LMFDB - Embedded newform 722.6.a.r.1.1

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			1.1
Root			$31.5298$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -29.6504 q^{3} +16.0000 q^{4} +89.4742 q^{5} -118.602 q^{6} -137.413 q^{7} +64.0000 q^{8} +636.149 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -29.6504 q^{3} +16.0000 q^{4} +89.4742 q^{5} -118.602 q^{6} -137.413 q^{7} +64.0000 q^{8} +636.149 q^{9} +357.897 q^{10} -305.058 q^{11} -474.407 q^{12} +91.8954 q^{13} -549.650 q^{14} -2652.95 q^{15} +256.000 q^{16} -57.7997 q^{17} +2544.60 q^{18} +1431.59 q^{20} +4074.34 q^{21} -1220.23 q^{22} +2902.73 q^{23} -1897.63 q^{24} +4880.63 q^{25} +367.582 q^{26} -11657.0 q^{27} -2198.60 q^{28} +5405.71 q^{29} -10611.8 q^{30} -5939.32 q^{31} +1024.00 q^{32} +9045.12 q^{33} -231.199 q^{34} -12294.9 q^{35} +10178.4 q^{36} -287.050 q^{37} -2724.74 q^{39} +5726.35 q^{40} -1384.19 q^{41} +16297.4 q^{42} +8073.58 q^{43} -4880.93 q^{44} +56918.9 q^{45} +11610.9 q^{46} +1572.58 q^{47} -7590.51 q^{48} +2075.21 q^{49} +19522.5 q^{50} +1713.79 q^{51} +1470.33 q^{52} -38737.7 q^{53} -46628.2 q^{54} -27294.9 q^{55} -8794.40 q^{56} +21622.8 q^{58} +2024.78 q^{59} -42447.2 q^{60} +21781.2 q^{61} -23757.3 q^{62} -87414.9 q^{63} +4096.00 q^{64} +8222.26 q^{65} +36180.5 q^{66} -63119.2 q^{67} -924.796 q^{68} -86067.3 q^{69} -49179.5 q^{70} -25190.3 q^{71} +40713.5 q^{72} +33979.6 q^{73} -1148.20 q^{74} -144713. q^{75} +41918.9 q^{77} -10899.0 q^{78} -13940.1 q^{79} +22905.4 q^{80} +191052. q^{81} -5536.78 q^{82} +80219.9 q^{83} +65189.5 q^{84} -5171.58 q^{85} +32294.3 q^{86} -160282. q^{87} -19523.7 q^{88} -49802.9 q^{89} +227676. q^{90} -12627.6 q^{91} +46443.7 q^{92} +176104. q^{93} +6290.32 q^{94} -30362.1 q^{96} +40755.9 q^{97} +8300.84 q^{98} -194063. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−29.6504	−1.90208	−0.951038	−	0.309072i	$-0.899981\pi$
$3$	−29.6504	−1.90208	−0.951038	+	0.309072i	$0.899981\pi$
$4$	16.0000	0.500000
$5$	89.4742	1.60056	0.800281	−	0.599624i	$-0.204683\pi$
$5$	89.4742	1.60056	0.800281	+	0.599624i	$0.204683\pi$
$6$	−118.602	−1.34497
$7$	−137.413	−1.05994	−0.529970	−	0.848016i	$-0.677797\pi$
$7$	−137.413	−1.05994	−0.529970	+	0.848016i	$0.677797\pi$
$8$	64.0000	0.353553
$9$	636.149	2.61790
$10$	357.897	1.13177
$11$	−305.058	−0.760154	−0.380077	−	0.924955i	$-0.624102\pi$
$11$	−305.058	−0.760154	−0.380077	+	0.924955i	$0.624102\pi$
$12$	−474.407	−0.951038
$13$	91.8954	0.150812	0.0754059	−	0.997153i	$-0.475975\pi$
$13$	91.8954	0.150812	0.0754059	+	0.997153i	$0.475975\pi$
$14$	−549.650	−0.749491
$15$	−2652.95	−3.04439
$16$	256.000	0.250000
$17$	−57.7997	−0.0485069	−0.0242534	−	0.999706i	$-0.507721\pi$
$17$	−57.7997	−0.0485069	−0.0242534	+	0.999706i	$0.507721\pi$
$18$	2544.60	1.85113
$19$	0	0
$19$	0	0
$20$	1431.59	0.800281
$21$	4074.34	2.01609
$22$	−1220.23	−0.537510
$23$	2902.73	1.14416	0.572081	−	0.820197i	$-0.306136\pi$
$23$	2902.73	1.14416	0.572081	+	0.820197i	$0.306136\pi$
$24$	−1897.63	−0.672486
$25$	4880.63	1.56180
$26$	367.582	0.106640
$27$	−11657.0	−3.07736
$28$	−2198.60	−0.529970
$29$	5405.71	1.19360	0.596799	−	0.802391i	$-0.296439\pi$
$29$	5405.71	1.19360	0.596799	+	0.802391i	$0.296439\pi$
$30$	−10611.8	−2.15271
$31$	−5939.32	−1.11002	−0.555012	−	0.831842i	$-0.687287\pi$
$31$	−5939.32	−1.11002	−0.555012	+	0.831842i	$0.687287\pi$
$32$	1024.00	0.176777
$33$	9045.12	1.44587
$34$	−231.199	−0.0342996
$35$	−12294.9	−1.69650
$36$	10178.4	1.30895
$37$	−287.050	−0.0344710	−0.0172355	−	0.999851i	$-0.505486\pi$
$37$	−287.050	−0.0344710	−0.0172355	+	0.999851i	$0.505486\pi$
$38$	0	0
$39$	−2724.74	−0.286856
$40$	5726.35	0.565884
$41$	−1384.19	−0.128599	−0.0642995	−	0.997931i	$-0.520481\pi$
$41$	−1384.19	−0.128599	−0.0642995	+	0.997931i	$0.520481\pi$
$42$	16297.4	1.42559
$43$	8073.58	0.665879	0.332939	−	0.942948i	$-0.391960\pi$
$43$	8073.58	0.665879	0.332939	+	0.942948i	$0.391960\pi$
$44$	−4880.93	−0.380077
$45$	56918.9	4.19011
$46$	11610.9	0.809045
$47$	1572.58	0.103841	0.0519204	−	0.998651i	$-0.483466\pi$
$47$	1572.58	0.103841	0.0519204	+	0.998651i	$0.483466\pi$
$48$	−7590.51	−0.475519
$49$	2075.21	0.123473
$50$	19522.5	1.10436
$51$	1713.79	0.0922639
$52$	1470.33	0.0754059
$53$	−38737.7	−1.89428	−0.947139	−	0.320822i	$-0.896041\pi$
$53$	−38737.7	−1.89428	−0.947139	+	0.320822i	$0.896041\pi$
$54$	−46628.2	−2.17603
$55$	−27294.9	−1.21667
$56$	−8794.40	−0.374745
$57$	0	0
$58$	21622.8	0.844001
$59$	2024.78	0.0757266	0.0378633	−	0.999283i	$-0.487945\pi$
$59$	2024.78	0.0757266	0.0378633	+	0.999283i	$0.487945\pi$
$60$	−42447.2	−1.52220
$61$	21781.2	0.749475	0.374738	−	0.927131i	$-0.377733\pi$
$61$	21781.2	0.749475	0.374738	+	0.927131i	$0.377733\pi$
$62$	−23757.3	−0.784906
$63$	−87414.9	−2.77481
$64$	4096.00	0.125000
$65$	8222.26	0.241384
$66$	36180.5	1.02238
$67$	−63119.2	−1.71781	−0.858903	−	0.512137i	$-0.828854\pi$
$67$	−63119.2	−1.71781	−0.858903	+	0.512137i	$0.828854\pi$
$68$	−924.796	−0.0242534
$69$	−86067.3	−2.17628
$70$	−49179.5	−1.19961
$71$	−25190.3	−0.593045	−0.296522	−	0.955026i	$-0.595827\pi$
$71$	−25190.3	−0.593045	−0.296522	+	0.955026i	$0.595827\pi$
$72$	40713.5	0.925566
$73$	33979.6	0.746296	0.373148	−	0.927772i	$-0.378278\pi$
$73$	33979.6	0.746296	0.373148	+	0.927772i	$0.378278\pi$
$74$	−1148.20	−0.0243747
$75$	−144713.	−2.97067
$76$	0	0
$77$	41918.9	0.805717
$78$	−10899.0	−0.202838
$79$	−13940.1	−0.251303	−0.125651	−	0.992074i	$-0.540102\pi$
$79$	−13940.1	−0.251303	−0.125651	+	0.992074i	$0.540102\pi$
$80$	22905.4	0.400141
$81$	191052.	3.23549
$82$	−5536.78	−0.0909332
