LMFDB - Embedded newform 722.6.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$115.797117905$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2871 x^{13} - 4674 x^{12} + 3170019 x^{11} + 9081402 x^{10} - 1680307373 x^{9} + \cdots - 34\!\cdots\!72 $ x^15 - 2871x^13 - 4674x^12 + 3170019x^11 + 9081402x^10 - 1680307373x^9 - 6060225486x^8 + 437045334939x^7 + 1625551725606x^6 - 51993847360191x^5 - 166593470925336x^4 + 2435236025483701x^3 + 5743342864926480x^2 - 19853455953893436*x - 34308015556724472
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 19^{6} $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$28.1551$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} -28.5024 q^{3} +16.0000 q^{4} -35.3418 q^{5} -114.010 q^{6} +85.8987 q^{7} +64.0000 q^{8} +569.386 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -28.5024 q^{3} +16.0000 q^{4} -35.3418 q^{5} -114.010 q^{6} +85.8987 q^{7} +64.0000 q^{8} +569.386 q^{9} -141.367 q^{10} +599.653 q^{11} -456.038 q^{12} +544.910 q^{13} +343.595 q^{14} +1007.33 q^{15} +256.000 q^{16} +1455.96 q^{17} +2277.54 q^{18} -565.469 q^{20} -2448.32 q^{21} +2398.61 q^{22} +3670.68 q^{23} -1824.15 q^{24} -1875.96 q^{25} +2179.64 q^{26} -9302.78 q^{27} +1374.38 q^{28} +102.312 q^{29} +4029.30 q^{30} -881.642 q^{31} +1024.00 q^{32} -17091.5 q^{33} +5823.85 q^{34} -3035.82 q^{35} +9110.18 q^{36} -8650.33 q^{37} -15531.2 q^{39} -2261.88 q^{40} +10661.8 q^{41} -9793.27 q^{42} -5021.94 q^{43} +9594.45 q^{44} -20123.1 q^{45} +14682.7 q^{46} +8122.59 q^{47} -7296.61 q^{48} -9428.41 q^{49} -7503.83 q^{50} -41498.4 q^{51} +8718.55 q^{52} +25891.9 q^{53} -37211.1 q^{54} -21192.8 q^{55} +5497.52 q^{56} +409.248 q^{58} +36154.1 q^{59} +16117.2 q^{60} +39364.4 q^{61} -3526.57 q^{62} +48909.5 q^{63} +4096.00 q^{64} -19258.1 q^{65} -68366.2 q^{66} -13695.9 q^{67} +23295.4 q^{68} -104623. q^{69} -12143.3 q^{70} -74750.5 q^{71} +36440.7 q^{72} -59055.8 q^{73} -34601.3 q^{74} +53469.2 q^{75} +51509.4 q^{77} -62124.9 q^{78} +6009.40 q^{79} -9047.50 q^{80} +126791. q^{81} +42647.4 q^{82} +73164.8 q^{83} -39173.1 q^{84} -51456.3 q^{85} -20087.8 q^{86} -2916.14 q^{87} +38377.8 q^{88} +15304.5 q^{89} -80492.5 q^{90} +46807.0 q^{91} +58730.8 q^{92} +25128.9 q^{93} +32490.4 q^{94} -29186.4 q^{96} -107152. q^{97} -37713.6 q^{98} +341434. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−28.5024	−1.82843	−0.914215	−	0.405231i	$-0.867191\pi$
$3$	−28.5024	−1.82843	−0.914215	+	0.405231i	$0.867191\pi$
$4$	16.0000	0.500000
$5$	−35.3418	−0.632213	−0.316107	−	0.948724i	$-0.602376\pi$
$5$	−35.3418	−0.632213	−0.316107	+	0.948724i	$0.602376\pi$
$6$	−114.010	−1.29289
$7$	85.8987	0.662585	0.331292	−	0.943528i	$-0.392515\pi$
$7$	85.8987	0.662585	0.331292	+	0.943528i	$0.392515\pi$
$8$	64.0000	0.353553
$9$	569.386	2.34315
$10$	−141.367	−0.447042
$11$	599.653	1.49423	0.747117	−	0.664693i	$-0.231438\pi$
$11$	599.653	1.49423	0.747117	+	0.664693i	$0.231438\pi$
$12$	−456.038	−0.914215
$13$	544.910	0.894265	0.447132	−	0.894468i	$-0.352445\pi$
$13$	544.910	0.894265	0.447132	+	0.894468i	$0.352445\pi$
$14$	343.595	0.468518
$15$	1007.33	1.15596
$16$	256.000	0.250000
$17$	1455.96	1.22188	0.610939	−	0.791678i	$-0.290792\pi$
$17$	1455.96	1.22188	0.610939	+	0.791678i	$0.290792\pi$
$18$	2277.54	1.65686
$19$	0	0
$19$	0	0
$20$	−565.469	−0.316107
$21$	−2448.32	−1.21149
$22$	2398.61	1.05658
$23$	3670.68	1.44686	0.723430	−	0.690398i	$-0.242564\pi$
$23$	3670.68	1.44686	0.723430	+	0.690398i	$0.242564\pi$
$24$	−1824.15	−0.646447
$25$	−1875.96	−0.600306
$26$	2179.64	0.632341
$27$	−9302.78	−2.45586
$28$	1374.38	0.331292
$29$	102.312	0.0225908	0.0112954	−	0.999936i	$-0.496404\pi$
$29$	102.312	0.0225908	0.0112954	+	0.999936i	$0.496404\pi$
$30$	4029.30	0.817385
$31$	−881.642	−0.164774	−0.0823869	−	0.996600i	$-0.526254\pi$
$31$	−881.642	−0.164774	−0.0823869	+	0.996600i	$0.526254\pi$
$32$	1024.00	0.176777
$33$	−17091.5	−2.73210
