LMFDB - Embedded newform 722.6.a.q.1.11

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			1.11
Root			$10.3629$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} +10.7102 q^{3} +16.0000 q^{4} +59.4057 q^{5} -42.8408 q^{6} -230.434 q^{7} -64.0000 q^{8} -128.291 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +10.7102 q^{3} +16.0000 q^{4} +59.4057 q^{5} -42.8408 q^{6} -230.434 q^{7} -64.0000 q^{8} -128.291 q^{9} -237.623 q^{10} -57.4759 q^{11} +171.363 q^{12} +1077.85 q^{13} +921.736 q^{14} +636.248 q^{15} +256.000 q^{16} -863.265 q^{17} +513.165 q^{18} +950.492 q^{20} -2468.00 q^{21} +229.903 q^{22} +1593.33 q^{23} -685.454 q^{24} +404.043 q^{25} -4311.40 q^{26} -3976.61 q^{27} -3686.94 q^{28} +7237.73 q^{29} -2544.99 q^{30} -1203.68 q^{31} -1024.00 q^{32} -615.579 q^{33} +3453.06 q^{34} -13689.1 q^{35} -2052.66 q^{36} -14445.2 q^{37} +11544.0 q^{39} -3801.97 q^{40} -14657.9 q^{41} +9871.99 q^{42} +17365.8 q^{43} -919.614 q^{44} -7621.24 q^{45} -6373.33 q^{46} -4521.13 q^{47} +2741.81 q^{48} +36292.9 q^{49} -1616.17 q^{50} -9245.75 q^{51} +17245.6 q^{52} -610.009 q^{53} +15906.4 q^{54} -3414.40 q^{55} +14747.8 q^{56} -28950.9 q^{58} +10875.7 q^{59} +10180.0 q^{60} +17011.2 q^{61} +4814.74 q^{62} +29562.7 q^{63} +4096.00 q^{64} +64030.5 q^{65} +2462.32 q^{66} +7498.58 q^{67} -13812.2 q^{68} +17064.9 q^{69} +54756.4 q^{70} +29544.3 q^{71} +8210.65 q^{72} +32333.6 q^{73} +57780.9 q^{74} +4327.38 q^{75} +13244.4 q^{77} -46176.1 q^{78} +30819.1 q^{79} +15207.9 q^{80} -11415.5 q^{81} +58631.5 q^{82} +37446.2 q^{83} -39488.0 q^{84} -51282.9 q^{85} -69463.1 q^{86} +77517.6 q^{87} +3678.46 q^{88} +8350.69 q^{89} +30485.0 q^{90} -248374. q^{91} +25493.3 q^{92} -12891.7 q^{93} +18084.5 q^{94} -10967.3 q^{96} +42085.2 q^{97} -145171. q^{98} +7373.66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	10.7102	0.687060	0.343530	−	0.939142i	$-0.388377\pi$
$3$	10.7102	0.687060	0.343530	+	0.939142i	$0.388377\pi$
$4$	16.0000	0.500000
$5$	59.4057	1.06268	0.531341	−	0.847158i	$-0.321688\pi$
$5$	59.4057	1.06268	0.531341	+	0.847158i	$0.321688\pi$
$6$	−42.8408	−0.485825
$7$	−230.434	−1.77747	−0.888734	−	0.458424i	$-0.848414\pi$
$7$	−230.434	−1.77747	−0.888734	+	0.458424i	$0.848414\pi$
$8$	−64.0000	−0.353553
$9$	−128.291	−0.527948
$10$	−237.623	−0.751430
$11$	−57.4759	−0.143220	−0.0716100	−	0.997433i	$-0.522814\pi$
$11$	−57.4759	−0.143220	−0.0716100	+	0.997433i	$0.522814\pi$
$12$	171.363	0.343530
$13$	1077.85	1.76889	0.884444	−	0.466646i	$-0.154538\pi$
$13$	1077.85	1.76889	0.884444	+	0.466646i	$0.154538\pi$
$14$	921.736	1.25686
$15$	636.248	0.730127
$16$	256.000	0.250000
$17$	−863.265	−0.724472	−0.362236	−	0.932086i	$-0.617987\pi$
$17$	−863.265	−0.724472	−0.362236	+	0.932086i	$0.617987\pi$
$18$	513.165	0.373316
$19$	0	0
$19$	0	0
$20$	950.492	0.531341
$21$	−2468.00	−1.22123
$22$	229.903	0.101272
$23$	1593.33	0.628039	0.314020	−	0.949417i	$-0.398324\pi$
$23$	1593.33	0.628039	0.314020	+	0.949417i	$0.398324\pi$
$24$	−685.454	−0.242913
$25$	404.043	0.129294
$26$	−4311.40	−1.25079
$27$	−3976.61	−1.04979
$28$	−3686.94	−0.888734
$29$	7237.73	1.59811	0.799056	−	0.601256i	$-0.205333\pi$
$29$	7237.73	1.59811	0.799056	+	0.601256i	$0.205333\pi$
$30$	−2544.99	−0.516278
$31$	−1203.68	−0.224962	−0.112481	−	0.993654i	$-0.535880\pi$
$31$	−1203.68	−0.224962	−0.112481	+	0.993654i	$0.535880\pi$
$32$	−1024.00	−0.176777
$33$	−615.579	−0.0984008
$34$	3453.06	0.512279
$35$	−13689.1	−1.88888
$36$	−2052.66	−0.263974
$37$	−14445.2	−1.73468	−0.867342	−	0.497713i	$-0.834173\pi$
$37$	−14445.2	−1.73468	−0.867342	+	0.497713i	$0.834173\pi$
$38$	0	0
$39$	11544.0	1.21533
$40$	−3801.97	−0.375715
$41$	−14657.9	−1.36179	−0.680897	−	0.732379i	$-0.738410\pi$
$41$	−14657.9	−1.36179	−0.680897	+	0.732379i	$0.738410\pi$
$42$	9871.99	0.863538
$43$	17365.8	1.43226	0.716132	−	0.697965i	$-0.245911\pi$
$43$	17365.8	1.43226	0.716132	+	0.697965i	$0.245911\pi$
$44$	−919.614	−0.0716100
$45$	−7621.24	−0.561041
$46$	−6373.33	−0.444091
$47$	−4521.13	−0.298540	−0.149270	−	0.988797i	$-0.547692\pi$
$47$	−4521.13	−0.298540	−0.149270	+	0.988797i	$0.547692\pi$
$48$	2741.81	0.171765
$49$	36292.9	2.15939
$50$	−1616.17	−0.0914244
$51$	−9245.75	−0.497756
$52$	17245.6	0.884444
$53$	−610.009	−0.0298295	−0.0149148	−	0.999889i	$-0.504748\pi$
$53$	−610.009	−0.0298295	−0.0149148	+	0.999889i	$0.504748\pi$
$54$	15906.4	0.742315
$55$	−3414.40	−0.152197
$56$	14747.8	0.628430
$57$	0	0
$58$	−28950.9	−1.13004
$59$	10875.7	0.406749	0.203374	−	0.979101i	$-0.434809\pi$
$59$	10875.7	0.406749	0.203374	+	0.979101i	$0.434809\pi$
$60$	10180.0	0.365063
$61$	17011.2	0.585344	0.292672	−	0.956213i	$-0.405456\pi$
$61$	17011.2	0.585344	0.292672	+	0.956213i	$0.405456\pi$
$62$	4814.74	0.159072
$63$	29562.7	0.938410
$64$	4096.00	0.125000
$65$	64030.5	1.87977
$66$	2462.32	0.0695799
$67$	7498.58	0.204076	0.102038	−	0.994780i	$-0.467464\pi$
$67$	7498.58	0.204076	0.102038	+	0.994780i	$0.467464\pi$
$68$	−13812.2	−0.362236
$69$	17064.9	0.431501
$70$	54756.4	1.33564
$71$	29544.3	0.695550	0.347775	−	0.937578i	$-0.386937\pi$
$71$	29544.3	0.695550	0.347775	+	0.937578i	$0.386937\pi$
$72$	8210.65	0.186658
$73$	32333.6	0.710145	0.355072	−	0.934839i	$-0.384456\pi$
$73$	32333.6	0.710145	0.355072	+	0.934839i	$0.384456\pi$
$74$	57780.9	1.22661
$75$	4327.38	0.0888325
$76$	0	0
$77$	13244.4	0.254569
$78$	−46176.1	−0.859370
$79$	30819.1	0.555588	0.277794	−	0.960641i	$-0.410397\pi$
$79$	30819.1	0.555588	0.277794	+	0.960641i	$0.410397\pi$
$80$	15207.9	0.265671
$81$	−11415.5	−0.193323
$82$	58631.5	0.962934
$83$	37446.2	0.596641	0.298321	−	0.954466i	$-0.403574\pi$