$83$	80219.9	1.27816	0.639082	−	0.769138i	$-0.279314\pi$
$83$	80219.9	1.27816	0.639082	+	0.769138i	$0.279314\pi$
$84$	65189.5	1.00804
$85$	−5171.58	−0.0776383
$86$	32294.3	0.470847
$87$	−160282.	−2.27031
$88$	−19523.7	−0.268755
$89$	−49802.9	−0.666468	−0.333234	−	0.942844i	$-0.608140\pi$
$89$	−49802.9	−0.666468	−0.333234	+	0.942844i	$0.608140\pi$
$90$	227676.	2.96285
$91$	−12627.6	−0.159851
$92$	46443.7	0.572081
$93$	176104.	2.11135
$94$	6290.32	0.0734265
$95$	0	0
$96$	−30362.1	−0.336243
$97$	40755.9	0.439806	0.219903	−	0.975522i	$-0.429426\pi$
$97$	40755.9	0.439806	0.219903	+	0.975522i	$0.429426\pi$
$98$	8300.84	0.0873086
$99$	−194063.	−1.99000
$100$	78090.1	0.780901
$101$	130307.	1.27105	0.635526	−	0.772080i	$-0.280783\pi$
$101$	130307.	1.27105	0.635526	+	0.772080i	$0.280783\pi$
$102$	6855.15	0.0652404
$103$	171128.	1.58938	0.794691	−	0.607015i	$-0.207633\pi$
$103$	171128.	1.58938	0.794691	+	0.607015i	$0.207633\pi$
$104$	5881.30	0.0533200
$105$	364549.	3.22688
$106$	−154951.	−1.33946
$107$	148459.	1.25357	0.626784	−	0.779193i	$-0.284371\pi$
$107$	148459.	1.25357	0.626784	+	0.779193i	$0.284371\pi$
$108$	−186513.	−1.53868
$109$	−21915.2	−0.176677	−0.0883384	−	0.996091i	$-0.528156\pi$
$109$	−21915.2	−0.176677	−0.0883384	+	0.996091i	$0.528156\pi$
$110$	−109179.	−0.860318
$111$	8511.17	0.0655665
$112$	−35177.6	−0.264985
$113$	96750.2	0.712780	0.356390	−	0.934337i	$-0.384007\pi$
$113$	96750.2	0.712780	0.356390	+	0.934337i	$0.384007\pi$
$114$	0	0
$115$	259720.	1.83130
$116$	86491.4	0.596799
$117$	58459.1	0.394810
$118$	8099.13	0.0535468
$119$	7942.41	0.0514144
$120$	−169789.	−1.07636
$121$	−67990.4	−0.422167
$122$	87124.8	0.529959
$123$	41042.0	0.244605
$124$	−95029.2	−0.555012
$125$	157084.	0.899199
$126$	−349659.	−1.96209
$127$	164778.	0.906547	0.453273	−	0.891372i	$-0.350256\pi$
$127$	164778.	0.906547	0.453273	+	0.891372i	$0.350256\pi$
$128$	16384.0	0.0883883
$129$	−239385.	−1.26655
$130$	32889.1	0.170684
$131$	127787.	0.650589	0.325295	−	0.945613i	$-0.394537\pi$
$131$	127787.	0.650589	0.325295	+	0.945613i	$0.394537\pi$
$132$	144722.	0.722935
$133$	0	0
$134$	−252477.	−1.21467
$135$	−1.04300e6	−4.92552
$136$	−3699.18	−0.0171498
$137$	−13455.4	−0.0612483	−0.0306241	−	0.999531i	$-0.509749\pi$
$137$	−13455.4	−0.0612483	−0.0306241	+	0.999531i	$0.509749\pi$
$138$	−344269.	−1.53887
$139$	−110649.	−0.485746	−0.242873	−	0.970058i	$-0.578090\pi$
$139$	−110649.	−0.485746	−0.242873	+	0.970058i	$0.578090\pi$
$140$	−196718.	−0.848250
$141$	−46627.7	−0.197513
$142$	−100761.	−0.419346
$143$	−28033.5	−0.114640
$144$	162854.	0.654474
$145$	483672.	1.91043
$146$	135918.	0.527711
$147$	−61530.9	−0.234855
$148$	−4592.80	−0.0172355
$149$	254245.	0.938183	0.469091	−	0.883150i	$-0.344582\pi$
$149$	254245.	0.938183	0.469091	+	0.883150i	$0.344582\pi$
$150$	−578852.	−2.10058
$151$	312599.	1.11569	0.557847	−	0.829944i	$-0.311627\pi$
$151$	312599.	1.11569	0.557847	+	0.829944i	$0.311627\pi$
$152$	0	0
$153$	−36769.2	−0.126986
$154$	167675.	0.569728
$155$	−531416.	−1.77666
$156$	−43595.8	−0.143428
$157$	−247715.	−0.802054	−0.401027	−	0.916066i	$-0.631347\pi$
$157$	−247715.	−0.802054	−0.401027	+	0.916066i	$0.631347\pi$
$158$	−55760.3	−0.177698
$159$	1.14859e6	3.60306
$160$	91621.6	0.282942
$161$	−398872.	−1.21274
$162$	764209.	2.28783
$163$	374109.	1.10288	0.551441	−	0.834214i	$-0.314078\pi$
$163$	374109.	1.10288	0.551441	+	0.834214i	$0.314078\pi$
$164$	−22147.1	−0.0642995
$165$	809305.	2.31421
$166$	320880.	0.903799
$167$	620828.	1.72258	0.861291	−	0.508112i	$-0.169657\pi$
$167$	620828.	1.72258	0.861291	+	0.508112i	$0.169657\pi$
$168$	260758.	0.712795
$169$	−362848.	−0.977256
$170$	−20686.3	−0.0548986
$171$	0	0
$172$	129177.	0.332939
$173$	222921.	0.566286	0.283143	−	0.959078i	$-0.408623\pi$
$173$	222921.	0.566286	0.283143	+	0.959078i	$0.408623\pi$
$174$	−641127.	−1.60535
$175$	−670660.	−1.65542
$176$	−78095.0	−0.190038
$177$	−60035.7	−0.144038
$178$	−199211.	−0.471264
$179$	−429508.	−1.00193	−0.500967	−	0.865467i	$-0.667022\pi$
$179$	−429508.	−1.00193	−0.500967	+	0.865467i	$0.667022\pi$
$180$	910703.	2.09505
$181$	448322.	1.01717	0.508586	−	0.861011i	$-0.330169\pi$
$181$	448322.	1.01717	0.508586	+	0.861011i	$0.330169\pi$
$182$	−50510.3	−0.113032
$183$	−645822.	−1.42556
$184$	185775.	0.404522
$185$	−25683.6	−0.0551730
$186$	704414.	1.49295
$187$	17632.3	0.0368727
$188$	25161.3	0.0519204
$189$	1.60182e6	3.26182
$190$	0	0
$191$	−154108.	−0.305663	−0.152832	−	0.988252i	$-0.548839\pi$
$191$	−154108.	−0.305663	−0.152832	+	0.988252i	$0.548839\pi$
$192$	−121448.	−0.237760
$193$	937750.	1.81215	0.906074	−	0.423119i	$-0.139065\pi$
$193$	937750.	1.81215	0.906074	+	0.423119i	$0.139065\pi$
$194$	163024.	0.310990
$195$	−243794.	−0.459131
$196$	33203.4	0.0617365
$197$	7673.96	0.0140881	0.00704407	−	0.999975i	$-0.497758\pi$
$197$	7673.96	0.0140881	0.00704407	+	0.999975i	$0.497758\pi$
$198$	−776250.	−1.40715
$199$	224858.	0.402509	0.201255	−	0.979539i	$-0.435498\pi$
$199$	224858.	0.402509	0.201255	+	0.979539i	$0.435498\pi$
$200$	312360.	0.552180
$201$	1.87151e6	3.26740
$202$	521227.	0.898769
$203$	−742813.	−1.26514
$204$	27420.6	0.0461319
$205$	−123850.	−0.205831
$206$	684512.	1.12386
$207$	1.84657e6	2.99530
$208$	23525.2	0.0377029
$209$	0	0
$210$	1.45819e6	2.28175
$211$	−120258.	−0.185955	−0.0929777	−	0.995668i	$-0.529639\pi$
$211$	−120258.	−0.185955	−0.0929777	+	0.995668i	$0.529639\pi$
$212$	−619803.	−0.947139
$213$	746903.	1.12802
$214$	593837.	0.886407
$215$	722377.	1.06578
$216$	−746051.	−1.08801
$217$	816138.	1.17656
$218$	−87660.9	−0.124929
$219$	−1.00751e6	−1.41951