$34$	5823.85	0.863998
$35$	−3035.82	−0.418895
$36$	9110.18	1.17158
$37$	−8650.33	−1.03879	−0.519396	−	0.854534i	$-0.673843\pi$
$37$	−8650.33	−1.03879	−0.519396	+	0.854534i	$0.673843\pi$
$38$	0	0
$39$	−15531.2	−1.63510
$40$	−2261.88	−0.223521
$41$	10661.8	0.990541	0.495271	−	0.868739i	$-0.335069\pi$
$41$	10661.8	0.990541	0.495271	+	0.868739i	$0.335069\pi$
$42$	−9793.27	−0.856652
$43$	−5021.94	−0.414191	−0.207095	−	0.978321i	$-0.566401\pi$
$43$	−5021.94	−0.414191	−0.207095	+	0.978321i	$0.566401\pi$
$44$	9594.45	0.747117
$45$	−20123.1	−1.48137
$46$	14682.7	1.02308
$47$	8122.59	0.536352	0.268176	−	0.963370i	$-0.413579\pi$
$47$	8122.59	0.536352	0.268176	+	0.963370i	$0.413579\pi$
$48$	−7296.61	−0.457107
$49$	−9428.41	−0.560981
$50$	−7503.83	−0.424481
$51$	−41498.4	−2.23412
$52$	8718.55	0.447132
$53$	25891.9	1.26612	0.633060	−	0.774103i	$-0.281799\pi$
$53$	25891.9	1.26612	0.633060	+	0.774103i	$0.281799\pi$
$54$	−37211.1	−1.73655
$55$	−21192.8	−0.944674
$56$	5497.52	0.234259
$57$	0	0
$58$	409.248	0.0159741
$59$	36154.1	1.35216	0.676078	−	0.736830i	$-0.263678\pi$
$59$	36154.1	1.35216	0.676078	+	0.736830i	$0.263678\pi$
$60$	16117.2	0.577979
$61$	39364.4	1.35450	0.677250	−	0.735753i	$-0.263171\pi$
$61$	39364.4	1.35450	0.677250	+	0.735753i	$0.263171\pi$
$62$	−3526.57	−0.116513
$63$	48909.5	1.55254
$64$	4096.00	0.125000
$65$	−19258.1	−0.565366
$66$	−68366.2	−1.93189
$67$	−13695.9	−0.372738	−0.186369	−	0.982480i	$-0.559672\pi$
$67$	−13695.9	−0.372738	−0.186369	+	0.982480i	$0.559672\pi$
$68$	23295.4	0.610939
$69$	−104623.	−2.64548
$70$	−12143.3	−0.296204
$71$	−74750.5	−1.75982	−0.879910	−	0.475140i	$-0.842397\pi$
$71$	−74750.5	−1.75982	−0.879910	+	0.475140i	$0.842397\pi$
$72$	36440.7	0.828430
$73$	−59055.8	−1.29705	−0.648523	−	0.761195i	$-0.724613\pi$
$73$	−59055.8	−1.29705	−0.648523	+	0.761195i	$0.724613\pi$
$74$	−34601.3	−0.734536
$75$	53469.2	1.09762
$76$	0	0
$77$	51509.4	0.990056
$78$	−62124.9	−1.15619
$79$	6009.40	0.108334	0.0541668	−	0.998532i	$-0.482750\pi$
$79$	6009.40	0.108334	0.0541668	+	0.998532i	$0.482750\pi$
$80$	−9047.50	−0.158053
$81$	126791.	2.14721
$82$	42647.4	0.700418
$83$	73164.8	1.16575	0.582877	−	0.812560i	$-0.301927\pi$
$83$	73164.8	1.16575	0.582877	+	0.812560i	$0.301927\pi$
$84$	−39173.1	−0.605745
$85$	−51456.3	−0.772488
$86$	−20087.8	−0.292877
$87$	−2916.14	−0.0413057
$88$	38377.8	0.528291
$89$	15304.5	0.204806	0.102403	−	0.994743i	$-0.467347\pi$
$89$	15304.5	0.204806	0.102403	+	0.994743i	$0.467347\pi$
$90$	−80492.5	−1.04749
$91$	46807.0	0.592526
$92$	58730.8	0.723430
$93$	25128.9	0.301277
$94$	32490.4	0.379258
$95$	0	0
$96$	−29186.4	−0.323224
$97$	−107152.	−1.15630	−0.578151	−	0.815930i	$-0.696226\pi$
$97$	−107152.	−1.15630	−0.578151	+	0.815930i	$0.696226\pi$
$98$	−37713.6	−0.396674
$99$	341434.	3.50122
$100$	−30015.3	−0.300153
$101$	77662.0	0.757539	0.378769	−	0.925491i	$-0.376347\pi$
$101$	77662.0	0.757539	0.378769	+	0.925491i	$0.376347\pi$
$102$	−165994.	−1.57976
$103$	6237.83	0.0579349	0.0289675	−	0.999580i	$-0.490778\pi$
$103$	6237.83	0.0579349	0.0289675	+	0.999580i	$0.490778\pi$
$104$	34874.2	0.316170
$105$	86528.0	0.765920
$106$	103568.	0.895282
$107$	−148187.	−1.25127	−0.625633	−	0.780118i	$-0.715159\pi$
$107$	−148187.	−1.25127	−0.625633	+	0.780118i	$0.715159\pi$
$108$	−148845.	−1.22793
$109$	13497.3	0.108813	0.0544064	−	0.998519i	$-0.482673\pi$
$109$	13497.3	0.108813	0.0544064	+	0.998519i	$0.482673\pi$
$110$	−84771.3	−0.667986
$111$	246555.	1.89936
$112$	21990.1	0.165646
$113$	113460.	0.835882	0.417941	−	0.908474i	$-0.362752\pi$
$113$	113460.	0.835882	0.417941	+	0.908474i	$0.362752\pi$
$114$	0	0
$115$	−129728.	−0.914724
$116$	1636.99	0.0112954
$117$	310264.	2.09540
$118$	144616.	0.956119
$119$	125065.	0.809598
$120$	64468.9	0.408693
$121$	198533.	1.23273
$122$	157458.	0.957777
$123$	−303888.	−1.81113
$124$	−14106.3	−0.0823869
$125$	176743.	1.01174
$126$	195638.	1.09781