$83$	37446.2	0.596641	0.298321	+	0.954466i	$0.403574\pi$
$84$	−39488.0	−0.610614
$85$	−51282.9	−0.769884
$86$	−69463.1	−1.01276
$87$	77517.6	1.09800
$88$	3678.46	0.0506359
$89$	8350.69	0.111750	0.0558750	−	0.998438i	$-0.482205\pi$
$89$	8350.69	0.111750	0.0558750	+	0.998438i	$0.482205\pi$
$90$	30485.0	0.396716
$91$	−248374.	−3.14414
$92$	25493.3	0.314020
$93$	−12891.7	−0.154562
$94$	18084.5	0.211099
$95$	0	0
$96$	−10967.3	−0.121456
$97$	42085.2	0.454151	0.227076	−	0.973877i	$-0.427084\pi$
$97$	42085.2	0.454151	0.227076	+	0.973877i	$0.427084\pi$
$98$	−145171.	−1.52692
$99$	7373.66	0.0756127
$100$	6464.68	0.0646468
$101$	−51365.0	−0.501030	−0.250515	−	0.968113i	$-0.580600\pi$
$101$	−51365.0	−0.501030	−0.250515	+	0.968113i	$0.580600\pi$
$102$	36983.0	0.351967
$103$	28090.6	0.260897	0.130448	−	0.991455i	$-0.458358\pi$
$103$	28090.6	0.260897	0.130448	+	0.991455i	$0.458358\pi$
$104$	−68982.5	−0.625396
$105$	−146613.	−1.29778
$106$	2440.04	0.0210927
$107$	142335.	1.20186	0.600929	−	0.799303i	$-0.294798\pi$
$107$	142335.	1.20186	0.600929	+	0.799303i	$0.294798\pi$
$108$	−63625.7	−0.524896
$109$	−52692.8	−0.424800	−0.212400	−	0.977183i	$-0.568128\pi$
$109$	−52692.8	−0.424800	−0.212400	+	0.977183i	$0.568128\pi$
$110$	13657.6	0.107620
$111$	−154712.	−1.19183
$112$	−58991.1	−0.444367
$113$	−88516.5	−0.652121	−0.326060	−	0.945349i	$-0.605721\pi$
$113$	−88516.5	−0.652121	−0.326060	+	0.945349i	$0.605721\pi$
$114$	0	0
$115$	94653.1	0.667406
$116$	115804.	0.799056
$117$	−138279.	−0.933881
$118$	−43502.7	−0.287615
$119$	198926.	1.28773
$120$	−40719.9	−0.258139
$121$	−157748.	−0.979488
$122$	−68044.9	−0.413900
$123$	−156989.	−0.935635
$124$	−19259.0	−0.112481
$125$	−161641.	−0.925284
$126$	−118251.	−0.663556
$127$	114887.	0.632065	0.316033	−	0.948748i	$-0.397649\pi$
$127$	114887.	0.632065	0.316033	+	0.948748i	$0.397649\pi$
$128$	−16384.0	−0.0883883
$129$	185991.	0.984052
$130$	−256122.	−1.32920
$131$	282064.	1.43605	0.718025	−	0.696017i	$-0.245046\pi$
$131$	282064.	1.43605	0.718025	+	0.696017i	$0.245046\pi$
$132$	−9849.26	−0.0492004
$133$	0	0
$134$	−29994.3	−0.144304
$135$	−236233.	−1.11560
$136$	55249.0	0.256140
$137$	383656.	1.74639	0.873193	−	0.487375i	$-0.162046\pi$
$137$	383656.	1.74639	0.873193	+	0.487375i	$0.162046\pi$
$138$	−68259.7	−0.305117
$139$	−264702.	−1.16204	−0.581019	−	0.813890i	$-0.697346\pi$
$139$	−264702.	−1.16204	−0.581019	+	0.813890i	$0.697346\pi$
$140$	−219026.	−0.944441
$141$	−48422.2	−0.205115
$142$	−118177.	−0.491828
$143$	−61950.4	−0.253340
$144$	−32842.6	−0.131987
$145$	429963.	1.69829
$146$	−129334.	−0.502148
$147$	388704.	1.48363
$148$	−231124.	−0.867342
$149$	414622.	1.52998	0.764991	−	0.644040i	$-0.222743\pi$
$149$	414622.	1.52998	0.764991	+	0.644040i	$0.222743\pi$
$150$	−17309.5	−0.0628141
$151$	207430.	0.740338	0.370169	−	0.928964i	$-0.379300\pi$
$151$	207430.	0.740338	0.370169	+	0.928964i	$0.379300\pi$
$152$	0	0
$153$	110749.	0.382484
$154$	−52977.6	−0.180007
$155$	−71505.8	−0.239063
$156$	184704.	0.607667
$157$	76133.6	0.246506	0.123253	−	0.992375i	$-0.460667\pi$
$157$	76133.6	0.246506	0.123253	+	0.992375i	$0.460667\pi$
$158$	−123276.	−0.392860
$159$	−6533.32	−0.0204947
$160$	−60831.5	−0.187857
$161$	−367158.	−1.11632
$162$	45662.1	0.136700
$163$	462791.	1.36432	0.682159	−	0.731204i	$-0.261041\pi$
$163$	462791.	1.36432	0.682159	+	0.731204i	$0.261041\pi$
$164$	−234526.	−0.680897
$165$	−36568.9	−0.104569
$166$	−149785.	−0.421889
$167$	584798.	1.62261	0.811306	−	0.584622i	$-0.198757\pi$
$167$	584798.	1.62261	0.811306	+	0.584622i	$0.198757\pi$
$168$	157952.	0.431769
$169$	790470.	2.12897
$170$	205132.	0.544390
$171$	0	0
$172$	277852.	0.716132
$173$	−181323.	−0.460614	−0.230307	−	0.973118i	$-0.573973\pi$
$173$	−181323.	−0.460614	−0.230307	+	0.973118i	$0.573973\pi$
$174$	−310070.	−0.776403
$175$	−93105.2	−0.229815
$176$	−14713.8	−0.0358050
$177$	116481.	0.279461
$178$	−33402.8	−0.0790192
$179$	−132775.	−0.309731	−0.154866	−	0.987936i	$-0.549494\pi$
$179$	−132775.	−0.309731	−0.154866	+	0.987936i	$0.549494\pi$
$180$	−121940.	−0.280520
$181$	−691575.	−1.56907	−0.784536	−	0.620083i	$-0.787099\pi$
$181$	−691575.	−1.56907	−0.784536	+	0.620083i	$0.787099\pi$
$182$	993494.	2.22324
$183$	182194.	0.402166
$184$	−101973.	−0.222045
$185$	−858130.	−1.84342
$186$	51566.9	0.109292
$187$	49616.9	0.103759
$188$	−72338.0	−0.149270
$189$	916346.	1.86597
$190$	0	0
$191$	210150.	0.416818	0.208409	−	0.978042i	$-0.433171\pi$
$191$	210150.	0.416818	0.208409	+	0.978042i	$0.433171\pi$
$192$	43869.0	0.0858826
$193$	−192123.	−0.371267	−0.185633	−	0.982619i	$-0.559434\pi$
$193$	−192123.	−0.371267	−0.185633	+	0.982619i	$0.559434\pi$
$194$	−168341.	−0.321133
$195$	685781.	1.29151
$196$	580686.	1.07969
$197$	−151632.	−0.278372	−0.139186	−	0.990266i	$-0.544449\pi$
$197$	−151632.	−0.278372	−0.139186	+	0.990266i	$0.544449\pi$
$198$	−29494.6	−0.0534663
$199$	283510.	0.507500	0.253750	−	0.967270i	$-0.418336\pi$
$199$	283510.	0.507500	0.253750	+	0.967270i	$0.418336\pi$
$200$	−25858.7	−0.0457122
$201$	80311.4	0.140213
$202$	205460.	0.354282
$203$	−1.66782e6	−2.84059
$204$	−147932.	−0.248878
$205$	−870762.	−1.44715
$206$	−112363.	−0.184482
$207$	−204411.	−0.331572
$208$	275930.	0.442222
$209$	0	0
$210$	586453.	0.917667
$211$	137732.	0.212975	0.106487	−	0.994314i	$-0.466040\pi$
$211$	137732.	0.212975	0.106487	+	0.994314i	$0.466040\pi$
$212$	−9760.14	−0.0149148
$213$	316426.	0.477885
$214$	−569341.	−0.849841
$215$	1.03163e6	1.52204
$216$	254503.	0.371158
$217$	277370.	0.399862
$218$	210771.	0.300379
$219$	346300.	0.487913
