811e7	0.725305
$896$	−3.14210e6	−0.130752
$897$	−1.34579e7	−0.558466
$898$	−1.14669e7	−0.474522
$899$	3.32522e7	1.37221
$900$	1.39222e7	0.572931
$901$	−3.03759e7	−1.24657
$902$	1.41643e7	0.579667
$903$	−4.89775e7	−1.99884
$904$	226193.	0.00920574
$905$	−2.36557e7	−0.960095
$906$	1.60394e7	0.649184
$907$	2.99211e6	0.120770	0.0603851	−	0.998175i	$-0.480767\pi$
$907$	2.99211e6	0.120770	0.0603851	+	0.998175i	$0.480767\pi$
$908$	−2.76332e6	−0.111229
$909$	−3.25655e7	−1.30722
$910$	−2.71264e7	−1.08590
$911$	9.95825e6	0.397546	0.198773	−	0.980046i	$-0.436304\pi$
$911$	9.95825e6	0.397546	0.198773	+	0.980046i	$0.436304\pi$
$912$	0	0
$913$	3.61843e7	1.43662
$914$	2.51652e7	0.996402
$915$	2.89550e7	1.14333
$916$	1.70068e6	0.0669704
$917$	4.19722e6	0.164831
$918$	2.41387e6	0.0945381
$919$	−5.59078e6	−0.218365	−0.109183	−	0.994022i	$-0.534823\pi$
$919$	−5.59078e6	−0.218365	−0.109183	+	0.994022i	$0.534823\pi$
$920$	−6.82884e6	−0.265997
$921$	5.76464e6	0.223936
$922$	−1.79635e7	−0.695926
$923$	−7.35744e6	−0.284264
$924$	2.48971e7	0.959331
$925$	−4.26160e7	−1.63764
$926$	−2.42701e7	−0.930132
$927$	−1.67514e7	−0.640255
$928$	−5.19747e6	−0.198117
$929$	2.46507e7	0.937107	0.468553	−	0.883435i	$-0.344775\pi$
$929$	2.46507e7	0.937107	0.468553	+	0.883435i	$0.344775\pi$
$930$	4.72885e7	1.79287
$931$	0	0
$932$	8.09937e6	0.305430
$933$	5.42311e7	2.03960
$934$	2.75419e7	1.03306
$935$	−2.83113e7	−1.05909
$936$	−7.66487e6	−0.285966
$937$	−3.14819e7	−1.17142	−0.585709	−	0.810522i	$-0.699184\pi$
$937$	−3.14819e7	−1.17142	−0.585709	+	0.810522i	$0.699184\pi$
$938$	1.70108e7	0.631274
$939$	−1.28480e7	−0.475524
$940$	3.59074e7	1.32545
$941$	1.02201e7	0.376254	0.188127	−	0.982145i	$-0.439758\pi$
$941$	1.02201e7	0.376254	0.188127	+	0.982145i	$0.439758\pi$
$942$	3.09591e6	0.113674
$943$	1.32347e7	0.484659
$944$	1.05323e7	0.384674
$945$	−9.29914e6	−0.338738
$946$	1.61614e7	0.587151
$947$	1.55025e7	0.561728	0.280864	−	0.959748i	$-0.409379\pi$
$947$	1.55025e7	0.561728	0.280864	+	0.959748i	$0.409379\pi$
$948$	−3.28079e7	−1.18565
$949$	2.69972e6	0.0973091
$950$	0	0
$951$	2.66976e7	0.957239
$952$	−1.21717e7	−0.435272
$953$	3.57658e7	1.27566	0.637832	−	0.770176i	$-0.279832\pi$
$953$	3.57658e7	1.27566	0.637832	+	0.770176i	$0.279832\pi$
$954$	3.30652e7	1.17625
$955$	8.66424e6	0.307413
$956$	−1.22057e7	−0.431935
$957$	4.11832e7	1.45358
$958$	−2.44586e7	−0.861028
$959$	−6.52669e6	−0.229164
$960$	−7.39139e6	−0.258850
$961$	1.42907e7	0.499167
$962$	2.34622e7	0.817394
$963$	−4.70182e6	−0.163380
$964$	−3.62030e6	−0.125473
$965$	−3.45479e7	−1.19427
$966$	2.32632e7	0.802095
$967$	1.25453e7	0.431434	0.215717	−	0.976456i	$-0.430791\pi$
$967$	1.25453e7	0.431434	0.215717	+	0.976456i	$0.430791\pi$
$968$	2.09185e6	0.0717534
$969$	0	0
$970$	−2.60662e7	−0.889507
$971$	−2.46429e7	−0.838772	−0.419386	−	0.907808i	$-0.637755\pi$
$971$	−2.46429e7	−0.838772	−0.419386	+	0.907808i	$0.637755\pi$
$972$	2.11346e7	0.717509
$973$	1.07771e7	0.364940
$974$	−7.68559e6	−0.259585
$975$	−3.24046e7	−1.09168
$976$	−4.10769e6	−0.138030