$127$	273734.	1.50598	0.752990	−	0.658032i	$-0.228611\pi$
$127$	273734.	1.50598	0.752990	+	0.658032i	$0.228611\pi$
$128$	16384.0	0.0883883
$129$	143137.	0.757319
$130$	−77032.4	−0.399774
$131$	271140.	1.38043	0.690217	−	0.723603i	$-0.257515\pi$
$131$	271140.	1.38043	0.690217	+	0.723603i	$0.257515\pi$
$132$	−273465.	−1.36605
$133$	0	0
$134$	−54783.6	−0.263565
$135$	328777.	1.55263
$136$	93181.6	0.431999
$137$	−370058.	−1.68449	−0.842245	−	0.539094i	$-0.818767\pi$
$137$	−370058.	−1.68449	−0.842245	+	0.539094i	$0.818767\pi$
$138$	−418492.	−1.87064
$139$	−274200.	−1.20374	−0.601868	−	0.798596i	$-0.705577\pi$
$139$	−274200.	−1.20374	−0.601868	+	0.798596i	$0.705577\pi$
$140$	−48573.0	−0.209448
$141$	−231513.	−0.980682
$142$	−299002.	−1.24438
$143$	326757.	1.33624
$144$	145763.	0.585788
$145$	−3615.89	−0.0142822
$146$	−236223.	−0.917150
$147$	268732.	1.02571
$148$	−138405.	−0.519396
$149$	−312678.	−1.15380	−0.576902	−	0.816813i	$-0.695739\pi$
$149$	−312678.	−1.15380	−0.576902	+	0.816813i	$0.695739\pi$
$150$	213877.	0.776133
$151$	−444816.	−1.58759	−0.793794	−	0.608187i	$-0.791897\pi$
$151$	−444816.	−1.58759	−0.793794	+	0.608187i	$0.791897\pi$
$152$	0	0
$153$	829005.	2.86305
$154$	206038.	0.700076
$155$	31158.8	0.104172
$156$	−248500.	−0.817550
$157$	531353.	1.72042	0.860210	−	0.509941i	$-0.170333\pi$
$157$	531353.	1.72042	0.860210	+	0.509941i	$0.170333\pi$
$158$	24037.6	0.0766034
$159$	−737982.	−2.31501
$160$	−36190.0	−0.111761
$161$	315306.	0.958668
$162$	507163.	1.51831
$163$	−134875.	−0.397614	−0.198807	−	0.980039i	$-0.563707\pi$
$163$	−134875.	−0.397614	−0.198807	+	0.980039i	$0.563707\pi$
$164$	170589.	0.495271
$165$	604046.	1.72727
$166$	292659.	0.824313
$167$	88574.0	0.245762	0.122881	−	0.992421i	$-0.460787\pi$
$167$	88574.0	0.245762	0.122881	+	0.992421i	$0.460787\pi$
$168$	−156692.	−0.428326
$169$	−74366.6	−0.200291
$170$	−205825.	−0.546231
$171$	0	0
$172$	−80351.1	−0.207095
$173$	443029.	1.12543	0.562713	−	0.826652i	$-0.309758\pi$
$173$	443029.	1.12543	0.562713	+	0.826652i	$0.309758\pi$
$174$	−11664.6	−0.0292075
$175$	−161142.	−0.397754
$176$	153511.	0.373558
$177$	−1.03048e6	−2.47232
$178$	61217.9	0.144820
$179$	−190225.	−0.443746	−0.221873	−	0.975076i	$-0.571217\pi$
$179$	−190225.	−0.443746	−0.221873	+	0.975076i	$0.571217\pi$
$180$	−321970.	−0.740686
$181$	−98267.2	−0.222952	−0.111476	−	0.993767i	$-0.535558\pi$
$181$	−98267.2	−0.222952	−0.111476	+	0.993767i	$0.535558\pi$
$182$	187228.	0.418979
$183$	−1.12198e6	−2.47661
$184$	234923.	0.511542
$185$	305718.	0.656738
$186$	100516.	0.213035
$187$	873072.	1.82577
$188$	129962.	0.268176
$189$	−799097.	−1.62722
$190$	0	0
$191$	160536.	0.318411	0.159206	−	0.987245i	$-0.449107\pi$
$191$	160536.	0.318411	0.159206	+	0.987245i	$0.449107\pi$
$192$	−116746.	−0.228554
$193$	−127631.	−0.246640	−0.123320	−	0.992367i	$-0.539354\pi$
$193$	−127631.	−0.246640	−0.123320	+	0.992367i	$0.539354\pi$
$194$	−428608.	−0.817629
$195$	548902.	1.03373
$196$	−150855.	−0.280491
$197$	416067.	0.763832	0.381916	−	0.924197i	$-0.375264\pi$
$197$	416067.	0.763832	0.381916	+	0.924197i	$0.375264\pi$
$198$	1.36574e6	2.47573
$199$	539312.	0.965400	0.482700	−	0.875786i	$-0.339656\pi$
$199$	539312.	0.965400	0.482700	+	0.875786i	$0.339656\pi$
$200$	−120061.	−0.212240
$201$	390366.	0.681525
$202$	310648.	0.535661
$203$	8788.48	0.0149683
$204$	−663974.	−1.11706
$205$	−376809.	−0.626234
$206$	24951.3	0.0409662
$207$	2.09003e6	3.39021
$208$	139497.	0.223566
$209$	0	0
$210$	346112.	0.541587
$211$	−298201.	−0.461108	−0.230554	−	0.973060i	$-0.574054\pi$
$211$	−298201.	−0.461108	−0.230554	+	0.973060i	$0.574054\pi$
$212$	414271.	0.633060
$213$	2.13057e6	3.21771
$214$	−592746.	−0.884778
$215$	177484.	0.261857
$216$	−595378.	−0.868277
$217$	−75731.9	−0.109177
$218$	53989.1	0.0769422
$219$	1.68323e6	2.37156
$220$	−339085.	−0.472337
$221$	793368.	1.09268
$222$	986220.	1.34305
$223$	−521554.	−0.702324	−0.351162	−	0.936315i	$-0.614213\pi$