$220$	−54630.4	−0.0760987
$221$	−930471.	−1.28151
$222$	618846.	0.842753
$223$	250278.	0.337023	0.168512	−	0.985700i	$-0.446104\pi$
$223$	250278.	0.337023	0.168512	+	0.985700i	$0.446104\pi$
$224$	235964.	0.314215
$225$	−51835.2	−0.0682603
$226$	354066.	0.461119
$227$	1.40294e6	1.80707	0.903535	−	0.428513i	$-0.140963\pi$
$227$	1.40294e6	1.80707	0.903535	+	0.428513i	$0.140963\pi$
$228$	0	0
$229$	538672.	0.678790	0.339395	−	0.940644i	$-0.389778\pi$
$229$	538672.	0.678790	0.339395	+	0.940644i	$0.389778\pi$
$230$	−378612.	−0.471927
$231$	141850.	0.174904
$232$	−463215.	−0.565018
$233$	761095.	0.918437	0.459218	−	0.888323i	$-0.348130\pi$
$233$	761095.	0.918437	0.459218	+	0.888323i	$0.348130\pi$
$234$	553116.	0.660354
$235$	−268581.	−0.317253
$236$	174011.	0.203374
$237$	330079.	0.381722
$238$	−795703.	−0.910560
$239$	791495.	0.896300	0.448150	−	0.893958i	$-0.352083\pi$
$239$	791495.	0.896300	0.448150	+	0.893958i	$0.352083\pi$
$240$	162880.	0.182532
$241$	−428817.	−0.475587	−0.237793	−	0.971316i	$-0.576424\pi$
$241$	−428817.	−0.475587	−0.237793	+	0.971316i	$0.576424\pi$
$242$	630990.	0.692603
$243$	844053.	0.916968
$244$	272180.	0.292672
$245$	2.15600e6	2.29474
$246$	627956.	0.661594
$247$	0	0
$248$	77035.8	0.0795360
$249$	401057.	0.409928
$250$	646562.	0.654275
$251$	1.67250e6	1.67565	0.837823	−	0.545942i	$-0.183828\pi$
$251$	1.67250e6	1.67565	0.837823	+	0.545942i	$0.183828\pi$
$252$	473003.	0.469205
$253$	−91578.1	−0.0899478
$254$	−459548.	−0.446938
$255$	−549251.	−0.528957
$256$	65536.0	0.0625000
$257$	−657822.	−0.621263	−0.310631	−	0.950530i	$-0.600540\pi$
$257$	−657822.	−0.621263	−0.310631	+	0.950530i	$0.600540\pi$
$258$	−743964.	−0.695830
$259$	3.32867e6	3.08334
$260$	1.02449e6	0.939883
$261$	−928538.	−0.843720
$262$	−1.12826e6	−1.01544
$263$	−1.58346e6	−1.41162	−0.705810	−	0.708401i	$-0.749417\pi$
$263$	−1.58346e6	−1.41162	−0.705810	+	0.708401i	$0.749417\pi$
$264$	39397.0	0.0347899
$265$	−36238.0	−0.0316993
$266$	0	0
$267$	89437.7	0.0767790
$268$	119977.	0.102038
$269$	−22834.2	−0.0192400	−0.00961998	−	0.999954i	$-0.503062\pi$
$269$	−22834.2	−0.0192400	−0.00961998	+	0.999954i	$0.503062\pi$
$270$	944934.	0.788845
$271$	−272037.	−0.225012	−0.112506	−	0.993651i	$-0.535888\pi$
$271$	−272037.	−0.225012	−0.112506	+	0.993651i	$0.535888\pi$
$272$	−220996.	−0.181118
$273$	−2.66013e6	−2.16021
$274$	−1.53462e6	−1.23488
$275$	−23222.7	−0.0185174
$276$	273039.	0.215750
$277$	−2.25937e6	−1.76924	−0.884621	−	0.466312i	$-0.845583\pi$
$277$	−2.25937e6	−1.76924	−0.884621	+	0.466312i	$0.845583\pi$
$278$	1.05881e6	0.821685
$279$	154422.	0.118768
$280$	876103.	0.667821
$281$	1.02574e6	0.774946	0.387473	−	0.921881i	$-0.373348\pi$
$281$	1.02574e6	0.774946	0.387473	+	0.921881i	$0.373348\pi$
$282$	193689.	0.145038
$283$	322624.	0.239459	0.119729	−	0.992807i	$-0.461797\pi$
$283$	322624.	0.239459	0.119729	+	0.992807i	$0.461797\pi$
$284$	472709.	0.347775
$285$	0	0
$286$	247802.	0.179139
$287$	3.37767e6	2.42054
$288$	131370.	0.0933289
$289$	−674631.	−0.475140
$290$	−1.71985e6	−1.20087
$291$	450742.	0.312029
$292$	517338.	0.355072
$293$	−1.42198e6	−0.967662	−0.483831	−	0.875161i	$-0.660755\pi$
$293$	−1.42198e6	−0.967662	−0.483831	+	0.875161i	$0.660755\pi$
$294$	−1.55482e6	−1.04909
$295$	646078.	0.432245
$296$	924495.	0.613303
$297$	228559.	0.150351
$298$	−1.65849e6	−1.08186
$299$	1.71737e6	1.11093
$300$	69238.1	0.0444163
$301$	−4.00167e6	−2.54580
$302$	−829721.	−0.523498
$303$	−550130.	−0.344238
$304$	0	0
$305$	1.01056e6	0.622034
$306$	−442998.	−0.270457
$307$	−1.48661e6	−0.900225	−0.450112	−	0.892972i	$-0.648616\pi$
$307$	−1.48661e6	−0.900225	−0.450112	+	0.892972i	$0.648616\pi$
$308$	211910.	0.127284
$309$	300857.	0.179252
$310$	286023.	0.169043
$311$	2.49920e6	1.46521	0.732606	−	0.680653i	$-0.238304\pi$
$311$	2.49920e6	1.46521	0.732606	+	0.680653i	$0.238304\pi$
$312$	−738817.	−0.429685
$313$	2.05577e6	1.18608	0.593041	−	0.805172i	$-0.297927\pi$
$313$	2.05577e6	1.18608	0.593041	+	0.805172i	$0.297927\pi$
$314$	−304535.	−0.174306
$315$	1.75619e6	0.997232
$316$	493106.	0.277794
$317$	−712882.	−0.398446	−0.199223	−	0.979954i	$-0.563842\pi$
$317$	−712882.	−0.398446	−0.199223	+	0.979954i	$0.563842\pi$
$318$	26133.3	0.0144919
$319$	−415995.	−0.228882
$320$	243326.	0.132835
$321$	1.52444e6	0.825749
$322$	1.46863e6	0.789357
$323$	0	0
$324$	−182648.	−0.0966615
$325$	435498.	0.228706
$326$	−1.85116e6	−0.964719
$327$	−564351.	−0.291863
$328$	938104.	0.481467
$329$	1.04182e6	0.530644
$330$	146276.	0.0739413
$331$	3.40084e6	1.70615	0.853073	−	0.521791i	$-0.174736\pi$
$331$	3.40084e6	1.70615	0.853073	+	0.521791i	$0.174736\pi$
$332$	599140.	0.298321
$333$	1.85320e6	0.915823
$334$	−2.33919e6	−1.14736
$335$	445459.	0.216868
$336$	−631807.	−0.305307
$337$	−1.72830e6	−0.828981	−0.414491	−	0.910054i	$-0.636040\pi$
$337$	−1.72830e6	−0.828981	−0.414491	+	0.910054i	$0.636040\pi$
$338$	−3.16188e6	−1.50541
$339$	−948031.	−0.448047
$340$	−820526.	−0.384942
$341$	69182.8	0.0322190
$342$	0	0
$343$	−4.49020e6	−2.06078
$344$	−1.11141e6	−0.506382
$345$	1.01375e6	0.458548
$346$	725290.	0.325703
$347$	−1.21228e6	−0.540482	−0.270241	−	0.962793i	$-0.587103\pi$
$347$	−1.21228e6	−0.540482	−0.270241	+	0.962793i	$0.587103\pi$
$348$	1.24028e6	0.549000
$349$	−1.54539e6	−0.679165	−0.339582	−	0.940576i	$-0.610286\pi$
$349$	−1.54539e6	−0.679165	−0.339582	+	0.940576i	$0.610286\pi$
$350$	372421.	0.162504
$351$	−4.28619e6	−1.85697
$352$	58855.3	0.0253180
$353$	3.32474e6	1.42011	0.710053	−	0.704148i	$-0.248671\pi$
$353$	3.32474e6	1.42011	0.710053	+	0.704148i	$0.248671\pi$
$354$	−465923.	−0.197609