$220$	−436718.	−0.608337
$221$	−5311.53	−0.00731541
$222$	34044.7	0.0463625
$223$	22043.1	0.0296832	0.0148416	−	0.999890i	$-0.495276\pi$
$223$	22043.1	0.0296832	0.0148416	+	0.999890i	$0.495276\pi$
$224$	−140710.	−0.187373
$225$	3.10481e6	4.08864
$226$	387001.	0.504012
$227$	1.27626e6	1.64390	0.821949	−	0.569561i	$-0.192887\pi$
$227$	1.27626e6	1.64390	0.821949	+	0.569561i	$0.192887\pi$
$228$	0	0
$229$	77951.9	0.0982286	0.0491143	−	0.998793i	$-0.484360\pi$
$229$	77951.9	0.0982286	0.0491143	+	0.998793i	$0.484360\pi$
$230$	1.03888e6	1.29493
$231$	−1.24291e6	−1.53254
$232$	345966.	0.422000
$233$	242827.	0.293027	0.146513	−	0.989209i	$-0.453195\pi$
$233$	242827.	0.293027	0.146513	+	0.989209i	$0.453195\pi$
$234$	233837.	0.279173
$235$	140705.	0.166204
$236$	32396.5	0.0378633
$237$	413329.	0.477997
$238$	31769.6	0.0363555
$239$	−139047.	−0.157459	−0.0787293	−	0.996896i	$-0.525086\pi$
$239$	−139047.	−0.157459	−0.0787293	+	0.996896i	$0.525086\pi$
$240$	−679155.	−0.761099
$241$	−620154.	−0.687791	−0.343896	−	0.939008i	$-0.611747\pi$
$241$	−620154.	−0.687791	−0.343896	+	0.939008i	$0.611747\pi$
$242$	−271961.	−0.298517
$243$	−2.83212e6	−3.07678
$244$	348499.	0.374738
$245$	185678.	0.197626
$246$	164168.	0.172962
$247$	0	0
$248$	−380117.	−0.392453
$249$	−2.37856e6	−2.43117
$250$	628335.	0.635830
$251$	883397.	0.885058	0.442529	−	0.896754i	$-0.354081\pi$
$251$	883397.	0.885058	0.442529	+	0.896754i	$0.354081\pi$
$252$	−1.39864e6	−1.38741
$253$	−885503.	−0.869739
$254$	659112.	0.641025
$255$	153340.	0.147674
$256$	65536.0	0.0625000
$257$	1.61819e6	1.52826	0.764129	−	0.645064i	$-0.223169\pi$
$257$	1.61819e6	1.52826	0.764129	+	0.645064i	$0.223169\pi$
$258$	−957541.	−0.895588
$259$	39444.3	0.0365372
$260$	131556.	0.120692
$261$	3.43884e6	3.12472
$262$	511146.	0.460036
$263$	−515394.	−0.459462	−0.229731	−	0.973254i	$-0.573785\pi$
$263$	−515394.	−0.459462	−0.229731	+	0.973254i	$0.573785\pi$
$264$	578888.	0.511192
$265$	−3.46602e6	−3.03191
$266$	0	0
$267$	1.47668e6	1.26767
$268$	−1.00991e6	−0.858903
$269$	620209.	0.522586	0.261293	−	0.965260i	$-0.415851\pi$
$269$	620209.	0.522586	0.261293	+	0.965260i	$0.415851\pi$
$270$	−4.17202e6	−3.48287
$271$	1.12306e6	0.928927	0.464463	−	0.885592i	$-0.346247\pi$
$271$	1.12306e6	0.928927	0.464463	+	0.885592i	$0.346247\pi$
$272$	−14796.7	−0.0121267
$273$	374413.	0.304050
$274$	−53821.4	−0.0433091
$275$	−1.48888e6	−1.18721
$276$	−1.37708e6	−1.08814
$277$	1.93274e6	1.51347	0.756734	−	0.653723i	$-0.226794\pi$
$277$	1.93274e6	1.51347	0.756734	+	0.653723i	$0.226794\pi$
$278$	−442594.	−0.343474
$279$	−3.77829e6	−2.90593
$280$	−786872.	−0.599804
$281$	937880.	0.708568	0.354284	−	0.935138i	$-0.384725\pi$
$281$	937880.	0.708568	0.354284	+	0.935138i	$0.384725\pi$
$282$	−186511.	−0.139663
$283$	−471066.	−0.349635	−0.174818	−	0.984601i	$-0.555934\pi$
$283$	−471066.	−0.349635	−0.174818	+	0.984601i	$0.555934\pi$
$284$	−403045.	−0.296522
$285$	0	0
$286$	−112134.	−0.0810628
$287$	190206.	0.136307
$288$	651417.	0.462783
$289$	−1.41652e6	−0.997647
$290$	1.93469e6	1.35088
$291$	−1.20843e6	−0.836545
$292$	543674.	0.373148
$293$	−450229.	−0.306383	−0.153191	−	0.988197i	$-0.548955\pi$
$293$	−450229.	−0.306383	−0.153191	+	0.988197i	$0.548955\pi$
$294$	−246124.	−0.166068
$295$	181166.	0.121205
$296$	−18371.2	−0.0121873
$297$	3.55608e6	2.33927
$298$	1.01698e6	0.663395
$299$	266748.	0.172553
$300$	−2.31541e6	−1.48533
$301$	−1.10941e6	−0.705791
$302$	1.25040e6	0.788915
$303$	−3.86365e6	−2.41764
$304$	0	0
$305$	1.94886e6	1.19958
$306$	−147077.	−0.0897927
$307$	−203545.	−0.123258	−0.0616290	−	0.998099i	$-0.519630\pi$
$307$	−203545.	−0.123258	−0.0616290	+	0.998099i	$0.519630\pi$
$308$	670702.	0.402859
$309$	−5.07402e6	−3.02313
$310$	−2.12566e6	−1.25629
$311$	−2.34359e6	−1.37398	−0.686991	−	0.726666i	$-0.741069\pi$
$311$	−2.34359e6	−1.37398	−0.686991	+	0.726666i	$0.741069\pi$
$312$	−174383.	−0.101419
$313$	−2.13780e6	−1.23340	−0.616702	−	0.787196i	$-0.711532\pi$
$313$	−2.13780e6	−1.23340	−0.616702	+	0.787196i	$0.711532\pi$
$314$	−990861.	−0.567138
$315$	−7.82137e6	−4.44126
$316$	−223041.	−0.125651
$317$	−693759.	−0.387758	−0.193879	−	0.981025i	$-0.562107\pi$
$317$	−693759.	−0.387758	−0.193879	+	0.981025i	$0.562107\pi$
$318$	4.59436e6	2.54775
$319$	−1.64906e6	−0.907317
$320$	366486.	0.200070
$321$	−4.40189e6	−2.38438
$322$	−1.59549e6	−0.857539
$323$	0	0
$324$	3.05684e6	1.61774
$325$	448507.	0.235538
$326$	1.49644e6	0.779856
$327$	649796.	0.336053
$328$	−88588.4	−0.0454666
$329$	−216092.	−0.110065
$330$	3.23722e6	1.63639
$331$	1.44824e6	0.726560	0.363280	−	0.931680i	$-0.381657\pi$
$331$	1.44824e6	0.726560	0.363280	+	0.931680i	$0.381657\pi$
$332$	1.28352e6	0.639082
$333$	−182607.	−0.0902415
$334$	2.48331e6	1.21805
$335$	−5.64754e6	−2.74946
$336$	1.04303e6	0.504022
$337$	−1.34450e6	−0.644889	−0.322445	−	0.946588i	$-0.604505\pi$
$337$	−1.34450e6	−0.644889	−0.322445	+	0.946588i	$0.604505\pi$
$338$	−1.45139e6	−0.691024
$339$	−2.86869e6	−1.35576
$340$	−82745.3	−0.0388192
$341$	1.81184e6	0.843789
$342$	0	0
$343$	2.02433e6	0.929066
$344$	516709.	0.235424
$345$	−7.70080e6	−3.48328
$346$	891684.	0.400425
$347$	3.05115e6	1.36031	0.680157	−	0.733066i	$-0.261911\pi$
$347$	3.05115e6	1.36031	0.680157	+	0.733066i	$0.261911\pi$
$348$	−2.56451e6	−1.13516
$349$	−120829.	−0.0531018	−0.0265509	−	0.999647i	$-0.508452\pi$
$349$	−120829.	−0.0531018	−0.0265509	+	0.999647i	$0.508452\pi$
$350$	−2.68264e6	−1.17056
$351$	−1.07123e6	−0.464103
$352$	−312380.	−0.134377
$353$	1.65561e6	0.707165	0.353582	−	0.935403i	$-0.384963\pi$
$353$	1.65561e6	0.707165	0.353582	+	0.935403i	$0.384963\pi$