$223$	−521554.	−0.702324	−0.351162	+	0.936315i	$0.614213\pi$
$224$	87960.3	0.117130
$225$	−1.06814e6	−1.40661
$226$	453838.	0.591058
$227$	15711.0	0.0202367	0.0101184	−	0.999949i	$-0.496779\pi$
$227$	15711.0	0.0202367	0.0101184	+	0.999949i	$0.496779\pi$
$228$	0	0
$229$	1.14920e6	1.44813	0.724065	−	0.689732i	$-0.242272\pi$
$229$	1.14920e6	1.44813	0.724065	+	0.689732i	$0.242272\pi$
$230$	−518913.	−0.646808
$231$	−1.46814e6	−1.81025
$232$	6547.97	0.00798706
$233$	−280581.	−0.338585	−0.169293	−	0.985566i	$-0.554148\pi$
$233$	−280581.	−0.338585	−0.169293	+	0.985566i	$0.554148\pi$
$234$	1.24106e6	1.48167
$235$	−287067.	−0.339089
$236$	578465.	0.676078
$237$	−171282.	−0.198080
$238$	500261.	0.572472
$239$	259293.	0.293628	0.146814	−	0.989164i	$-0.453098\pi$
$239$	259293.	0.293628	0.146814	+	0.989164i	$0.453098\pi$
$240$	257875.	0.288989
$241$	806220.	0.894151	0.447076	−	0.894496i	$-0.352465\pi$
$241$	806220.	0.894151	0.447076	+	0.894496i	$0.352465\pi$
$242$	794132.	0.871674
$243$	−1.35326e6	−1.47017
$244$	629831.	0.677250
$245$	333217.	0.354660
$246$	−1.21555e6	−1.28067
$247$	0	0
$248$	−56425.1	−0.0582563
$249$	−2.08537e6	−2.13150
$250$	706971.	0.715405
$251$	−956381.	−0.958179	−0.479089	−	0.877766i	$-0.659033\pi$
$251$	−956381.	−0.958179	−0.479089	+	0.877766i	$0.659033\pi$
$252$	782552.	0.776269
$253$	2.20113e6	2.16195
$254$	1.09494e6	1.06489
$255$	1.46663e6	1.41244
$256$	65536.0	0.0625000
$257$	−611198.	−0.577230	−0.288615	−	0.957445i	$-0.593195\pi$
$257$	−611198.	−0.577230	−0.288615	+	0.957445i	$0.593195\pi$
$258$	572549.	0.535505
$259$	−743052.	−0.688287
$260$	−308129.	−0.282683
$261$	58255.1	0.0529337
$262$	1.08456e6	0.976114
$263$	−676741.	−0.603300	−0.301650	−	0.953419i	$-0.597537\pi$
$263$	−676741.	−0.603300	−0.301650	+	0.953419i	$0.597537\pi$
$264$	−1.09386e6	−0.965943
$265$	−915068.	−0.800458
$266$	0	0
$267$	−436214.	−0.374474
$268$	−219134.	−0.186369
$269$	427755.	0.360425	0.180212	−	0.983628i	$-0.442321\pi$
$269$	427755.	0.360425	0.180212	+	0.983628i	$0.442321\pi$
$270$	1.31511e6	1.09787
$271$	360343.	0.298052	0.149026	−	0.988833i	$-0.452386\pi$
$271$	360343.	0.298052	0.149026	+	0.988833i	$0.452386\pi$
$272$	372726.	0.305469
$273$	−1.33411e6	−1.08339
$274$	−1.48023e6	−1.19112
$275$	−1.12492e6	−0.896997
$276$	−1.67397e6	−1.32274
$277$	1.80424e6	1.41285	0.706423	−	0.707790i	$-0.250308\pi$
$277$	1.80424e6	1.41285	0.706423	+	0.707790i	$0.250308\pi$
$278$	−1.09680e6	−0.851169
$279$	−501995.	−0.386090
$280$	−194292.	−0.148102
$281$	804377.	0.607707	0.303853	−	0.952719i	$-0.401727\pi$
$281$	804377.	0.607707	0.303853	+	0.952719i	$0.401727\pi$
$282$	−926053.	−0.693447
$283$	−893159.	−0.662923	−0.331461	−	0.943469i	$-0.607542\pi$
$283$	−893159.	−0.662923	−0.331461	+	0.943469i	$0.607542\pi$
$284$	−1.19601e6	−0.879910
$285$	0	0
$286$	1.30703e6	0.944864
$287$	915838.	0.656318
$288$	583051.	0.414215
$289$	699969.	0.492986
$290$	−14463.6	−0.0100991
$291$	3.05409e6	2.11422
$292$	−944893.	−0.648523
$293$	−1.46208e6	−0.994951	−0.497476	−	0.867478i	$-0.665740\pi$
$293$	−1.46208e6	−0.994951	−0.497476	+	0.867478i	$0.665740\pi$
$294$	1.07493e6	0.725290
$295$	−1.27775e6	−0.854852
$296$	−553621.	−0.367268
$297$	−5.57844e6	−3.66963
$298$	−1.25071e6	−0.815863
$299$	2.00019e6	1.29388
$300$	855508.	0.548809
$301$	−431378.	−0.274437
$302$	−1.77926e6	−1.12259
$303$	−2.21355e6	−1.38511
$304$	0	0
$305$	−1.39121e6	−0.856334
$306$	3.31602e6	2.02448
$307$	1.05702e6	0.640087	0.320043	−	0.947403i	$-0.396302\pi$
$307$	1.05702e6	0.640087	0.320043	+	0.947403i	$0.396302\pi$
$308$	824151.	0.495028
$309$	−177793.	−0.105930
$310$	124635.	0.0736608
$311$	−2.28076e6	−1.33714	−0.668572	−	0.743647i	$-0.733094\pi$
$311$	−2.28076e6	−1.33714	−0.668572	+	0.743647i	$0.733094\pi$
$312$	−993998.	−0.578095
$313$	129263.	0.0745786	0.0372893	−	0.999305i	$-0.488128\pi$
$313$	129263.	0.0745786	0.0372893	+	0.999305i	$0.488128\pi$
$314$	2.12541e6	1.21652