$355$	1.75510e6	0.739149
$356$	133611.	0.0558750
$357$	2.13054e6	0.884745
$358$	531102.	0.219013
$359$	−1.51122e6	−0.618859	−0.309430	−	0.950922i	$-0.600138\pi$
$359$	−1.51122e6	−0.618859	−0.309430	+	0.950922i	$0.600138\pi$
$360$	487760.	0.198358
$361$	0	0
$362$	2.76630e6	1.10950
$363$	−1.68951e6	−0.672967
$364$	−3.97398e6	−1.57207
$365$	1.92080e6	0.754658
$366$	−728775.	−0.284375
$367$	−712916.	−0.276295	−0.138147	−	0.990412i	$-0.544115\pi$
$367$	−712916.	−0.276295	−0.138147	+	0.990412i	$0.544115\pi$
$368$	407893.	0.157010
$369$	1.88048e6	0.718957
$370$	3.43252e6	1.30349
$371$	140567.	0.0530210
$372$	−206267.	−0.0772811
$373$	−228224.	−0.0849356	−0.0424678	−	0.999098i	$-0.513522\pi$
$373$	−228224.	−0.0849356	−0.0424678	+	0.999098i	$0.513522\pi$
$374$	−198468.	−0.0733687
$375$	−1.73120e6	−0.635726
$376$	289352.	0.105550
$377$	7.80119e6	2.82688
$378$	−3.66538e6	−1.31944
$379$	3.66205e6	1.30956	0.654781	−	0.755819i	$-0.272761\pi$
$379$	3.66205e6	1.30956	0.654781	+	0.755819i	$0.272761\pi$
$380$	0	0
$381$	1.23046e6	0.434267
$382$	−840601.	−0.294735
$383$	2.91364e6	1.01494	0.507468	−	0.861670i	$-0.330581\pi$
$383$	2.91364e6	1.01494	0.507468	+	0.861670i	$0.330581\pi$
$384$	−175476.	−0.0607281
$385$	786793.	0.270526
$386$	768492.	0.262525
$387$	−2.22788e6	−0.756161
$388$	673364.	0.227076
$389$	−563568.	−0.188830	−0.0944152	−	0.995533i	$-0.530098\pi$
$389$	−563568.	−0.188830	−0.0944152	+	0.995533i	$0.530098\pi$
$390$	−2.74312e6	−0.913238
$391$	−1.37547e6	−0.454997
$392$	−2.32274e6	−0.763459
$393$	3.02097e6	0.986653
$394$	606529.	0.196839
$395$	1.83083e6	0.590413
$396$	117979.	0.0378064
$397$	3.58102e6	1.14033	0.570165	−	0.821531i	$-0.306879\pi$
$397$	3.58102e6	1.14033	0.570165	+	0.821531i	$0.306879\pi$
$398$	−1.13404e6	−0.358857
$399$	0	0
$400$	103435.	0.0323234
$401$	361734.	0.112339	0.0561693	−	0.998421i	$-0.482111\pi$
$401$	361734.	0.112339	0.0561693	+	0.998421i	$0.482111\pi$
$402$	−321246.	−0.0991453
$403$	−1.29739e6	−0.397932
$404$	−821839.	−0.250515
$405$	−678148.	−0.205441
$406$	6.67128e6	2.00860
$407$	830252.	0.248442
$408$	591728.	0.175983
$409$	−1.77787e6	−0.525522	−0.262761	−	0.964861i	$-0.584633\pi$
$409$	−1.77787e6	−0.525522	−0.262761	+	0.964861i	$0.584633\pi$
$410$	3.48305e6	1.02329
$411$	4.10903e6	1.19987
$412$	449450.	0.130448
$413$	−2.50613e6	−0.722983
$414$	817643.	0.234457
$415$	2.22452e6	0.634040
$416$	−1.10372e6	−0.312698
$417$	−2.83501e6	−0.798390
$418$	0	0
$419$	−6.03219e6	−1.67857	−0.839286	−	0.543690i	$-0.817027\pi$
$419$	−6.03219e6	−1.67857	−0.839286	+	0.543690i	$0.817027\pi$
$420$	−2.34581e6	−0.648888
$421$	5.13129e6	1.41098	0.705491	−	0.708719i	$-0.250727\pi$
$421$	5.13129e6	1.41098	0.705491	+	0.708719i	$0.250727\pi$
$422$	−550928.	−0.150596
$423$	580021.	0.157613
$424$	39040.6	0.0105463
$425$	−348796.	−0.0936697
$426$	−1.26570e6	−0.337916
$427$	−3.91996e6	−1.04043
$428$	2.27736e6	0.600929
$429$	−663502.	−0.174060
$430$	−4.12651e6	−1.07625
$431$	−2.13211e6	−0.552861	−0.276430	−	0.961034i	$-0.589151\pi$
$431$	−2.13211e6	−0.552861	−0.276430	+	0.961034i	$0.589151\pi$
$432$	−1.01801e6	−0.262448
$433$	1.24666e6	0.319542	0.159771	−	0.987154i	$-0.448924\pi$
$433$	1.24666e6	0.319542	0.159771	+	0.987154i	$0.448924\pi$
$434$	−1.10948e6	−0.282745
$435$	4.60499e6	1.16683
$436$	−843084.	−0.212400
$437$	0	0
$438$	−1.38520e6	−0.345006
$439$	1.35155e6	0.334711	0.167356	−	0.985897i	$-0.446477\pi$
$439$	1.35155e6	0.334711	0.167356	+	0.985897i	$0.446477\pi$
$440$	218521.	0.0538099
$441$	−4.65606e6	−1.14005
$442$	3.72188e6	0.906165
$443$	−548879.	−0.132882	−0.0664412	−	0.997790i	$-0.521164\pi$
$443$	−548879.	−0.132882	−0.0664412	+	0.997790i	$0.521164\pi$
$444$	−2.47538e6	−0.595916
$445$	496079.	0.118755
$446$	−1.00111e6	−0.238311
$447$	4.44069e6	1.05119
$448$	−943858.	−0.222183
$449$	−7.31923e6	−1.71336	−0.856682	−	0.515844i	$-0.827478\pi$
$449$	−7.31923e6	−1.71336	−0.856682	+	0.515844i	$0.827478\pi$
$450$	207341.	0.0482673
$451$	842474.	0.195036
$452$	−1.41626e6	−0.326060
$453$	2.22162e6	0.508657
$454$	−5.61177e6	−1.27779
$455$	−1.47548e7	−3.34122
$456$	0	0
$457$	5.17857e6	1.15990	0.579949	−	0.814653i	$-0.303073\pi$
$457$	5.17857e6	1.15990	0.579949	+	0.814653i	$0.303073\pi$
$458$	−2.15469e6	−0.479977
$459$	3.43287e6	0.760546
$460$	1.51445e6	0.333703
$461$	1.03393e6	0.226590	0.113295	−	0.993561i	$-0.463860\pi$
$461$	1.03393e6	0.226590	0.113295	+	0.993561i	$0.463860\pi$
$462$	−567401.	−0.123676
$463$	−2.23229e6	−0.483947	−0.241973	−	0.970283i	$-0.577795\pi$
$463$	−2.23229e6	−0.483947	−0.241973	+	0.970283i	$0.577795\pi$
$464$	1.85286e6	0.399528
$465$	−765842.	−0.164251
$466$	−3.04438e6	−0.649433
$467$	−2.04756e6	−0.434454	−0.217227	−	0.976121i	$-0.569701\pi$
$467$	−2.04756e6	−0.434454	−0.217227	+	0.976121i	$0.569701\pi$
$468$	−2.21246e6	−0.466940
$469$	−1.72793e6	−0.362739
$470$	1.07432e6	0.224332
$471$	815407.	0.169364
$472$	−696043.	−0.143807
$473$	−998113.	−0.205129
$474$	−1.32032e6	−0.269918
$475$	0	0
$476$	3.18281e6	0.643863
$477$	78258.9	0.0157484
$478$	−3.16598e6	−0.633780
$479$	−747900.	−0.148938	−0.0744689	−	0.997223i	$-0.523726\pi$
$479$	−747900.	−0.148938	−0.0744689	+	0.997223i	$0.523726\pi$
$480$	−651518.	−0.129069
$481$	−1.55698e7	−3.06846
$482$	1.71527e6	0.336291
$483$	−3.93234e6	−0.766978
$484$	−2.52396e6	−0.489744
$485$	2.50010e6	0.482618
$486$	−3.37621e6	−0.648394
$487$	−7.05382e6	−1.34773	−0.673863	−	0.738856i	$-0.735366\pi$
$487$	−7.05382e6	−1.34773	−0.673863	+	0.738856i	$0.735366\pi$
$488$	−1.08872e6	−0.206950
$489$	4.95659e6	0.937369
$490$	−8.62402e6	−1.62263
$491$	−6.37713e6	−1.19377	−0.596886	−	0.802326i	$-0.703596\pi$