$354$	−240143.	−0.101850
$355$	−2.25388e6	−0.949205
$356$	−796846.	−0.333234
$357$	−235496.	−0.0977942
$358$	−1.71803e6	−0.708474
$359$	4.67094e6	1.91279	0.956397	−	0.292069i	$-0.0943438\pi$
$359$	4.67094e6	1.91279	0.956397	+	0.292069i	$0.0943438\pi$
$360$	3.64281e6	1.48143
$361$	0	0
$362$	1.79329e6	0.719249
$363$	2.01594e6	0.802993
$364$	−202041.	−0.0799257
$365$	3.04030e6	1.19449
$366$	−2.58329e6	−1.00802
$367$	−4.01217e6	−1.55494	−0.777471	−	0.628919i	$-0.783498\pi$
$367$	−4.01217e6	−1.55494	−0.777471	+	0.628919i	$0.783498\pi$
$368$	743100.	0.286040
$369$	−880554.	−0.336659
$370$	−102734.	−0.0390132
$371$	5.32304e6	2.00782
$372$	2.81766e6	1.05568
$373$	−1.17250e6	−0.436357	−0.218178	−	0.975909i	$-0.570011\pi$
$373$	−1.17250e6	−0.436357	−0.218178	+	0.975909i	$0.570011\pi$
$374$	70529.2	0.0260729
$375$	−4.65760e6	−1.71035
$376$	100645.	0.0367133
$377$	496760.	0.180009
$378$	6.40730e6	2.30646
$379$	1.22032e6	0.436391	0.218196	−	0.975905i	$-0.429983\pi$
$379$	1.22032e6	0.436391	0.218196	+	0.975905i	$0.429983\pi$
$380$	0	0
$381$	−4.88574e6	−1.72432
$382$	−616434.	−0.216136
$383$	2.51400e6	0.875726	0.437863	−	0.899042i	$-0.355736\pi$
$383$	2.51400e6	0.875726	0.437863	+	0.899042i	$0.355736\pi$
$384$	−485793.	−0.168121
$385$	3.75066e6	1.28960
$386$	3.75100e6	1.28138
$387$	5.13600e6	1.74320
$388$	652094.	0.219903
$389$	3.00920e6	1.00827	0.504135	−	0.863625i	$-0.331811\pi$
$389$	3.00920e6	1.00827	0.504135	+	0.863625i	$0.331811\pi$
$390$	−975175.	−0.324654
$391$	−167777.	−0.0554997
$392$	132813.	0.0436543
$393$	−3.78893e6	−1.23747
$394$	30695.8	0.00996182
$395$	−1.24728e6	−0.402226
$396$	−3.10500e6	−0.995002
$397$	−3.31110e6	−1.05438	−0.527189	−	0.849748i	$-0.676754\pi$
$397$	−3.31110e6	−1.05438	−0.527189	+	0.849748i	$0.676754\pi$
$398$	899432.	0.284617
$399$	0	0
$400$	1.24944e6	0.390450
$401$	4.73680e6	1.47104	0.735519	−	0.677504i	$-0.236938\pi$
$401$	4.73680e6	1.47104	0.735519	+	0.677504i	$0.236938\pi$
$402$	7.48605e6	2.31040
$403$	−545796.	−0.167405
$404$	2.08491e6	0.635526
$405$	1.70942e7	5.17860
$406$	−2.97125e6	−0.894590
$407$	87567.1	0.0262032
$408$	109682.	0.0326202
$409$	−1.81464e6	−0.536392	−0.268196	−	0.963364i	$-0.586428\pi$
$409$	−1.81464e6	−0.536392	−0.268196	+	0.963364i	$0.586428\pi$
$410$	−495399.	−0.145544
$411$	398957.	0.116499
$412$	2.73805e6	0.794691
$413$	−278231.	−0.0802657
$414$	7.38628e6	2.11800
$415$	7.17761e6	2.04578
$416$	94100.9	0.0266600
$417$	3.28078e6	0.923925
$418$	0	0
$419$	−4.58004e6	−1.27448	−0.637242	−	0.770664i	$-0.719925\pi$
$419$	−4.58004e6	−1.27448	−0.637242	+	0.770664i	$0.719925\pi$
$420$	5.83278e6	1.61344
$421$	−3.27447e6	−0.900399	−0.450200	−	0.892928i	$-0.648647\pi$
$421$	−3.27447e6	−0.900399	−0.450200	+	0.892928i	$0.648647\pi$
$422$	−481033.	−0.131490
$423$	1.00039e6	0.271844
$424$	−2.47921e6	−0.669729
$425$	−282099.	−0.0757582
$426$	2.98761e6	0.797628
$427$	−2.99301e6	−0.794399
$428$	2.37535e6	0.626784
$429$	831205.	0.218054
$430$	2.88951e6	0.753621
$431$	−3.35332e6	−0.869525	−0.434763	−	0.900545i	$-0.643168\pi$
$431$	−3.35332e6	−0.869525	−0.434763	+	0.900545i	$0.643168\pi$
$432$	−2.98420e6	−0.769341
$433$	6.67093e6	1.70988	0.854942	−	0.518724i	$-0.173593\pi$
$433$	6.67093e6	1.70988	0.854942	+	0.518724i	$0.173593\pi$
$434$	3.26455e6	0.831953
$435$	−1.43411e7	−3.63378
$436$	−350644.	−0.0883384
$437$	0	0
$438$	−4.03004e6	−1.00375
$439$	−3.13067e6	−0.775312	−0.387656	−	0.921804i	$-0.626715\pi$
$439$	−3.13067e6	−0.775312	−0.387656	+	0.921804i	$0.626715\pi$
$440$	−1.74687e6	−0.430159
$441$	1.32014e6	0.323239
$442$	−21246.1	−0.00517278
$443$	−1.67860e6	−0.406385	−0.203192	−	0.979139i	$-0.565132\pi$
$443$	−1.67860e6	−0.406385	−0.203192	+	0.979139i	$0.565132\pi$
$444$	136179.	0.0327832
$445$	−4.45607e6	−1.06672
$446$	88172.4	0.0209892
$447$	−7.53849e6	−1.78450
$448$	−562842.	−0.132493
$449$	2.63028e6	0.615725	0.307862	−	0.951431i	$-0.400386\pi$
$449$	2.63028e6	0.615725	0.307862	+	0.951431i	$0.400386\pi$
$450$	1.24192e7	2.89110
$451$	422260.	0.0977550
$452$	1.54800e6	0.356390
$453$	−9.26870e6	−2.12214
$454$	5.10504e6	1.16241
$455$	−1.12984e6	−0.255852
$456$	0	0
$457$	−8.76096e6	−1.96228	−0.981141	−	0.193296i	$-0.938082\pi$
$457$	−8.76096e6	−1.96228	−0.981141	+	0.193296i	$0.938082\pi$
$458$	311807.	0.0694581
$459$	673774.	0.149273
$460$	4.15551e6	0.915652
$461$	−3.09497e6	−0.678272	−0.339136	−	0.940737i	$-0.610135\pi$
$461$	−3.09497e6	−0.678272	−0.339136	+	0.940737i	$0.610135\pi$
$462$	−4.97165e6	−1.08367
$463$	−1.30572e6	−0.283071	−0.141536	−	0.989933i	$-0.545204\pi$
$463$	−1.30572e6	−0.283071	−0.141536	+	0.989933i	$0.545204\pi$
$464$	1.38386e6	0.298399
$465$	1.57567e7	3.37935
$466$	971309.	0.207201
$467$	4.16658e6	0.884072	0.442036	−	0.896997i	$-0.354256\pi$
$467$	4.16658e6	0.884072	0.442036	+	0.896997i	$0.354256\pi$
$468$	935346.	0.197405
$469$	8.67337e6	1.82077
$470$	562821.	0.117524
$471$	7.34487e6	1.52557
$472$	129586.	0.0267734
$473$	−2.46291e6	−0.506170
$474$	1.65332e6	0.337995
$475$	0	0
$476$	127079.	0.0257072
$477$	−2.46429e7	−4.95903
$478$	−556187.	−0.111340
$479$	5.06058e6	1.00777	0.503885	−	0.863770i	$-0.331903\pi$
$479$	5.06058e6	1.00777	0.503885	+	0.863770i	$0.331903\pi$
$480$	−2.71662e6	−0.538178
$481$	−26378.6	−0.00519863
$482$	−2.48061e6	−0.486342
$483$	1.18267e7	2.30673
$484$	−1.08785e6	−0.211083
$485$	3.64660e6	0.703937
$486$	−1.13285e7	−2.17561
$487$	−2.89146e6	−0.552452	−0.276226	−	0.961093i	$-0.589084\pi$
$487$	−2.89146e6	−0.552452	−0.276226	+	0.961093i	$0.589084\pi$
$488$	1.39400e6	0.264980
$489$	−1.10925e7	−2.09777
$490$	742711.	0.139743