$315$	−1.72855e6	−0.981535
$316$	96150.3	0.0541668
$317$	−554212.	−0.309762	−0.154881	−	0.987933i	$-0.549499\pi$
$317$	−554212.	−0.309762	−0.154881	+	0.987933i	$0.549499\pi$
$318$	−2.95193e6	−1.63696
$319$	61351.8	0.0337560
$320$	−144760.	−0.0790267
$321$	4.22367e6	2.28785
$322$	1.26123e6	0.677880
$323$	0	0
$324$	2.02865e6	1.07361
$325$	−1.02223e6	−0.536833
$326$	−539499.	−0.281156
$327$	−384705.	−0.198956
$328$	682358.	0.350209
$329$	697720.	0.355379
$330$	2.41618e6	1.22136
$331$	−1.49260e6	−0.748813	−0.374407	−	0.927265i	$-0.622154\pi$
$331$	−1.49260e6	−0.748813	−0.374407	+	0.927265i	$0.622154\pi$
$332$	1.17064e6	0.582877
$333$	−4.92538e6	−2.43405
$334$	354296.	0.173780
$335$	484038.	0.235650
$336$	−626769.	−0.302872
$337$	91534.0	0.0439043	0.0219522	−	0.999759i	$-0.493012\pi$
$337$	91534.0	0.0439043	0.0219522	+	0.999759i	$0.493012\pi$
$338$	−297466.	−0.141627
$339$	−3.23387e6	−1.52835
$340$	−823301.	−0.386244
$341$	−528679.	−0.246210
$342$	0	0
$343$	−2.25359e6	−1.03428
$344$	−321404.	−0.146439
$345$	3.69757e6	1.67251
$346$	1.77212e6	0.795797
$347$	−531827.	−0.237108	−0.118554	−	0.992948i	$-0.537826\pi$
$347$	−531827.	−0.237108	−0.118554	+	0.992948i	$0.537826\pi$
$348$	−46658.2	−0.0206529
$349$	2.03777e6	0.895553	0.447777	−	0.894145i	$-0.352216\pi$
$349$	2.03777e6	0.895553	0.447777	+	0.894145i	$0.352216\pi$
$350$	−644569.	−0.281254
$351$	−5.06918e6	−2.19619
$352$	614045.	0.264146
$353$	−471656.	−0.201460	−0.100730	−	0.994914i	$-0.532118\pi$
$353$	−471656.	−0.201460	−0.100730	+	0.994914i	$0.532118\pi$
$354$	−4.12191e6	−1.74820
$355$	2.64182e6	1.11258
$356$	244871.	0.102403
$357$	−3.56466e6	−1.48029
$358$	−760899.	−0.313776
$359$	314120.	0.128635	0.0643175	−	0.997929i	$-0.479513\pi$
$359$	314120.	0.128635	0.0643175	+	0.997929i	$0.479513\pi$
$360$	−1.28788e6	−0.523744
$361$	0	0
$362$	−393069.	−0.157651
$363$	−5.65866e6	−2.25396
$364$	748912.	0.296263
$365$	2.08714e6	0.820010
$366$	−4.48792e6	−1.75123
$367$	−1.71417e6	−0.664337	−0.332168	−	0.943220i	$-0.607780\pi$
$367$	−1.71417e6	−0.664337	−0.332168	+	0.943220i	$0.607780\pi$
$368$	939693.	0.361715
$369$	6.07070e6	2.32099
$370$	1.22287e6	0.464384
$371$	2.22408e6	0.838912
$372$	402062.	0.150639
$373$	2.57602e6	0.958687	0.479344	−	0.877627i	$-0.340875\pi$
$373$	2.57602e6	0.958687	0.479344	+	0.877627i	$0.340875\pi$
$374$	3.49229e6	1.29101
$375$	−5.03759e6	−1.84989
$376$	519846.	0.189629
$377$	55750.8	0.0202022
$378$	−3.19639e6	−1.15062
$379$	2.53694e6	0.907218	0.453609	−	0.891201i	$-0.350136\pi$
$379$	2.53694e6	0.907218	0.453609	+	0.891201i	$0.350136\pi$
$380$	0	0
$381$	−7.80207e6	−2.75358
$382$	642143.	0.225151
$383$	−354368.	−0.123440	−0.0617202	−	0.998093i	$-0.519659\pi$
$383$	−354368.	−0.123440	−0.0617202	+	0.998093i	$0.519659\pi$
$384$	−466983.	−0.161612
$385$	−1.82044e6	−0.625927
$386$	−510525.	−0.174401
$387$	−2.85942e6	−0.970513
$388$	−1.71443e6	−0.578151
$389$	2.30013e6	0.770688	0.385344	−	0.922773i	$-0.374083\pi$
$389$	2.30013e6	0.770688	0.385344	+	0.922773i	$0.374083\pi$
$390$	2.19561e6	0.730959
$391$	5.34437e6	1.76789
$392$	−603418.	−0.198337
$393$	−7.72814e6	−2.52402
$394$	1.66427e6	0.540111
$395$	−212383.	−0.0684899
$396$	5.46295e6	1.75061
$397$	1.23932e6	0.394647	0.197323	−	0.980338i	$-0.436775\pi$
$397$	1.23932e6	0.394647	0.197323	+	0.980338i	$0.436775\pi$
$398$	2.15725e6	0.682641
$399$	0	0
$400$	−480245.	−0.150077
$401$	−2.37426e6	−0.737341	−0.368670	−	0.929560i	$-0.620187\pi$
$401$	−2.37426e6	−0.737341	−0.368670	+	0.929560i	$0.620187\pi$
$402$	1.56146e6	0.481911
$403$	−480415.	−0.147351
$404$	1.24259e6	0.378769
$405$	−4.48101e6	−1.35750
$406$	35153.9	0.0105842
$407$	−5.18720e6	−1.55220
$408$	−2.65590e6	−0.789880
$409$	−2.22681e6	−0.658225	−0.329113	−	0.944291i	$-0.606750\pi$
$409$	−2.22681e6	−0.658225	−0.329113	+	0.944291i	$0.606750\pi$
$410$	−1.50723e6	−0.442814
$411$	1.05475e7	3.07997
$412$	99805.2	0.0289675
$413$	3.10559e6	0.895919