$491$	−6.37713e6	−1.19377	−0.596886	+	0.802326i	$0.703596\pi$
$492$	−2.51182e6	−0.467817
$493$	−6.24808e6	−1.15779
$494$	0	0
$495$	438038.	0.0803523
$496$	−308143.	−0.0562404
$497$	−6.80802e6	−1.23632
$498$	−1.60423e6	−0.289863
$499$	8.78382e6	1.57918	0.789591	−	0.613634i	$-0.210293\pi$
$499$	8.78382e6	1.57918	0.789591	+	0.613634i	$0.210293\pi$
$500$	−2.58625e6	−0.462642
$501$	6.26331e6	1.11483
$502$	−6.69001e6	−1.18486
$503$	7.24790e6	1.27730	0.638649	−	0.769498i	$-0.279494\pi$
$503$	7.24790e6	1.27730	0.638649	+	0.769498i	$0.279494\pi$
$504$	−1.89201e6	−0.331778
$505$	−3.05137e6	−0.532436
$506$	366313.	0.0636027
$507$	8.46610e6	1.46273
$508$	1.83819e6	0.316033
$509$	5.98071e6	1.02320	0.511598	−	0.859225i	$-0.329054\pi$
$509$	5.98071e6	1.02320	0.511598	+	0.859225i	$0.329054\pi$
$510$	2.19700e6	0.374029
$511$	−7.45076e6	−1.26226
$512$	−262144.	−0.0441942
$513$	0	0
$514$	2.63129e6	0.439299
$515$	1.66875e6	0.277250
$516$	2.97586e6	0.492026
$517$	259856.	0.0427569
$518$	−1.33147e7	−2.18025
$519$	−1.94200e6	−0.316469
$520$	−4.09795e6	−0.664598
$521$	−3.17340e6	−0.512189	−0.256095	−	0.966652i	$-0.582436\pi$
$521$	−3.17340e6	−0.512189	−0.256095	+	0.966652i	$0.582436\pi$
$522$	3.71415e6	0.596600
$523$	−1.94205e6	−0.310461	−0.155230	−	0.987878i	$-0.549612\pi$
$523$	−1.94205e6	−0.310461	−0.155230	+	0.987878i	$0.549612\pi$
$524$	4.51302e6	0.718025
$525$	−997176.	−0.157897
$526$	6.33384e6	0.998166
$527$	1.03910e6	0.162979
$528$	−157588.	−0.0246002
$529$	−3.89764e6	−0.605567
$530$	144952.	0.0224148
$531$	−1.39526e6	−0.214742
$532$	0	0
$533$	−1.57990e7	−2.40886
$534$	−357751.	−0.0542910
$535$	8.45553e6	1.27719
$536$	−479909.	−0.0721518
$537$	−1.42205e6	−0.212804
$538$	91336.6	0.0136047
$539$	−2.08596e6	−0.309268
$540$	−3.77973e6	−0.557798
$541$	9.39147e6	1.37956	0.689780	−	0.724019i	$-0.257707\pi$
$541$	9.39147e6	1.37956	0.689780	+	0.724019i	$0.257707\pi$
$542$	1.08815e6	0.159107
$543$	−7.40691e6	−1.07805
$544$	883983.	0.128070
$545$	−3.13025e6	−0.451428
$546$	1.06405e7	1.52750
$547$	−1.10539e6	−0.157960	−0.0789800	−	0.996876i	$-0.525166\pi$
$547$	−1.10539e6	−0.157960	−0.0789800	+	0.996876i	$0.525166\pi$
$548$	6.13849e6	0.873193
$549$	−2.18239e6	−0.309031
$550$	92890.8	0.0130938
$551$	0	0
$552$	−1.09216e6	−0.152559
$553$	−7.10178e6	−0.987539
$554$	9.03746e6	1.25104
$555$	−9.19075e6	−1.26654
$556$	−4.23523e6	−0.581019
$557$	−1.09427e7	−1.49447	−0.747236	−	0.664559i	$-0.768619\pi$
$557$	−1.09427e7	−1.49447	−0.747236	+	0.664559i	$0.768619\pi$
$558$	−617689.	−0.0839817
$559$	1.87177e7	2.53351
$560$	−3.50441e6	−0.472221
$561$	531408.	0.0712887
$562$	−4.10296e6	−0.547970
$563$	−2.58933e6	−0.344283	−0.172142	−	0.985072i	$-0.555069\pi$
$563$	−2.58933e6	−0.344283	−0.172142	+	0.985072i	$0.555069\pi$
$564$	−774755.	−0.102557
$565$	−5.25839e6	−0.692997
$566$	−1.29050e6	−0.169323
$567$	2.63053e6	0.343625
$568$	−1.89084e6	−0.245914
$569$	−1.79026e6	−0.231812	−0.115906	−	0.993260i	$-0.536977\pi$
$569$	−1.79026e6	−0.231812	−0.115906	+	0.993260i	$0.536977\pi$
$570$	0	0
$571$	4.81010e6	0.617396	0.308698	−	0.951160i	$-0.400107\pi$
$571$	4.81010e6	0.617396	0.308698	+	0.951160i	$0.400107\pi$
$572$	−991207.	−0.126670
$573$	2.25075e6	0.286379
$574$	−1.35107e7	−1.71158
$575$	643774.	0.0812015
$576$	−525481.	−0.0659935
$577$	1.41680e7	1.77161	0.885807	−	0.464055i	$-0.153606\pi$
$577$	1.41680e7	1.77161	0.885807	+	0.464055i	$0.153606\pi$
$578$	2.69852e6	0.335975
$579$	−2.05768e6	−0.255083
$580$	6.87940e6	0.849143
$581$	−8.62889e6	−1.06051
$582$	−1.80297e6	−0.220638
$583$	35060.8	0.00427219
$584$	−2.06935e6	−0.251074
$585$	−8.21457e6	−0.992419
$586$	5.68791e6	0.684240
$587$	9.33500e6	1.11820	0.559100	−	0.829100i	$-0.311147\pi$
$587$	9.33500e6	1.11820	0.559100	+	0.829100i	$0.311147\pi$
$588$	6.21927e6	0.741815
$589$	0	0
$590$	−2.58431e6	−0.305643
$591$	−1.62401e6	−0.191259
$592$	−3.69798e6	−0.433671
$593$	190413.	0.0222362	0.0111181	−	0.999938i	$-0.496461\pi$
$593$	190413.	0.0222362	0.0111181	+	0.999938i	$0.496461\pi$
$594$	−914236.	−0.106314
$595$	1.18173e7	1.36844
$596$	6.63395e6	0.764991
$597$	3.03645e6	0.348683
$598$	−6.86950e6	−0.785547
$599$	−1.38193e7	−1.57369	−0.786843	−	0.617153i	$-0.788286\pi$
$599$	−1.38193e7	−1.57369	−0.786843	+	0.617153i	$0.788286\pi$
$600$	−276952.	−0.0314070
$601$	4.76185e6	0.537761	0.268881	−	0.963173i	$-0.413346\pi$
$601$	4.76185e6	0.537761	0.268881	+	0.963173i	$0.413346\pi$
$602$	1.60067e7	1.80015
$603$	−962003.	−0.107742
$604$	3.31888e6	0.370169
$605$	−9.37111e6	−1.04088
$606$	2.20052e6	0.243413
$607$	−1.26279e7	−1.39110	−0.695552	−	0.718476i	$-0.744840\pi$
$607$	−1.26279e7	−1.39110	−0.695552	+	0.718476i	$0.744840\pi$
$608$	0	0
$609$	−1.78627e7	−1.95166
$610$	−4.04226e6	−0.439845
$611$	−4.87310e6	−0.528083
$612$	1.77199e6	0.191242
$613$	−3.20361e6	−0.344340	−0.172170	−	0.985067i	$-0.555078\pi$
$613$	−3.20361e6	−0.344340	−0.172170	+	0.985067i	$0.555078\pi$
$614$	5.94644e6	0.636555
$615$	−9.32605e6	−0.994283
$616$	−847641.	−0.0900037
$617$	3.51248e6	0.371450	0.185725	−	0.982602i	$-0.440537\pi$
$617$	3.51248e6	0.371450	0.185725	+	0.982602i	$0.440537\pi$
$618$	−1.20343e6	−0.126750
$619$	1.23431e7	1.29479	0.647394	−	0.762156i	$-0.275859\pi$
$619$	1.23431e7	1.29479	0.647394	+	0.762156i	$0.275859\pi$
$620$	−1.14409e6	−0.119531
$621$	−6.33606e6	−0.659311
$622$	−9.99681e6	−1.03606
$623$	−1.92428e6	−0.198632
$624$	2.95527e6	0.303833
$625$	−1.08650e7	−1.11258
$626$	−8.22310e6	−0.838686
$627$	0	0
$628$	1.21814e6	0.123253
$629$	1.24701e7	1.25673
$630$	−7.02478e6	−0.705149
$631$	2.65988e6	0.265944	0.132972	−	0.991120i	$-0.457548\pi$