$491$	4.37371e6	0.818741	0.409370	−	0.912368i	$-0.365748\pi$
$491$	4.37371e6	0.818741	0.409370	+	0.912368i	$0.365748\pi$
$492$	656672.	0.122303
$493$	−312449.	−0.0578977
$494$	0	0
$495$	−1.73636e7	−3.18513
$496$	−1.52047e6	−0.277506
$497$	3.46146e6	0.628592
$498$	−9.51422e6	−1.71910
$499$	−8.84744e6	−1.59062	−0.795310	−	0.606203i	$-0.792692\pi$
$499$	−8.84744e6	−1.59062	−0.795310	+	0.606203i	$0.792692\pi$
$500$	2.51334e6	0.449600
$501$	−1.84078e7	−3.27648
$502$	3.53359e6	0.625830
$503$	−1.01056e7	−1.78090	−0.890452	−	0.455077i	$-0.849612\pi$
$503$	−1.01056e7	−1.78090	−0.890452	+	0.455077i	$0.849612\pi$
$504$	−5.59455e6	−0.981045
$505$	1.16591e7	2.03440
$506$	−3.54201e6	−0.614998
$507$	1.07586e7	1.85882
$508$	2.63645e6	0.453273
$509$	−6.09045e6	−1.04197	−0.520984	−	0.853566i	$-0.674435\pi$
$509$	−6.09045e6	−1.04197	−0.520984	+	0.853566i	$0.674435\pi$
$510$	613359.	0.104421
$511$	−4.66923e6	−0.791029
$512$	262144.	0.0441942
$513$	0	0
$514$	6.47276e6	1.08064
$515$	1.53115e7	2.54391
$516$	−3.83016e6	−0.633276
$517$	−479729.	−0.0789349
$518$	157777.	0.0258357
$519$	−6.60971e6	−1.07712
$520$	526225.	0.0853421
$521$	4.32269e6	0.697686	0.348843	−	0.937181i	$-0.386575\pi$
$521$	4.32269e6	0.697686	0.348843	+	0.937181i	$0.386575\pi$
$522$	1.37554e7	2.20951
$523$	−5.46637e6	−0.873866	−0.436933	−	0.899494i	$-0.643935\pi$
$523$	−5.46637e6	−0.873866	−0.436933	+	0.899494i	$0.643935\pi$
$524$	2.04458e6	0.325295
$525$	1.98854e7	3.14873
$526$	−2.06158e6	−0.324889
$527$	343291.	0.0538439
$528$	2.31555e6	0.361468
$529$	1.98952e6	0.309106
$530$	−1.38641e7	−2.14389
$531$	1.28806e6	0.198244
$532$	0	0
$533$	−127201.	−0.0193942
$534$	5.90671e6	0.896381
$535$	1.32833e7	2.00642
$536$	−4.03963e6	−0.607336
$537$	1.27351e7	1.90575
$538$	2.48084e6	0.369524
$539$	−633060.	−0.0938584
$540$	−1.66881e7	−2.46276
$541$	−5.90997e6	−0.868144	−0.434072	−	0.900878i	$-0.642924\pi$
$541$	−5.90997e6	−0.868144	−0.434072	+	0.900878i	$0.642924\pi$
$542$	4.49226e6	0.656850
$543$	−1.32930e7	−1.93474
$544$	−59186.9	−0.00857489
$545$	−1.96085e6	−0.282782
$546$	1.49765e6	0.214996
$547$	−1.03070e7	−1.47286	−0.736431	−	0.676513i	$-0.763490\pi$
$547$	−1.03070e7	−1.47286	−0.736431	+	0.676513i	$0.763490\pi$
$548$	−215286.	−0.0306241
$549$	1.38561e7	1.96205
$550$	−5.95551e6	−0.839484
$551$	0	0
$552$	−5.50831e6	−0.769433
$553$	1.91554e6	0.266366
$554$	7.73095e6	1.07018
$555$	761530.	0.104943
$556$	−1.77038e6	−0.242873
$557$	1.11828e7	1.52726	0.763631	−	0.645653i	$-0.223415\pi$
$557$	1.11828e7	1.52726	0.763631	+	0.645653i	$0.223415\pi$
$558$	−1.51132e7	−2.05480
$559$	741925.	0.100422
$560$	−3.14749e6	−0.424125
$561$	−522805.	−0.0701347
$562$	3.75152e6	0.501033
$563$	4.25299e6	0.565487	0.282744	−	0.959195i	$-0.408755\pi$
$563$	4.25299e6	0.565487	0.282744	+	0.959195i	$0.408755\pi$
$564$	−746043.	−0.0987566
$565$	8.65664e6	1.14085
$566$	−1.88426e6	−0.247230
$567$	−2.62530e7	−3.42942
$568$	−1.61218e6	−0.209673
$569$	2.55215e6	0.330465	0.165233	−	0.986255i	$-0.447163\pi$
$569$	2.55215e6	0.330465	0.165233	+	0.986255i	$0.447163\pi$
$570$	0	0
$571$	−5.71384e6	−0.733395	−0.366698	−	0.930340i	$-0.619512\pi$
$571$	−5.71384e6	−0.733395	−0.366698	+	0.930340i	$0.619512\pi$
$572$	−448535.	−0.0573201
$573$	4.56938e6	0.581395
$574$	760823.	0.0963837
$575$	1.41672e7	1.78695
$576$	2.60567e6	0.327237
$577$	1.55345e7	1.94248	0.971240	−	0.238104i	$-0.0765260\pi$
$577$	1.55345e7	1.94248	0.971240	+	0.238104i	$0.0765260\pi$
$578$	−5.66606e6	−0.705443
$579$	−2.78047e7	−3.44685
$580$	7.73875e6	0.955214
$581$	−1.10232e7	−1.35478
$582$	−4.83372e6	−0.591527
$583$	1.18173e7	1.43994
$584$	2.17470e6	0.263856
$585$	5.23059e6	0.631918
$586$	−1.80092e6	−0.216645
$587$	1.60932e7	1.92773	0.963865	−	0.266392i	$-0.0858315\pi$
$587$	1.60932e7	1.92773	0.963865	+	0.266392i	$0.0858315\pi$
$588$	−984495.	−0.117428
$589$	0	0
$590$	724663.	0.0857050
$591$	−227536.	−0.0267967
$592$	−73484.9	−0.00861775
$593$	1.09783e7	1.28203	0.641013	−	0.767530i	$-0.278514\pi$
$593$	1.09783e7	1.28203	0.641013	+	0.767530i	$0.278514\pi$
$594$	1.42243e7	1.65411
$595$	710641.	0.0822920
$596$	4.06793e6	0.469091
$597$	−6.66714e6	−0.765603
$598$	1.06699e6	0.122013
$599$	1.43906e7	1.63875	0.819374	−	0.573260i	$-0.194321\pi$
$599$	1.43906e7	1.63875	0.819374	+	0.573260i	$0.194321\pi$
$600$	−9.26162e6	−1.05029
$601$	1.66130e6	0.187612	0.0938062	−	0.995590i	$-0.470097\pi$
$601$	1.66130e6	0.187612	0.0938062	+	0.995590i	$0.470097\pi$
$602$	−4.43765e6	−0.499070
$603$	−4.01532e7	−4.49704
$604$	5.00159e6	0.557847
$605$	−6.08338e6	−0.675704
$606$	−1.54546e7	−1.70953
$607$	−2.67042e6	−0.294177	−0.147088	−	0.989123i	$-0.546990\pi$
$607$	−2.67042e6	−0.294177	−0.147088	+	0.989123i	$0.546990\pi$
$608$	0	0
$609$	2.20247e7	2.40640
$610$	7.79542e6	0.848233
$611$	144513.	0.0156604
$612$	−588308.	−0.0634930
$613$	878479.	0.0944236	0.0472118	−	0.998885i	$-0.484966\pi$
$613$	878479.	0.0944236	0.0472118	+	0.998885i	$0.484966\pi$
$614$	−814182.	−0.0871566
$615$	3.67220e6	0.391506
$616$	2.68281e6	0.284864
$617$	−1.38295e7	−1.46249	−0.731244	−	0.682116i	$-0.761060\pi$
$617$	−1.38295e7	−1.46249	−0.731244	+	0.682116i	$0.761060\pi$
$618$	−2.02961e7	−2.13767
$619$	6.67997e6	0.700726	0.350363	−	0.936614i	$-0.386058\pi$
$619$	6.67997e6	0.700726	0.350363	+	0.936614i	$0.386058\pi$
$620$	−8.50266e6	−0.888332
$621$	−3.38373e7	−3.52100
$622$	−9.37436e6	−0.971551
$623$	6.84354e6	0.706416
$624$	−697533.	−0.0717139
$625$	−1.19704e6	−0.122577
$626$	−8.55119e6	−0.872149
$627$	0	0
$628$	−3.96344e6	−0.401027
$629$	16591.4	0.00167208
$630$	−3.12855e7	−3.14045
$631$	1.15223e7	1.15204	0.576018	−	0.817437i	$-0.304606\pi$