$414$	8.36013e6	2.39724
$415$	−2.58578e6	−0.737006
$416$	557987.	0.158085
$417$	7.81536e6	2.20094
$418$	0	0
$419$	3.64392e6	1.01399	0.506995	−	0.861949i	$-0.330756\pi$
$419$	3.64392e6	1.01399	0.506995	+	0.861949i	$0.330756\pi$
$420$	1.38445e6	0.382960
$421$	−2.98439e6	−0.820635	−0.410317	−	0.911943i	$-0.634582\pi$
$421$	−2.98439e6	−0.820635	−0.410317	+	0.911943i	$0.634582\pi$
$422$	−1.19280e6	−0.326053
$423$	4.62489e6	1.25676
$424$	1.65708e6	0.447641
$425$	−2.73132e6	−0.733501
$426$	8.52227e6	2.27526
$427$	3.38135e6	0.897472
$428$	−2.37098e6	−0.625633
$429$	−9.31335e6	−2.44322
$430$	709938.	0.185161
$431$	4.26210e6	1.10517	0.552587	−	0.833455i	$-0.313641\pi$
$431$	4.26210e6	1.10517	0.552587	+	0.833455i	$0.313641\pi$
$432$	−2.38151e6	−0.613965
$433$	203824.	0.0522439	0.0261219	−	0.999659i	$-0.491684\pi$
$433$	203824.	0.0522439	0.0261219	+	0.999659i	$0.491684\pi$
$434$	−302928.	−0.0771995
$435$	103062.	0.0261140
$436$	215956.	0.0544064
$437$	0	0
$438$	6.73292e6	1.67694
$439$	803281.	0.198933	0.0994663	−	0.995041i	$-0.468286\pi$
$439$	803281.	0.198933	0.0994663	+	0.995041i	$0.468286\pi$
$440$	−1.35634e6	−0.333993
$441$	−5.36841e6	−1.31446
$442$	3.17347e6	0.772643
$443$	−2.26274e6	−0.547805	−0.273902	−	0.961758i	$-0.588315\pi$
$443$	−2.26274e6	−0.547805	−0.273902	+	0.961758i	$0.588315\pi$
$444$	3.94488e6	0.949678
$445$	−540887.	−0.129481
$446$	−2.08622e6	−0.496618
$447$	8.91208e6	2.10965
$448$	351841.	0.0828231
$449$	−777935.	−0.182107	−0.0910537	−	0.995846i	$-0.529023\pi$
$449$	−777935.	−0.182107	−0.0910537	+	0.995846i	$0.529023\pi$
$450$	−4.27257e6	−0.994623
$451$	6.39341e6	1.48010
$452$	1.81535e6	0.417941
$453$	1.26783e7	2.90279
$454$	62844.2	0.0143095
$455$	−1.65424e6	−0.374603
$456$	0	0
$457$	6.92747e6	1.55162	0.775808	−	0.630969i	$-0.217343\pi$
$457$	6.92747e6	1.55162	0.775808	+	0.630969i	$0.217343\pi$
$458$	4.59681e6	1.02398
$459$	−1.35445e7	−3.00076
$460$	−2.07565e6	−0.457362
$461$	−3.90569e6	−0.855945	−0.427972	−	0.903792i	$-0.640772\pi$
$461$	−3.90569e6	−0.855945	−0.427972	+	0.903792i	$0.640772\pi$
$462$	−5.87257e6	−1.28004
$463$	6.53732e6	1.41725	0.708626	−	0.705584i	$-0.249315\pi$
$463$	6.53732e6	1.41725	0.708626	+	0.705584i	$0.249315\pi$
$464$	26191.9	0.00564770
$465$	−888101.	−0.190471
$466$	−1.12232e6	−0.239416
$467$	2.74697e6	0.582857	0.291429	−	0.956593i	$-0.405869\pi$
$467$	2.74697e6	0.582857	0.291429	+	0.956593i	$0.405869\pi$
$468$	4.96422e6	1.04770
$469$	−1.17646e6	−0.246970
$470$	−1.14827e6	−0.239772
$471$	−1.51448e7	−3.14566
$472$	2.31386e6	0.478060
$473$	−3.01142e6	−0.618898
$474$	−685129.	−0.140064
$475$	0	0
$476$	2.00104e6	0.404799
$477$	1.47425e7	2.96671
$478$	1.03717e6	0.207626
$479$	−7.22542e6	−1.43888	−0.719440	−	0.694555i	$-0.755601\pi$
$479$	−7.22542e6	−1.43888	−0.719440	+	0.694555i	$0.755601\pi$
$480$	1.03150e6	0.204346
$481$	−4.71365e6	−0.928954
$482$	3.22488e6	0.632260
$483$	−8.98699e6	−1.75286
$484$	3.17653e6	0.616367
$485$	3.78695e6	0.731030
$486$	−5.41305e6	−1.03956
$487$	−451719.	−0.0863070	−0.0431535	−	0.999068i	$-0.513740\pi$
$487$	−451719.	−0.0863070	−0.0431535	+	0.999068i	$0.513740\pi$
$488$	2.51932e6	0.478888
$489$	3.84425e6	0.727009
$490$	1.33287e6	0.250782
$491$	−8.35122e6	−1.56331	−0.781657	−	0.623708i	$-0.785625\pi$
$491$	−8.35122e6	−1.56331	−0.781657	+	0.623708i	$0.785625\pi$
$492$	−4.86221e6	−0.905567
$493$	148963.	0.0276032
$494$	0	0
$495$	−1.20669e7	−2.21352
$496$	−225700.	−0.0411934
$497$	−6.42097e6	−1.16603
$498$	−8.34149e6	−1.50720
$499$	8.52846e6	1.53327	0.766636	−	0.642082i	$-0.221929\pi$
$499$	8.52846e6	1.53327	0.766636	+	0.642082i	$0.221929\pi$
$500$	2.82789e6	0.505868
$501$	−2.52457e6	−0.449359
$502$	−3.82552e6	−0.677535
$503$	−761171.	−0.134141	−0.0670706	−	0.997748i	$-0.521365\pi$
$503$	−761171.	−0.134141	−0.0670706	+	0.997748i	$0.521365\pi$
$504$	3.13021e6	0.548905
$505$	−2.74471e6	−0.478926
$506$	8.80453e6	1.52873
$507$	2.11962e6	0.366217
$508$	4.37974e6	0.752990