$631$	2.65988e6	0.265944	0.132972	+	0.991120i	$0.457548\pi$
$632$	−1.97242e6	−0.196430
$633$	1.47514e6	0.146327
$634$	2.85153e6	0.281744
$635$	6.82495e6	0.671684
$636$	−104533.	−0.0102473
$637$	3.91183e7	3.81972
$638$	1.66398e6	0.161844
$639$	−3.79028e6	−0.367214
$640$	−973304.	−0.0939287
$641$	−8.18607e6	−0.786920	−0.393460	−	0.919342i	$-0.628722\pi$
$641$	−8.18607e6	−0.786920	−0.393460	+	0.919342i	$0.628722\pi$
$642$	−6.09776e6	−0.583892
$643$	1.34593e7	1.28380	0.641898	−	0.766790i	$-0.278147\pi$
$643$	1.34593e7	1.28380	0.641898	+	0.766790i	$0.278147\pi$
$644$	−5.87453e6	−0.558159
$645$	1.10489e7	1.04573
$646$	0	0
$647$	−3.71015e6	−0.348442	−0.174221	−	0.984707i	$-0.555741\pi$
$647$	−3.71015e6	−0.348442	−0.174221	+	0.984707i	$0.555741\pi$
$648$	730594.	0.0683500
$649$	−625089.	−0.0582546
$650$	−1.74199e6	−0.161720
$651$	2.97069e6	0.274729
$652$	7.40466e6	0.682159
$653$	9.26010e6	0.849831	0.424916	−	0.905233i	$-0.360304\pi$
$653$	9.26010e6	0.849831	0.424916	+	0.905233i	$0.360304\pi$
$654$	2.25740e6	0.206379
$655$	1.67562e7	1.52606
$656$	−3.75242e6	−0.340449
$657$	−4.14812e6	−0.374920
$658$	−4.16728e6	−0.375222
$659$	−1.88307e7	−1.68909	−0.844546	−	0.535483i	$-0.820129\pi$
$659$	−1.88307e7	−1.68909	−0.844546	+	0.535483i	$0.820129\pi$
$660$	−585103.	−0.0522844
$661$	1.94005e7	1.72706	0.863532	−	0.504294i	$-0.168247\pi$
$661$	1.94005e7	1.72706	0.863532	+	0.504294i	$0.168247\pi$
$662$	−1.36034e7	−1.20643
$663$	−9.96554e6	−0.880475
$664$	−2.39656e6	−0.210944
$665$	0	0
$666$	−7.41280e6	−0.647584
$667$	1.15321e7	1.00368
$668$	9.35677e6	0.811306
$669$	2.68053e6	0.231555
$670$	−1.78184e6	−0.153349
$671$	−977735.	−0.0838329
$672$	2.52723e6	0.215885
$673$	8.04822e6	0.684955	0.342478	−	0.939526i	$-0.388734\pi$
$673$	8.04822e6	0.684955	0.342478	+	0.939526i	$0.388734\pi$
$674$	6.91320e6	0.586178
$675$	−1.60672e6	−0.135732
$676$	1.26475e7	1.06448
$677$	9.58469e6	0.803723	0.401862	−	0.915700i	$-0.368363\pi$
$677$	9.58469e6	0.803723	0.401862	+	0.915700i	$0.368363\pi$
$678$	3.79212e6	0.316817
$679$	−9.69787e6	−0.807239
$680$	3.28211e6	0.272195
$681$	1.50258e7	1.24157
$682$	−276731.	−0.0227823
$683$	−1.10372e6	−0.0905327	−0.0452664	−	0.998975i	$-0.514414\pi$
$683$	−1.10372e6	−0.0905327	−0.0452664	+	0.998975i	$0.514414\pi$
$684$	0	0
$685$	2.27913e7	1.85585
$686$	1.79608e7	1.45719
$687$	5.76929e6	0.466370
$688$	4.44564e6	0.358066
$689$	−657499.	−0.0527651
$690$	−4.05502e6	−0.324243
$691$	−1.76135e7	−1.40330	−0.701651	−	0.712521i	$-0.747553\pi$
$691$	−1.76135e7	−1.40330	−0.701651	+	0.712521i	$0.747553\pi$
$692$	−2.90116e6	−0.230307
$693$	−1.69914e6	−0.134399
$694$	4.84914e6	0.382178
$695$	−1.57248e7	−1.23488
$696$	−4.96113e6	−0.388202
$697$	1.26536e7	0.986582
$698$	6.18157e6	0.480242
$699$	8.15149e6	0.631022
$700$	−1.48968e6	−0.114908
$701$	−1.09217e7	−0.839448	−0.419724	−	0.907652i	$-0.637873\pi$
$701$	−1.09217e7	−0.839448	−0.419724	+	0.907652i	$0.637873\pi$
$702$	1.71448e7	1.31307
$703$	0	0
$704$	−235421.	−0.0179025
$705$	−2.87656e6	−0.217972
$706$	−1.32990e7	−1.00417
$707$	1.18362e7	0.890564
$708$	1.86369e6	0.139730
$709$	1.66206e7	1.24174	0.620871	−	0.783913i	$-0.286779\pi$
$709$	1.66206e7	1.24174	0.620871	+	0.783913i	$0.286779\pi$
$710$	−7.02041e6	−0.522657
$711$	−3.95383e6	−0.293321
$712$	−534444.	−0.0395096
$713$	−1.91787e6	−0.141285
$714$	−8.52214e6	−0.625609
$715$	−3.68021e6	−0.269220
$716$	−2.12441e6	−0.154866
$717$	8.47708e6	0.615812
$718$	6.04488e6	0.437599
$719$	−2.55386e7	−1.84236	−0.921179	−	0.389138i	$-0.872773\pi$
$719$	−2.55386e7	−1.84236	−0.921179	+	0.389138i	$0.872773\pi$
$720$	−1.95104e6	−0.140260
$721$	−6.47304e6	−0.463735
$722$	0	0
$723$	−4.59273e6	−0.326757
$724$	−1.10652e7	−0.784536
$725$	2.92435e6	0.206626
$726$	6.75804e6	0.475860
$727$	−1.63800e7	−1.14941	−0.574707	−	0.818359i	$-0.694884\pi$
$727$	−1.63800e7	−1.14941	−0.574707	+	0.818359i	$0.694884\pi$
$728$	1.58959e7	1.11162
$729$	1.18140e7	0.823335
$730$	−7.68321e6	−0.533624
$731$	−1.49913e7	−1.03764
$732$	2.91510e6	0.201083
$733$	546964.	0.0376010	0.0188005	−	0.999823i	$-0.494015\pi$
$733$	546964.	0.0376010	0.0188005	+	0.999823i	$0.494015\pi$
$734$	2.85166e6	0.195370
$735$	2.30913e7	1.57663
$736$	−1.63157e6	−0.111023
$737$	−430988.	−0.0292278
$738$	−7.52192e6	−0.508379
$739$	−8.19614e6	−0.552075	−0.276037	−	0.961147i	$-0.589021\pi$
$739$	−8.19614e6	−0.552075	−0.276037	+	0.961147i	$0.589021\pi$
$740$	−1.37301e7	−0.921709
$741$	0	0
$742$	−562267.	−0.0374915
$743$	−1.35444e7	−0.900096	−0.450048	−	0.893004i	$-0.648593\pi$
$743$	−1.35444e7	−0.900096	−0.450048	+	0.893004i	$0.648593\pi$
$744$	825070.	0.0546460
$745$	2.46309e7	1.62589
$746$	912897.	0.0600585
$747$	−4.80403e6	−0.314995
$748$	793871.	0.0518795
$749$	−3.27989e7	−2.13626
$750$	6.92482e6	0.449526
$751$	1.09153e7	0.706215	0.353108	−	0.935583i	$-0.385125\pi$
$751$	1.09153e7	0.706215	0.353108	+	0.935583i	$0.385125\pi$
$752$	−1.15741e6	−0.0746349
$753$	1.79128e7	1.15127
$754$	−3.12048e7	−1.99891
$755$	1.23226e7	0.786744
$756$	1.46615e7	0.932986
$757$	1.56482e7	0.992489	0.496244	−	0.868183i	$-0.334712\pi$
$757$	1.56482e7	0.992489	0.496244	+	0.868183i	$0.334712\pi$
$758$	−1.46482e7	−0.926000
$759$	−980821.	−0.0617996
$760$	0	0
$761$	75073.8	0.00469923	0.00234961	−	0.999997i	$-0.499252\pi$
$761$	75073.8	0.00469923	0.00234961	+	0.999997i	$0.499252\pi$
$762$	−4.92186e6	−0.307073
$763$	1.21422e7	0.755068
$764$	3.36240e6	0.208409
$765$	6.57915e6	0.406459
$766$	−1.16546e7	−0.717668
$767$	1.17224e7	0.719493
$768$	701904.	0.0429413
$769$	−2.49525e7	−1.52159	−0.760795	−	0.648992i	$-0.775191\pi$