$631$	1.15223e7	1.15204	0.576018	+	0.817437i	$0.304606\pi$
$632$	−892164.	−0.0888489
$633$	3.56571e6	0.353702
$634$	−2.77504e6	−0.274186
$635$	1.47434e7	1.45098
$636$	1.83774e7	1.80153
$637$	190702.	0.0186212
$638$	−6.59623e6	−0.641570
$639$	−1.60248e7	−1.55253
$640$	1.46595e6	0.141471
$641$	1.55108e7	1.49104	0.745521	−	0.666482i	$-0.232201\pi$
$641$	1.55108e7	1.49104	0.745521	+	0.666482i	$0.232201\pi$
$642$	−1.76075e7	−1.68601
$643$	1.09813e7	1.04743	0.523717	−	0.851892i	$-0.324545\pi$
$643$	1.09813e7	1.04743	0.523717	+	0.851892i	$0.324545\pi$
$644$	−6.38195e6	−0.606372
$645$	−2.14188e7	−2.02720
$646$	0	0
$647$	670576.	0.0629778	0.0314889	−	0.999504i	$-0.489975\pi$
$647$	670576.	0.0629778	0.0314889	+	0.999504i	$0.489975\pi$
$648$	1.22273e7	1.14392
$649$	−617677.	−0.0575638
$650$	1.79403e6	0.166551
$651$	−2.41988e7	−2.23791
$652$	5.98575e6	0.551441
$653$	−1.94495e6	−0.178495	−0.0892475	−	0.996009i	$-0.528446\pi$
$653$	−1.94495e6	−0.178495	−0.0892475	+	0.996009i	$0.528446\pi$
$654$	2.59918e6	0.237625
$655$	1.14336e7	1.04131
$656$	−354354.	−0.0321497
$657$	2.16161e7	1.95373
$658$	−864369.	−0.0778277
$659$	−2.86870e6	−0.257319	−0.128660	−	0.991689i	$-0.541067\pi$
$659$	−2.86870e6	−0.257319	−0.128660	+	0.991689i	$0.541067\pi$
$660$	1.29489e7	1.15710
$661$	−5.73206e6	−0.510279	−0.255139	−	0.966904i	$-0.582121\pi$
$661$	−5.73206e6	−0.510279	−0.255139	+	0.966904i	$0.582121\pi$
$662$	5.79297e6	0.513756
$663$	157489.	0.0139145
$664$	5.13407e6	0.451899
$665$	0	0
$666$	−730427.	−0.0638104
$667$	1.56913e7	1.36567
$668$	9.93324e6	0.861291
$669$	−653588.	−0.0564597
$670$	−2.25902e7	−1.94416
$671$	−6.64454e6	−0.569716
$672$	4.17213e6	0.356397
$673$	−1.42986e7	−1.21690	−0.608452	−	0.793591i	$-0.708209\pi$
$673$	−1.42986e7	−1.21690	−0.608452	+	0.793591i	$0.708209\pi$
$674$	−5.37799e6	−0.456006
$675$	−5.68937e7	−4.80623
$676$	−5.80557e6	−0.488628
$677$	1.60430e7	1.34529	0.672643	−	0.739967i	$-0.265159\pi$
$677$	1.60430e7	1.34529	0.672643	+	0.739967i	$0.265159\pi$
$678$	−1.14747e7	−0.958669
$679$	−5.60037e6	−0.466168
$680$	−330981.	−0.0274493
$681$	−3.78417e7	−3.12682
$682$	7.24736e6	0.596649
$683$	−2.01746e6	−0.165483	−0.0827416	−	0.996571i	$-0.526368\pi$
$683$	−2.01746e6	−0.165483	−0.0827416	+	0.996571i	$0.526368\pi$
$684$	0	0
$685$	−1.20391e6	−0.0980317
$686$	8.09733e6	0.656949
$687$	−2.31131e6	−0.186838
$688$	2.06684e6	0.166470
$689$	−3.55981e6	−0.285680
$690$	−3.08032e7	−2.46305
$691$	3.44528e6	0.274492	0.137246	−	0.990537i	$-0.456175\pi$
$691$	3.44528e6	0.274492	0.137246	+	0.990537i	$0.456175\pi$
$692$	3.56674e6	0.283143
$693$	2.66666e7	2.10928
$694$	1.22046e7	0.961888
$695$	−9.90019e6	−0.777466
$696$	−1.02580e7	−0.802677
$697$	80006.1	0.00623794
$698$	−483317.	−0.0375486
$699$	−7.19993e6	−0.557360
$700$	−1.07306e7	−0.827708
$701$	−9.94555e6	−0.764423	−0.382212	−	0.924075i	$-0.624837\pi$
$701$	−9.94555e6	−0.764423	−0.382212	+	0.924075i	$0.624837\pi$
$702$	−4.28491e6	−0.328170
$703$	0	0
$704$	−1.24952e6	−0.0950192
$705$	−4.17197e6	−0.316132
$706$	6.62243e6	0.500041
$707$	−1.79058e7	−1.34724
$708$	−960571.	−0.0720189
$709$	−2.05813e7	−1.53765	−0.768824	−	0.639460i	$-0.779158\pi$
$709$	−2.05813e7	−1.53765	−0.768824	+	0.639460i	$0.779158\pi$
$710$	−9.01552e6	−0.671189
$711$	−8.86796e6	−0.657884
$712$	−3.18738e6	−0.235632
$713$	−1.72403e7	−1.27005
$714$	−941984.	−0.0691509
$715$	−2.50827e6	−0.183489
$716$	−6.87213e6	−0.500967
$717$	4.12280e6	0.299498
$718$	1.86838e7	1.35255
$719$	3.50194e6	0.252631	0.126315	−	0.991990i	$-0.459685\pi$
$719$	3.50194e6	0.252631	0.126315	+	0.991990i	$0.459685\pi$
$720$	1.45712e7	1.04753
$721$	−2.35151e7	−1.68465
$722$	0	0
$723$	1.83878e7	1.30823
$724$	7.17316e6	0.508586
$725$	2.63833e7	1.86416
$726$	8.06378e6	0.567802
$727$	2.12431e7	1.49067	0.745334	−	0.666691i	$-0.232290\pi$
$727$	2.12431e7	1.49067	0.745334	+	0.666691i	$0.232290\pi$
$728$	−808165.	−0.0565160
$729$	3.75480e7	2.61679
$730$	1.21612e7	0.844635
$731$	−466651.	−0.0322997
$732$	−1.03332e7	−0.712780
$733$	2.46594e7	1.69521	0.847603	−	0.530631i	$-0.178045\pi$
$733$	2.46594e7	1.69521	0.847603	+	0.530631i	$0.178045\pi$
$734$	−1.60487e7	−1.09951
$735$	−5.50543e6	−0.375900
$736$	2.97240e6	0.202261
$737$	1.92550e7	1.30580
$738$	−3.52222e6	−0.238054
$739$	9.89534e6	0.666530	0.333265	−	0.942833i	$-0.391850\pi$
$739$	9.89534e6	0.666530	0.333265	+	0.942833i	$0.391850\pi$
$740$	−410937.	−0.0275865
$741$	0	0
$742$	2.12922e7	1.41974
$743$	−1.32703e7	−0.881880	−0.440940	−	0.897537i	$-0.645355\pi$
$743$	−1.32703e7	−0.881880	−0.440940	+	0.897537i	$0.645355\pi$
$744$	1.12706e7	0.746476
$745$	2.27484e7	1.50162
$746$	−4.69001e6	−0.308551
$747$	5.10318e7	3.34610
$748$	282117.	0.0184363
$749$	−2.04002e7	−1.32871
$750$	−1.86304e7	−1.20940
$751$	1.94311e7	1.25718	0.628590	−	0.777737i	$-0.283633\pi$
$751$	1.94311e7	1.25718	0.628590	+	0.777737i	$0.283633\pi$
$752$	402580.	0.0259602
$753$	−2.61931e7	−1.68345
$754$	1.98704e6	0.127285
$755$	2.79695e7	1.78574
$756$	2.56292e7	1.63091
$757$	−1.79550e7	−1.13880	−0.569399	−	0.822061i	$-0.692824\pi$
$757$	−1.79550e7	−1.13880	−0.569399	+	0.822061i	$0.692824\pi$
$758$	4.88129e6	0.308575
$759$	2.62556e7	1.65431
$760$	0	0
$761$	−3.11076e7	−1.94717	−0.973587	−	0.228315i	$-0.926678\pi$
$761$	−3.11076e7	−1.94717	−0.973587	+	0.228315i	$0.926678\pi$
$762$	−1.95430e7	−1.21928
$763$	3.01143e6	0.187267
$764$	−2.46573e6	−0.152832
$765$	−3.28990e6	−0.203249
$766$	1.00560e7	0.619231
$767$	186068.	0.0114205
$768$	−1.94317e6	−0.118880
$769$	2.03912e7	1.24345	0.621724	−	0.783237i	$-0.286433\pi$