$509$	5.93524e6	1.01542	0.507708	−	0.861529i	$-0.330493\pi$
$509$	5.93524e6	1.01542	0.507708	+	0.861529i	$0.330493\pi$
$510$	5.86651e6	0.998745
$511$	−5.07282e6	−0.859403
$512$	262144.	0.0441942
$513$	0	0
$514$	−2.44479e6	−0.408163
$515$	−220456.	−0.0366272
$516$	2.29020e6	0.378659
$517$	4.87074e6	0.801435
$518$	−2.97221e6	−0.486693
$519$	−1.26274e7	−2.05776
$520$	−1.23252e6	−0.199887
$521$	9.02761e6	1.45706	0.728532	−	0.685012i	$-0.240203\pi$
$521$	9.02761e6	1.45706	0.728532	+	0.685012i	$0.240203\pi$
$522$	233020.	0.0374298
$523$	−121332.	−0.0193964	−0.00969822	−	0.999953i	$-0.503087\pi$
$523$	−121332.	−0.0193964	−0.00969822	+	0.999953i	$0.503087\pi$
$524$	4.33824e6	0.690217
$525$	4.59294e6	0.727265
$526$	−2.70696e6	−0.426597
$527$	−1.28364e6	−0.201333
$528$	−4.37544e6	−0.683025
$529$	7.03753e6	1.09340
$530$	−3.66027e6	−0.566009
$531$	2.05856e7	3.16831
$532$	0	0
$533$	5.80974e6	0.885806
$534$	−1.74486e6	−0.264793
$535$	5.23718e6	0.791067
$536$	−876538.	−0.131783
$537$	5.42186e6	0.811358
$538$	1.71102e6	0.254859
$539$	−5.65378e6	−0.838237
$540$	5.26043e6	0.776314
$541$	4.63341e6	0.680625	0.340312	−	0.940312i	$-0.389467\pi$
$541$	4.63341e6	0.680625	0.340312	+	0.940312i	$0.389467\pi$
$542$	1.44137e6	0.210755
$543$	2.80085e6	0.407653
$544$	1.49091e6	0.216000
$545$	−477018.	−0.0687929
$546$	−5.33645e6	−0.766074
$547$	8.93420e6	1.27670	0.638348	−	0.769748i	$-0.279618\pi$
$547$	8.93420e6	1.27670	0.638348	+	0.769748i	$0.279618\pi$
$548$	−5.92093e6	−0.842245
$549$	2.24136e7	3.17380
$550$	−4.49969e6	−0.634273
$551$	0	0
$552$	−6.69588e6	−0.935319
$553$	516199.	0.0717802
$554$	7.21696e6	0.999033
$555$	−8.71370e6	−1.20080
$556$	−4.38721e6	−0.601868
$557$	−7.43216e6	−1.01503	−0.507513	−	0.861644i	$-0.669435\pi$
$557$	−7.43216e6	−1.01503	−0.507513	+	0.861644i	$0.669435\pi$
$558$	−2.00798e6	−0.273007
$559$	−2.73650e6	−0.370396
$560$	−777169.	−0.104724
$561$	−2.48846e7	−3.33829
$562$	3.21751e6	0.429714
$563$	9.16494e6	1.21859	0.609297	−	0.792942i	$-0.291452\pi$
$563$	9.16494e6	1.21859	0.609297	+	0.792942i	$0.291452\pi$
$564$	−3.70421e6	−0.490341
$565$	−4.00987e6	−0.528456
$566$	−3.57264e6	−0.468757
$567$	1.08912e7	1.42271
$568$	−4.78403e6	−0.622190
$569$	660962.	0.0855846	0.0427923	−	0.999084i	$-0.486375\pi$
$569$	660962.	0.0855846	0.0427923	+	0.999084i	$0.486375\pi$
$570$	0	0
$571$	−1.00348e7	−1.28800	−0.644002	−	0.765024i	$-0.722727\pi$
$571$	−1.00348e7	−1.28800	−0.644002	+	0.765024i	$0.722727\pi$
$572$	5.22811e6	0.668120
$573$	−4.57566e6	−0.582193
$574$	3.66335e6	0.464087
$575$	−6.88603e6	−0.868559
$576$	2.33221e6	0.292894
$577$	8.91674e6	1.11498	0.557490	−	0.830184i	$-0.311765\pi$
$577$	8.91674e6	1.11498	0.557490	+	0.830184i	$0.311765\pi$
$578$	2.79988e6	0.348594
$579$	3.63779e6	0.450964
$580$	−57854.3	−0.00714111
$581$	6.28476e6	0.772411
$582$	1.22164e7	1.49498
$583$	1.55262e7	1.89188
$584$	−3.77957e6	−0.458575
$585$	−1.09653e7	−1.32474
$586$	−5.84832e6	−0.703537
$587$	−1.45281e7	−1.74026	−0.870128	−	0.492826i	$-0.835964\pi$
$587$	−1.45281e7	−1.74026	−0.870128	+	0.492826i	$0.835964\pi$
$588$	4.29972e6	0.512857
$589$	0	0
$590$	−5.11100e6	−0.604471
$591$	−1.18589e7	−1.39661
$592$	−2.21448e6	−0.259698
$593$	6.39752e6	0.747094	0.373547	−	0.927611i	$-0.378142\pi$
$593$	6.39752e6	0.747094	0.373547	+	0.927611i	$0.378142\pi$
$594$	−2.23138e7	−2.59482
$595$	−4.42003e6	−0.511839
$596$	−5.00285e6	−0.576902
$597$	−1.53717e7	−1.76517
$598$	8.00075e6	0.914908
$599$	−1.13510e7	−1.29261	−0.646306	−	0.763078i	$-0.723687\pi$
$599$	−1.13510e7	−1.29261	−0.646306	+	0.763078i	$0.723687\pi$
$600$	3.42203e6	0.388066
$601$	−826797.	−0.0933711	−0.0466856	−	0.998910i	$-0.514866\pi$
$601$	−826797.	−0.0933711	−0.0466856	+	0.998910i	$0.514866\pi$
$602$	−1.72551e6	−0.194056
$603$	−7.79826e6	−0.873382
$604$	−7.11705e6	−0.793794
$605$	−7.01651e6	−0.779350
$606$	−8.85420e6	−0.979418
$607$	8.36168e6	0.921132	0.460566	−	0.887626i	$-0.347647\pi$