$977$	−3.71024e7	−1.24356	−0.621778	−	0.783194i	$-0.713589\pi$
$977$	−3.71024e7	−1.24356	−0.621778	+	0.783194i	$0.713589\pi$
$978$	−1.37018e7	−0.458068
$979$	3.93906e7	1.31352
$980$	2.54627e7	0.846913
$981$	2.34876e7	0.779232
$982$	1.71293e7	0.566841
$983$	1.69378e7	0.559079	0.279539	−	0.960134i	$-0.409818\pi$
$983$	1.69378e7	0.559079	0.279539	+	0.960134i	$0.409818\pi$
$984$	1.43250e7	0.471636
$985$	−1.81883e7	−0.597313
$986$	−2.01337e7	−0.659526
$987$	−1.22322e8	−3.99680
$988$	0	0
$989$	1.51007e7	0.490916
$990$	3.08179e7	0.999343
$991$	−3.65959e6	−0.118372	−0.0591859	−	0.998247i	$-0.518850\pi$
$991$	−3.65959e6	−0.118372	−0.0591859	+	0.998247i	$0.518850\pi$
$992$	−6.70856e6	−0.216446
$993$	−1.51295e7	−0.486914
$994$	1.27180e7	0.408274
$995$	7.28950e7	2.33421
$996$	3.65948e7	1.16888
$997$	2.59425e7	0.826559	0.413280	−	0.910604i	$-0.364383\pi$
$997$	2.59425e7	0.826559	0.413280	+	0.910604i	$0.364383\pi$
$998$	−2.94867e7	−0.937129
$999$	8.04305e6	0.254980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.q.1.4		15
19.2	odd	18		38.6.e.b.23.4	yes	30
19.10	odd	18		38.6.e.b.5.4	✓	30
19.18	odd	2		722.6.a.r.1.12		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.5.4	✓	30	19.10	odd	18
38.6.e.b.23.4	yes	30	19.2	odd	18
722.6.a.q.1.4		15	1.1	even	1	trivial
722.6.a.r.1.12		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -22.6466 q^{3} +16.0000 q^{4} +79.6824 q^{5} +90.5866 q^{6} +191.779 q^{7} -64.0000 q^{8} +269.871 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -22.6466 q^{3} +16.0000 q^{4} +79.6824 q^{5} +90.5866 q^{6} +191.779 q^{7} -64.0000 q^{8} +269.871 q^{9} -318.730 q^{10} -358.282 q^{11} -362.346 q^{12} +443.782 q^{13} -767.114 q^{14} -1804.54 q^{15} +256.000 q^{16} +991.683 q^{17} -1079.48 q^{18} +1274.92 q^{20} -4343.14 q^{21} +1433.13 q^{22} +1339.07 q^{23} +1449.39 q^{24} +3224.28 q^{25} -1775.13 q^{26} -608.528 q^{27} +3068.46 q^{28} +5075.65 q^{29} +7218.16 q^{30} +6551.33 q^{31} -1024.00 q^{32} +8113.88 q^{33} -3966.73 q^{34} +15281.4 q^{35} +4317.93 q^{36} -13217.2 q^{37} -10050.2 q^{39} -5099.67 q^{40} +9883.49 q^{41} +17372.6 q^{42} +11277.0 q^{43} -5732.51 q^{44} +21503.9 q^{45} -5356.30 q^{46} +28164.4 q^{47} -5797.54 q^{48} +19972.0 q^{49} -12897.1 q^{50} -22458.3 q^{51} +7100.50 q^{52} -30630.6 q^{53} +2434.11 q^{54} -28548.7 q^{55} -12273.8 q^{56} -20302.6 q^{58} +41141.7 q^{59} -28872.6 q^{60} -16045.6 q^{61} -26205.3 q^{62} +51755.4 q^{63} +4096.00 q^{64} +35361.6 q^{65} -32455.5 q^{66} -22175.1 q^{67} +15866.9 q^{68} -30325.5 q^{69} -61125.5 q^{70} -16579.0 q^{71} -17271.7 q^{72} +6083.45 q^{73} +52868.9 q^{74} -73019.2 q^{75} -68710.7 q^{77} +40200.7 q^{78} +90542.9 q^{79} +20398.7 q^{80} -51797.4 q^{81} -39534.0 q^{82} -100994. q^{83} -69490.3 q^{84} +79019.7 q^{85} -45108.0 q^{86} -114946. q^{87} +22930.0 q^{88} -109943. q^{89} -86015.7 q^{90} +85107.8 q^{91} +21425.2 q^{92} -148366. q^{93} -112658. q^{94} +23190.2 q^{96} +81781.7 q^{97} -79888.0 q^{98} -96689.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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