$769$	2.03912e7	1.24345	0.621724	+	0.783237i	$0.286433\pi$
$770$	1.50026e7	0.911886
$771$	−4.79800e7	−2.90686
$772$	1.50040e7	0.906074
$773$	1.87138e7	1.12646	0.563228	−	0.826302i	$-0.309559\pi$
$773$	1.87138e7	1.12646	0.563228	+	0.826302i	$0.309559\pi$
$774$	2.05440e7	1.23263
$775$	−2.89876e7	−1.73364
$776$	2.60838e6	0.155495
$777$	−1.16954e6	−0.0694965
$778$	1.20368e7	0.712955
$779$	0	0
$780$	−3.90070e6	−0.229565
$781$	7.68451e6	0.450805
$782$	−671109.	−0.0392442
$783$	−6.30146e7	−3.67313
$784$	531254.	0.0308682
$785$	−2.21641e7	−1.28374
$786$	−1.51557e7	−0.875024
$787$	−2.18789e7	−1.25918	−0.629591	−	0.776927i	$-0.716778\pi$
$787$	−2.18789e7	−1.25918	−0.629591	+	0.776927i	$0.716778\pi$
$788$	122783.	0.00704407
$789$	1.52817e7	0.873933
$790$	−4.98910e6	−0.284417
$791$	−1.32947e7	−0.755504
$792$	−1.24200e7	−0.703573
$793$	2.00159e6	0.113030
$794$	−1.32444e7	−0.745558
$795$	1.02769e8	5.76693
$796$	3.59773e6	0.201255
$797$	−2.57470e7	−1.43576	−0.717879	−	0.696168i	$-0.754887\pi$
$797$	−2.57470e7	−1.43576	−0.717879	+	0.696168i	$0.754887\pi$
$798$	0	0
$799$	−90894.7	−0.00503699
$800$	4.99777e6	0.276090
$801$	−3.16820e7	−1.74474
$802$	1.89472e7	1.04018
$803$	−1.03658e7	−0.567300
$804$	2.99442e7	1.63370
$805$	−3.56887e7	−1.94107
$806$	−2.18319e6	−0.118373
$807$	−1.83895e7	−0.993999
$808$	8.33962e6	0.449385
$809$	1.55491e7	0.835285	0.417642	−	0.908611i	$-0.362856\pi$
$809$	1.55491e7	0.835285	0.417642	+	0.908611i	$0.362856\pi$
$810$	6.83770e7	3.66182
$811$	−2.31068e7	−1.23364	−0.616820	−	0.787104i	$-0.711579\pi$
$811$	−2.31068e7	−1.23364	−0.616820	+	0.787104i	$0.711579\pi$
$812$	−1.18850e7	−0.632571
$813$	−3.32994e7	−1.76689
$814$	350268.	0.0185285
$815$	3.34731e7	1.76523
$816$	438730.	0.0230660
$817$	0	0
$818$	−7.25857e6	−0.379287
$819$	−8.03302e6	−0.418475
$820$	−1.98159e6	−0.102915
$821$	6.21027e6	0.321553	0.160777	−	0.986991i	$-0.448600\pi$
$821$	6.21027e6	0.321553	0.160777	+	0.986991i	$0.448600\pi$
$822$	1.59583e6	0.0823772
$823$	−733552.	−0.0377512	−0.0188756	−	0.999822i	$-0.506009\pi$
$823$	−733552.	−0.0377512	−0.0188756	+	0.999822i	$0.506009\pi$
$824$	1.09522e7	0.561931
$825$	4.41459e7	2.25816
$826$	−1.11292e6	−0.0567564
$827$	1.86346e7	0.947452	0.473726	−	0.880672i	$-0.342909\pi$
$827$	1.86346e7	0.947452	0.473726	+	0.880672i	$0.342909\pi$
$828$	2.95451e7	1.49765
$829$	−1.75349e7	−0.886172	−0.443086	−	0.896479i	$-0.646116\pi$
$829$	−1.75349e7	−0.886172	−0.443086	+	0.896479i	$0.646116\pi$
$830$	2.87104e7	1.44659
$831$	−5.73065e7	−2.87873
$832$	376403.	0.0188515
$833$	−119947.	−0.00598929
$834$	1.31231e7	0.653314
$835$	5.55480e7	2.75710
$836$	0	0
$837$	6.92349e7	3.41595
$838$	−1.83202e7	−0.901196
$839$	−2.25214e7	−1.10456	−0.552282	−	0.833658i	$-0.686243\pi$
$839$	−2.25214e7	−1.10456	−0.552282	+	0.833658i	$0.686243\pi$
$840$	2.33311e7	1.14087
$841$	8.71058e6	0.424675
$842$	−1.30979e7	−0.636679
$843$	−2.78086e7	−1.34775
$844$	−1.92413e6	−0.0929777
$845$	−3.24656e7	−1.56416
$846$	4.00158e6	0.192223
$847$	9.34273e6	0.447471
$848$	−9.91684e6	−0.473570
$849$	1.39673e7	0.665033
$850$	−1.12840e6	−0.0535691
$851$	−833230.	−0.0394404
$852$	1.19505e7	0.564008
$853$	−1.99398e7	−0.938316	−0.469158	−	0.883114i	$-0.655443\pi$
$853$	−1.99398e7	−0.938316	−0.469158	+	0.883114i	$0.655443\pi$
$854$	−1.19720e7	−0.561725
$855$	0	0
$856$	9.50140e6	0.443203
$857$	−1.18082e7	−0.549203	−0.274602	−	0.961558i	$-0.588546\pi$
$857$	−1.18082e7	−0.549203	−0.274602	+	0.961558i	$0.588546\pi$
$858$	3.32482e6	0.154188
$859$	−9.16488e6	−0.423783	−0.211892	−	0.977293i	$-0.567962\pi$
$859$	−9.16488e6	−0.423783	−0.211892	+	0.977293i	$0.567962\pi$
$860$	1.15580e7	0.532890
$861$	−5.63968e6	−0.259267
$862$	−1.34133e7	−0.614847
$863$	−3.71519e7	−1.69807	−0.849033	−	0.528340i	$-0.822815\pi$
$863$	−3.71519e7	−1.69807	−0.849033	+	0.528340i	$0.822815\pi$
$864$	−1.19368e7	−0.544006
$865$	1.99457e7	0.906376
$866$	2.66837e7	1.20907
$867$	4.20003e7	1.89760
$868$	1.30582e7	0.588280
$869$	4.25253e6	0.191029
$870$	−5.73643e7	−2.56947
$871$	−5.80036e6	−0.259066
$872$	−1.40257e6	−0.0624647
$873$	2.59268e7	1.15137
$874$	0	0
$875$	−2.15853e7	−0.953097
$876$	−1.61202e7	−0.709757
$877$	4.63084e6	0.203311	0.101656	−	0.994820i	$-0.467586\pi$
$877$	4.63084e6	0.203311	0.101656	+	0.994820i	$0.467586\pi$
$878$	−1.25227e7	−0.548228
$879$	1.33495e7	0.582764
$880$	−6.98748e6	−0.304168
$881$	−2.79943e7	−1.21515	−0.607575	−	0.794262i	$-0.707858\pi$
$881$	−2.79943e7	−1.21515	−0.607575	+	0.794262i	$0.707858\pi$
$882$	5.28057e6	0.228565
$883$	2.49713e7	1.07780	0.538902	−	0.842369i	$-0.318839\pi$
$883$	2.49713e7	1.07780	0.538902	+	0.842369i	$0.318839\pi$
$884$	−84984.4	−0.00365771
$885$	−5.37165e6	−0.230542
$886$	−6.71439e6	−0.287357
$887$	2.54372e7	1.08557	0.542787	−	0.839870i	$-0.317369\pi$
$887$	2.54372e7	1.08557	0.542787	+	0.839870i	$0.317369\pi$
$888$	544715.	0.0231812
$889$	−2.26426e7	−0.960885
$890$	−1.78243e7	−0.754288
$891$	−5.82821e7	−2.45947
$892$	352690.	0.0148416
$893$	0	0
$894$	−3.01540e7	−1.26183
$895$	−3.84299e7	−1.60366
$896$	−2.25137e6	−0.0936864
$897$	−7.90919e6	−0.328209
$898$	1.05211e7	0.435383
$899$	−3.21063e7	−1.32492
$900$	4.96769e7	2.04432
$901$	2.23903e6	0.0918856
$902$	1.68904e6	0.0691232
$903$	3.28945e7	1.34247
$904$	6.19201e6	0.252006
$905$	4.01133e7	1.62805
$906$	−3.70748e7	−1.50058
$907$	9.49624e6	0.383295	0.191648	−	0.981464i	$-0.438617\pi$
$907$	9.49624e6	0.383295	0.191648	+	0.981464i	$0.438617\pi$
$908$	2.04202e7	0.821949
$909$	8.28944e7	3.32748
$910$	−4.51937e6	−0.180915
$911$	−6.43324e6	−0.256823	−0.128412	−	0.991721i	$-0.540988\pi$
$911$	−6.43324e6	−0.256823	−0.128412	+	0.991721i	$0.540988\pi$