$769$	−2.49525e7	−1.52159	−0.760795	+	0.648992i	$0.775191\pi$
$770$	−3.14717e6	−0.191291
$771$	−7.04541e6	−0.426845
$772$	−3.07397e6	−0.185633
$773$	−1.03261e6	−0.0621564	−0.0310782	−	0.999517i	$-0.509894\pi$
$773$	−1.03261e6	−0.0621564	−0.0310782	+	0.999517i	$0.509894\pi$
$774$	8.91151e6	0.534686
$775$	−486340.	−0.0290861
$776$	−2.69346e6	−0.160567
$777$	3.56508e7	2.11844
$778$	2.25427e6	0.133523
$779$	0	0
$780$	1.09725e7	0.645756
$781$	−1.69809e6	−0.0996167
$782$	5.50187e6	0.321731
$783$	−2.87816e7	−1.67769
$784$	9.29097e6	0.539847
$785$	4.52278e6	0.261958
$786$	−1.20839e7	−0.697669
$787$	−1.21015e7	−0.696470	−0.348235	−	0.937407i	$-0.613219\pi$
$787$	−1.21015e7	−0.696470	−0.348235	+	0.937407i	$0.613219\pi$
$788$	−2.42612e6	−0.139186
$789$	−1.69592e7	−0.969868
$790$	−7.32333e6	−0.417485
$791$	2.03972e7	1.15912
$792$	−471914.	−0.0267331
$793$	1.83356e7	1.03541
$794$	−1.43241e7	−0.806334
$795$	−388117.	−0.0217793
$796$	4.53616e6	0.253750
$797$	2.78159e7	1.55113	0.775563	−	0.631270i	$-0.217466\pi$
$797$	2.78159e7	1.55113	0.775563	+	0.631270i	$0.217466\pi$
$798$	0	0
$799$	3.90293e6	0.216284
$800$	−413740.	−0.0228561
$801$	−1.07132e6	−0.0589982
$802$	−1.44694e6	−0.0794353
$803$	−1.85840e6	−0.101707
$804$	1.28498e6	0.0701063
$805$	−2.18113e7	−1.18629
$806$	5.18957e6	0.281380
$807$	−244559.	−0.0132190
$808$	3.28736e6	0.177141
$809$	1.14101e7	0.612939	0.306470	−	0.951880i	$-0.400852\pi$
$809$	1.14101e7	0.612939	0.306470	+	0.951880i	$0.400852\pi$
$810$	2.71259e6	0.145269
$811$	−2.53199e6	−0.135179	−0.0675895	−	0.997713i	$-0.521531\pi$
$811$	−2.53199e6	−0.135179	−0.0675895	+	0.997713i	$0.521531\pi$
$812$	−2.66851e7	−1.42030
$813$	−2.91358e6	−0.154597
$814$	−3.32101e6	−0.175675
$815$	2.74924e7	1.44984
$816$	−2.36691e6	−0.124439
$817$	0	0
$818$	7.11146e6	0.371600
$819$	3.18642e7	1.65994
$820$	−1.39322e7	−0.723577
$821$	−3.17272e7	−1.64276	−0.821378	−	0.570384i	$-0.806795\pi$
$821$	−3.17272e7	−1.64276	−0.821378	+	0.570384i	$0.806795\pi$
$822$	−1.64361e7	−0.848438
$823$	−1.17557e7	−0.604989	−0.302495	−	0.953151i	$-0.597819\pi$
$823$	−1.17557e7	−0.604989	−0.302495	+	0.953151i	$0.597819\pi$
$824$	−1.79780e6	−0.0922409
$825$	−248720.	−0.0127226
$826$	1.00245e7	0.511226
$827$	−3.02191e6	−0.153645	−0.0768224	−	0.997045i	$-0.524477\pi$
$827$	−3.02191e6	−0.153645	−0.0768224	+	0.997045i	$0.524477\pi$
$828$	−3.27057e6	−0.165786
$829$	1.04508e7	0.528155	0.264077	−	0.964501i	$-0.414933\pi$
$829$	1.04508e7	0.528155	0.264077	+	0.964501i	$0.414933\pi$
$830$	−8.89809e6	−0.448334
$831$	−2.41983e7	−1.21558
$832$	4.41488e6	0.221111
$833$	−3.13304e7	−1.56442
$834$	1.13401e7	0.564547
$835$	3.47404e7	1.72432
$836$	0	0
$837$	4.78658e6	0.236163
$838$	2.41288e7	1.18693
$839$	−357553.	−0.0175362	−0.00876810	−	0.999962i	$-0.502791\pi$
$839$	−357553.	−0.0175362	−0.00876810	+	0.999962i	$0.502791\pi$
$840$	9.38325e6	0.458833
$841$	3.18736e7	1.55396
$842$	−2.05252e7	−0.997714
$843$	1.09859e7	0.532435
$844$	2.20371e6	0.106487
$845$	4.69585e7	2.26241
$846$	−2.32009e6	−0.111449
$847$	3.63504e7	1.74101
$848$	−156162.	−0.00745738
$849$	3.45537e6	0.164523
$850$	1.39518e6	0.0662345
$851$	−2.30161e7	−1.08945
$852$	5.06282e6	0.238942
$853$	2.15209e6	0.101272	0.0506359	−	0.998717i	$-0.483875\pi$
$853$	2.15209e6	0.101272	0.0506359	+	0.998717i	$0.483875\pi$
$854$	1.56799e7	0.735694
$855$	0	0
$856$	−9.10945e6	−0.424921
$857$	−3.52807e7	−1.64091	−0.820455	−	0.571711i	$-0.806280\pi$
$857$	−3.52807e7	−1.64091	−0.820455	+	0.571711i	$0.806280\pi$
$858$	2.65401e6	0.123079
$859$	−4.78733e6	−0.221366	−0.110683	−	0.993856i	$-0.535304\pi$
$859$	−4.78733e6	−0.221366	−0.110683	+	0.993856i	$0.535304\pi$
$860$	1.65060e7	0.761021
$861$	3.61756e7	1.66306
$862$	8.52842e6	0.390931
$863$	2.17189e7	0.992683	0.496342	−	0.868127i	$-0.334676\pi$
$863$	2.17189e7	0.992683	0.496342	+	0.868127i	$0.334676\pi$
$864$	4.07205e6	0.185579
$865$	−1.07716e7	−0.489486
$866$	−4.98664e6	−0.225951
$867$	−7.22544e6	−0.326450
$868$	4.43792e6	0.199931
$869$	−1.77136e6	−0.0795713
$870$	−1.84200e7	−0.825070
$871$	8.08236e6	0.360988
$872$	3.37234e6	0.150190
$873$	−5.39917e6	−0.239768
$874$	0	0
$875$	3.72475e7	1.64466
$876$	5.54080e6	0.243956
$877$	−2.66719e7	−1.17100	−0.585498	−	0.810674i	$-0.699101\pi$
$877$	−2.66719e7	−1.17100	−0.585498	+	0.810674i	$0.699101\pi$
$878$	−5.40619e6	−0.236677
$879$	−1.52297e7	−0.664842
$880$	−874086.	−0.0380494
$881$	−3.33412e7	−1.44724	−0.723622	−	0.690197i	$-0.757524\pi$
$881$	−3.33412e7	−1.44724	−0.723622	+	0.690197i	$0.757524\pi$
$882$	1.86242e7	0.806134
$883$	3.87723e6	0.167348	0.0836740	−	0.996493i	$-0.473335\pi$
$883$	3.87723e6	0.167348	0.0836740	+	0.996493i	$0.473335\pi$
$884$	−1.48875e7	−0.640755
$885$	6.91963e6	0.296978
$886$	2.19552e6	0.0939620
$887$	−2.62010e7	−1.11817	−0.559085	−	0.829110i	$-0.688848\pi$
$887$	−2.62010e7	−1.11817	−0.559085	+	0.829110i	$0.688848\pi$
$888$	9.90154e6	0.421376
$889$	−2.64739e7	−1.12348
$890$	−1.98432e6	−0.0839723
$891$	656117.	0.0276877
$892$	4.00444e6	0.168512
$893$	0	0
$894$	−1.77628e7	−0.743304
$895$	−7.88763e6	−0.329146
$896$	3.77543e6	0.157107
$897$	1.83934e7	0.763277
$898$	2.92769e7	1.21153
$899$	−8.71194e6	−0.359514
$900$	−829363.	−0.0341302
$901$	526599.	0.0216107
$902$	−3.36990e6	−0.137911
$903$	−4.28587e7	−1.74912
$904$	5.66506e6	0.230560
$905$	−4.10835e7	−1.66742
$906$	−8.88649e6	−0.359675
$907$	−1.56738e7	−0.632638	−0.316319	−	0.948653i	$-0.602447\pi$
$907$	−1.56738e7	−0.632638	−0.316319	+	0.948653i	$0.602447\pi$
$908$	2.24471e7	0.903535
$909$	6.58968e6	0.264518
$910$	5.90193e7	2.36260
$911$	3.66902e6	0.146472	0.0732360	−	0.997315i	$-0.476667\pi$