$912$	0	0
$913$	−2.44718e7	−0.971601
$914$	−3.50438e7	−1.38754
$915$	−5.77844e7	−2.28170
$916$	1.24723e6	0.0491143
$917$	−1.75595e7	−0.689586
$918$	2.69510e6	0.105552
$919$	−7.76851e6	−0.303423	−0.151712	−	0.988425i	$-0.548478\pi$
$919$	−7.76851e6	−0.303423	−0.151712	+	0.988425i	$0.548478\pi$
$920$	1.66221e7	0.647463
$921$	6.03521e6	0.234446
$922$	−1.23799e7	−0.479611
$923$	−2.31487e6	−0.0894381
$924$	−1.98866e7	−0.766268
$925$	−1.40099e6	−0.0538368
$926$	−5.22286e6	−0.200162
$927$	1.08863e8	4.16084
$928$	5.53545e6	0.211000
$929$	−3.46527e7	−1.31734	−0.658669	−	0.752433i	$-0.728880\pi$
$929$	−3.46527e7	−1.31734	−0.658669	+	0.752433i	$0.728880\pi$
$930$	6.30269e7	2.38956
$931$	0	0
$932$	3.88523e6	0.146513
$933$	6.94885e7	2.61342
$934$	1.66663e7	0.625133
$935$	1.57764e6	0.0590171
$936$	3.74139e6	0.139586
$937$	1.82455e6	0.0678903	0.0339451	−	0.999424i	$-0.489193\pi$
$937$	1.82455e6	0.0678903	0.0339451	+	0.999424i	$0.489193\pi$
$938$	3.46935e7	1.28748
$939$	6.33866e7	2.34603
$940$	2.25128e6	0.0831018
$941$	1.99896e7	0.735918	0.367959	−	0.929842i	$-0.380057\pi$
$941$	1.99896e7	0.735918	0.367959	+	0.929842i	$0.380057\pi$
$942$	2.93795e7	1.07874
$943$	−4.01795e6	−0.147138
$944$	518344.	0.0189316
$945$	1.43322e8	5.22075
$946$	−9.85165e6	−0.357916
$947$	−1.44410e7	−0.523265	−0.261632	−	0.965168i	$-0.584261\pi$
$947$	−1.44410e7	−0.523265	−0.261632	+	0.965168i	$0.584261\pi$
$948$	6.61327e6	0.238998
$949$	3.12257e6	0.112550
$950$	0	0
$951$	2.05703e7	0.737545
$952$	508314.	0.0181777
$953$	2.86149e7	1.02061	0.510304	−	0.859994i	$-0.329533\pi$
$953$	2.86149e7	1.02061	0.510304	+	0.859994i	$0.329533\pi$
$954$	−9.85717e7	−3.50656
$955$	−1.37887e7	−0.489233
$956$	−2.22475e6	−0.0787293
$957$	4.88953e7	1.72579
$958$	2.02423e7	0.712602
$959$	1.84893e6	0.0649195
$960$	−1.08665e7	−0.380549
$961$	6.64641e6	0.232155
$962$	−105514.	−0.00367599
$963$	9.44423e7	3.28171
$964$	−9.92246e6	−0.343896
$965$	8.39044e7	2.90046
$966$	4.73069e7	1.63110
$967$	−2.55539e7	−0.878803	−0.439402	−	0.898291i	$-0.644809\pi$
$967$	−2.55539e7	−0.878803	−0.439402	+	0.898291i	$0.644809\pi$
$968$	−4.35138e6	−0.149258
$969$	0	0
$970$	1.45864e7	0.497759
$971$	−5.93325e6	−0.201950	−0.100975	−	0.994889i	$-0.532196\pi$
$971$	−5.93325e6	−0.201950	−0.100975	+	0.994889i	$0.532196\pi$
$972$	−4.53140e7	−1.53839
$973$	1.52045e7	0.514861
$974$	−1.15658e7	−0.390643
$975$	−1.32984e7	−0.448012
$976$	5.57599e6	0.187369
$977$	2.57571e7	0.863297	0.431648	−	0.902042i	$-0.357932\pi$
$977$	2.57571e7	0.863297	0.431648	+	0.902042i	$0.357932\pi$
$978$	−4.43700e7	−1.48335
$979$	1.51928e7	0.506618
$980$	2.97084e6	0.0988131
$981$	−1.39413e7	−0.462522
$982$	1.74948e7	0.578937
$983$	2.56862e7	0.847843	0.423922	−	0.905699i	$-0.360653\pi$
$983$	2.56862e7	0.847843	0.423922	+	0.905699i	$0.360653\pi$
$984$	2.62669e6	0.0864810
$985$	686621.	0.0225490
$986$	−1.24979e6	−0.0409399
$987$	6.40723e6	0.209352
$988$	0	0
$989$	2.34354e7	0.761873
$990$	−6.94544e7	−2.25222
$991$	1.04473e7	0.337926	0.168963	−	0.985622i	$-0.445958\pi$
$991$	1.04473e7	0.337926	0.168963	+	0.985622i	$0.445958\pi$
$992$	−6.08187e6	−0.196227
$993$	−4.29411e7	−1.38197
$994$	1.38458e7	0.444481
$995$	2.01190e7	0.644241
$996$	−3.80569e7	−1.21558
$997$	1.98702e7	0.633089	0.316545	−	0.948578i	$-0.397477\pi$
$997$	1.98702e7	0.633089	0.316545	+	0.948578i	$0.397477\pi$
$998$	−3.53898e7	−1.12474
$999$	3.34616e6	0.106080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.r.1.1		15
19.9	even	9		38.6.e.b.5.1	✓	30
19.17	even	9		38.6.e.b.23.1	yes	30
19.18	odd	2		722.6.a.q.1.15		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.5.1	✓	30	19.9	even	9
38.6.e.b.23.1	yes	30	19.17	even	9
722.6.a.q.1.15		15	19.18	odd	2
722.6.a.r.1.1		15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -29.6504 q^{3} +16.0000 q^{4} +89.4742 q^{5} -118.602 q^{6} -137.413 q^{7} +64.0000 q^{8} +636.149 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -29.6504 q^{3} +16.0000 q^{4} +89.4742 q^{5} -118.602 q^{6} -137.413 q^{7} +64.0000 q^{8} +636.149 q^{9} +357.897 q^{10} -305.058 q^{11} -474.407 q^{12} +91.8954 q^{13} -549.650 q^{14} -2652.95 q^{15} +256.000 q^{16} -57.7997 q^{17} +2544.60 q^{18} +1431.59 q^{20} +4074.34 q^{21} -1220.23 q^{22} +2902.73 q^{23} -1897.63 q^{24} +4880.63 q^{25} +367.582 q^{26} -11657.0 q^{27} -2198.60 q^{28} +5405.71 q^{29} -10611.8 q^{30} -5939.32 q^{31} +1024.00 q^{32} +9045.12 q^{33} -231.199 q^{34} -12294.9 q^{35} +10178.4 q^{36} -287.050 q^{37} -2724.74 q^{39} +5726.35 q^{40} -1384.19 q^{41} +16297.4 q^{42} +8073.58 q^{43} -4880.93 q^{44} +56918.9 q^{45} +11610.9 q^{46} +1572.58 q^{47} -7590.51 q^{48} +2075.21 q^{49} +19522.5 q^{50} +1713.79 q^{51} +1470.33 q^{52} -38737.7 q^{53} -46628.2 q^{54} -27294.9 q^{55} -8794.40 q^{56} +21622.8 q^{58} +2024.78 q^{59} -42447.2 q^{60} +21781.2 q^{61} -23757.3 q^{62} -87414.9 q^{63} +4096.00 q^{64} +8222.26 q^{65} +36180.5 q^{66} -63119.2 q^{67} -924.796 q^{68} -86067.3 q^{69} -49179.5 q^{70} -25190.3 q^{71} +40713.5 q^{72} +33979.6 q^{73} -1148.20 q^{74} -144713. q^{75} +41918.9 q^{77} -10899.0 q^{78} -13940.1 q^{79} +22905.4 q^{80} +191052. q^{81} -5536.78 q^{82} +80219.9 q^{83} +65189.5 q^{84} -5171.58 q^{85} +32294.3 q^{86} -160282. q^{87} -19523.7 q^{88} -49802.9 q^{89} +227676. q^{90} -12627.6 q^{91} +46443.7 q^{92} +176104. q^{93} +6290.32 q^{94} -30362.1 q^{96} +40755.9 q^{97} +8300.84 q^{98} -194063. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} + 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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