$911$	3.66902e6	0.146472	0.0732360	+	0.997315i	$0.476667\pi$
$912$	0	0
$913$	−2.15226e6	−0.0854510
$914$	−2.07143e7	−0.820171
$915$	1.08234e7	0.427375
$916$	8.61875e6	0.339395
$917$	−6.49972e7	−2.55253
$918$	−1.37315e7	−0.537787
$919$	55850.3	0.00218141	0.00109070	−	0.999999i	$-0.499653\pi$
$919$	55850.3	0.00218141	0.00109070	+	0.999999i	$0.499653\pi$
$920$	−6.05780e6	−0.235964
$921$	−1.59219e7	−0.618509
$922$	−4.13573e6	−0.160223
$923$	3.18444e7	1.23035
$924$	2.26960e6	0.0874521
$925$	−5.83649e6	−0.224284
$926$	8.92915e6	0.342202
$927$	−3.60379e6	−0.137740
$928$	−7.41144e6	−0.282509
$929$	−2.83727e6	−0.107860	−0.0539301	−	0.998545i	$-0.517175\pi$
$929$	−2.83727e6	−0.107860	−0.0539301	+	0.998545i	$0.517175\pi$
$930$	3.06337e6	0.116143
$931$	0	0
$932$	1.21775e7	0.459218
$933$	2.67670e7	1.00669
$934$	8.19022e6	0.307205
$935$	2.94753e6	0.110263
$936$	8.84985e6	0.330177
$937$	−1.78307e7	−0.663466	−0.331733	−	0.943373i	$-0.607633\pi$
$937$	−1.78307e7	−0.663466	−0.331733	+	0.943373i	$0.607633\pi$
$938$	6.91172e6	0.256495
$939$	2.20178e7	0.814910
$940$	−4.29729e6	−0.158626
$941$	−3.62712e7	−1.33533	−0.667665	−	0.744462i	$-0.732706\pi$
$941$	−3.62712e7	−1.33533	−0.667665	+	0.744462i	$0.732706\pi$
$942$	−3.26163e6	−0.119759
$943$	−2.33549e7	−0.855260
$944$	2.78417e6	0.101687
$945$	5.44362e7	1.98294
$946$	3.99245e6	0.145048
$947$	3.00673e7	1.08948	0.544741	−	0.838604i	$-0.316628\pi$
$947$	3.00673e7	1.08948	0.544741	+	0.838604i	$0.316628\pi$
$948$	5.28127e6	0.190861
$949$	3.48508e7	1.25617
$950$	0	0
$951$	−7.63512e6	−0.273757
$952$	−1.27312e7	−0.455280
$953$	−3.04344e7	−1.08551	−0.542754	−	0.839892i	$-0.682618\pi$
$953$	−3.04344e7	−1.08551	−0.542754	+	0.839892i	$0.682618\pi$
$954$	−313035.	−0.0111358
$955$	1.24841e7	0.442945
$956$	1.26639e7	0.448150
$957$	−4.45539e6	−0.157256
$958$	2.99160e6	0.105315
$959$	−8.84073e7	−3.10414
$960$	2.60607e6	0.0912659
$961$	−2.71803e7	−0.949392
$962$	6.22792e7	2.16973
$963$	−1.82604e7	−0.634518
$964$	−6.86108e6	−0.237793
$965$	−1.14132e7	−0.394538
$966$	1.57294e7	0.542336
$967$	2.34588e7	0.806752	0.403376	−	0.915034i	$-0.367837\pi$
$967$	2.34588e7	0.806752	0.403376	+	0.915034i	$0.367837\pi$
$968$	1.00958e7	0.346301
$969$	0	0
$970$	−1.00004e7	−0.341263
$971$	−3.72160e7	−1.26672	−0.633361	−	0.773857i	$-0.718325\pi$
$971$	−3.72160e7	−1.26672	−0.633361	+	0.773857i	$0.718325\pi$
$972$	1.35049e7	0.458484
$973$	6.09964e7	2.06548
$974$	2.82153e7	0.952987
$975$	4.66427e6	0.157135
$976$	4.35487e6	0.146336
$977$	−2.66977e7	−0.894824	−0.447412	−	0.894328i	$-0.647654\pi$
$977$	−2.66977e7	−0.894824	−0.447412	+	0.894328i	$0.647654\pi$
$978$	−1.98264e7	−0.662820
$979$	−479963.	−0.0160048
$980$	3.44961e7	1.14737
$981$	6.76003e6	0.224272
$982$	2.55085e7	0.844124
$983$	−2.36413e7	−0.780346	−0.390173	−	0.920742i	$-0.627585\pi$
$983$	−2.36413e7	−0.780346	−0.390173	+	0.920742i	$0.627585\pi$
$984$	1.00473e7	0.330797
$985$	−9.00782e6	−0.295821
$986$	2.49923e7	0.818680
$987$	1.11581e7	0.364585
$988$	0	0
$989$	2.76694e7	0.899518
$990$	−1.75215e6	−0.0568177
$991$	−2.59822e7	−0.840412	−0.420206	−	0.907429i	$-0.638042\pi$
$991$	−2.59822e7	−0.840412	−0.420206	+	0.907429i	$0.638042\pi$
$992$	1.23257e6	0.0397680
$993$	3.64237e7	1.17223
$994$	2.72321e7	0.874208
$995$	1.68421e7	0.539311
$996$	6.41692e6	0.204964
$997$	4.12957e7	1.31573	0.657865	−	0.753136i	$-0.271460\pi$
$997$	4.12957e7	1.31573	0.657865	+	0.753136i	$0.271460\pi$
$998$	−3.51353e7	−1.11665
$999$	5.74431e7	1.82106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.q.1.11		15
19.3	odd	18		38.6.e.b.9.2	✓	30
19.13	odd	18		38.6.e.b.17.2	yes	30
19.18	odd	2		722.6.a.r.1.5		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.9.2	✓	30	19.3	odd	18
38.6.e.b.17.2	yes	30	19.13	odd	18
722.6.a.q.1.11		15	1.1	even	1	trivial
722.6.a.r.1.5		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +10.7102 q^{3} +16.0000 q^{4} +59.4057 q^{5} -42.8408 q^{6} -230.434 q^{7} -64.0000 q^{8} -128.291 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +10.7102 q^{3} +16.0000 q^{4} +59.4057 q^{5} -42.8408 q^{6} -230.434 q^{7} -64.0000 q^{8} -128.291 q^{9} -237.623 q^{10} -57.4759 q^{11} +171.363 q^{12} +1077.85 q^{13} +921.736 q^{14} +636.248 q^{15} +256.000 q^{16} -863.265 q^{17} +513.165 q^{18} +950.492 q^{20} -2468.00 q^{21} +229.903 q^{22} +1593.33 q^{23} -685.454 q^{24} +404.043 q^{25} -4311.40 q^{26} -3976.61 q^{27} -3686.94 q^{28} +7237.73 q^{29} -2544.99 q^{30} -1203.68 q^{31} -1024.00 q^{32} -615.579 q^{33} +3453.06 q^{34} -13689.1 q^{35} -2052.66 q^{36} -14445.2 q^{37} +11544.0 q^{39} -3801.97 q^{40} -14657.9 q^{41} +9871.99 q^{42} +17365.8 q^{43} -919.614 q^{44} -7621.24 q^{45} -6373.33 q^{46} -4521.13 q^{47} +2741.81 q^{48} +36292.9 q^{49} -1616.17 q^{50} -9245.75 q^{51} +17245.6 q^{52} -610.009 q^{53} +15906.4 q^{54} -3414.40 q^{55} +14747.8 q^{56} -28950.9 q^{58} +10875.7 q^{59} +10180.0 q^{60} +17011.2 q^{61} +4814.74 q^{62} +29562.7 q^{63} +4096.00 q^{64} +64030.5 q^{65} +2462.32 q^{66} +7498.58 q^{67} -13812.2 q^{68} +17064.9 q^{69} +54756.4 q^{70} +29544.3 q^{71} +8210.65 q^{72} +32333.6 q^{73} +57780.9 q^{74} +4327.38 q^{75} +13244.4 q^{77} -46176.1 q^{78} +30819.1 q^{79} +15207.9 q^{80} -11415.5 q^{81} +58631.5 q^{82} +37446.2 q^{83} -39488.0 q^{84} -51282.9 q^{85} -69463.1 q^{86} +77517.6 q^{87} +3678.46 q^{88} +8350.69 q^{89} +30485.0 q^{90} -248374. q^{91} +25493.3 q^{92} -12891.7 q^{93} +18084.5 q^{94} -10967.3 q^{96} +42085.2 q^{97} -145171. q^{98} +7373.66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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