$607$	8.36168e6	0.921132	0.460566	+	0.887626i	$0.347647\pi$
$608$	0	0
$609$	−250493.	−0.0273685
$610$	−5.56484e6	−0.605519
$611$	4.42608e6	0.479641
$612$	1.32641e7	1.43152
$613$	−500341.	−0.0537793	−0.0268897	−	0.999638i	$-0.508560\pi$
$613$	−500341.	−0.0537793	−0.0268897	+	0.999638i	$0.508560\pi$
$614$	4.22810e6	0.452610
$615$	1.07399e7	1.14502
$616$	3.29660e6	0.350038
$617$	1.19267e6	0.126127	0.0630636	−	0.998010i	$-0.479913\pi$
$617$	1.19267e6	0.126127	0.0630636	+	0.998010i	$0.479913\pi$
$618$	−711172.	−0.0749037
$619$	−1.32929e7	−1.39441	−0.697207	−	0.716870i	$-0.745574\pi$
$619$	−1.32929e7	−1.39441	−0.697207	+	0.716870i	$0.745574\pi$
$620$	498541.	0.0520861
$621$	−3.41475e7	−3.55329
$622$	−9.12303e6	−0.945504
$623$	1.31463e6	0.135701
$624$	−3.97599e6	−0.408775
$625$	−384046.	−0.0393263
$626$	517053.	0.0527350
$627$	0	0
$628$	8.50165e6	0.860210
$629$	−1.25946e7	−1.26928
$630$	−6.91420e6	−0.694050
$631$	−1.29254e7	−1.29232	−0.646160	−	0.763202i	$-0.723626\pi$
$631$	−1.29254e7	−1.29232	−0.646160	+	0.763202i	$0.723626\pi$
$632$	384601.	0.0383017
$633$	8.49943e6	0.843103
$634$	−2.21685e6	−0.219035
$635$	−9.67425e6	−0.952101
$636$	−1.18077e7	−1.15751
$637$	−5.13763e6	−0.501666
$638$	245407.	0.0238691
$639$	−4.25619e7	−4.12353
$640$	−579040.	−0.0558803
$641$	1.36102e7	1.30834	0.654169	−	0.756348i	$-0.273018\pi$
$641$	1.36102e7	1.30834	0.654169	+	0.756348i	$0.273018\pi$
$642$	1.68947e7	1.61775
$643$	−5.71725e6	−0.545330	−0.272665	−	0.962109i	$-0.587905\pi$
$643$	−5.71725e6	−0.545330	−0.272665	+	0.962109i	$0.587905\pi$
$644$	5.04490e6	0.479334
$645$	−5.05873e6	−0.478787
$646$	0	0
$647$	−5.37466e6	−0.504766	−0.252383	−	0.967627i	$-0.581214\pi$
$647$	−5.37466e6	−0.504766	−0.252383	+	0.967627i	$0.581214\pi$
$648$	8.11461e6	0.759154
$649$	2.16799e7	2.02044
$650$	−4.08891e6	−0.379598
$651$	2.15854e6	0.199622
$652$	−2.15800e6	−0.198807
$653$	1.28742e7	1.18151	0.590756	−	0.806851i	$-0.298830\pi$
$653$	1.28742e7	1.18151	0.590756	+	0.806851i	$0.298830\pi$
$654$	−1.53882e6	−0.140683
$655$	−9.58258e6	−0.872729
$656$	2.72943e6	0.247635
$657$	−3.36255e7	−3.03918
$658$	2.79088e6	0.251291
$659$	5.32239e6	0.477412	0.238706	−	0.971092i	$-0.423277\pi$
$659$	5.32239e6	0.477412	0.238706	+	0.971092i	$0.423277\pi$
$660$	9.66474e6	0.863635
$661$	8.94346e6	0.796162	0.398081	−	0.917350i	$-0.369676\pi$
$661$	8.94346e6	0.796162	0.398081	+	0.917350i	$0.369676\pi$
$662$	−5.97040e6	−0.529491
$663$	−2.26129e7	−1.99789
$664$	4.68255e6	0.412157
$665$	0	0
$666$	−1.97015e7	−1.72113
$667$	375555.	0.0326858
$668$	1.41718e6	0.122881
$669$	1.48655e7	1.28415
$670$	1.93615e6	0.166630
$671$	2.36050e7	2.02394
$672$	−2.50708e6	−0.214163
$673$	−511618.	−0.0435420	−0.0217710	−	0.999763i	$-0.506930\pi$
$673$	−511618.	−0.0435420	−0.0217710	+	0.999763i	$0.506930\pi$
$674$	366136.	0.0310451
$675$	1.74516e7	1.47427
$676$	−1.18986e6	−0.100145
$677$	−1.91857e7	−1.60882	−0.804408	−	0.594077i	$-0.797518\pi$
$677$	−1.91857e7	−1.60882	−0.804408	+	0.594077i	$0.797518\pi$
$678$	−1.29355e7	−1.08071
$679$	−9.20423e6	−0.766148
$680$	−3.29321e6	−0.273116
$681$	−447802.	−0.0370014
$682$	−2.11472e6	−0.174097
$683$	1.69775e7	1.39259	0.696294	−	0.717757i	$-0.254831\pi$
$683$	1.69775e7	1.39259	0.696294	+	0.717757i	$0.254831\pi$
$684$	0	0
$685$	1.30785e7	1.06496
$686$	−9.01435e6	−0.731348
$687$	−3.27550e7	−2.64780
$688$	−1.28562e6	−0.103548
$689$	1.41088e7	1.13225
$690$	1.47903e7	1.18264
$691$	−2.27773e7	−1.81471	−0.907355	−	0.420365i	$-0.861902\pi$
$691$	−2.27773e7	−1.81471	−0.907355	+	0.420365i	$0.861902\pi$
$692$	7.08847e6	0.562713
$693$	2.93288e7	2.31985
$694$	−2.12731e6	−0.167661
$695$	9.69074e6	0.761018
$696$	−186633.	−0.0146038
$697$	1.55232e7	1.21032
$698$	8.15108e6	0.633252
$699$	7.99722e6	0.619079
$700$	−2.57828e6	−0.198877
$701$	−1.35324e7	−1.04011	−0.520055	−	0.854133i	$-0.674088\pi$
$701$	−1.35324e7	−1.04011	−0.520055	+	0.854133i	$0.674088\pi$
$702$	−2.02767e7	−1.55294
$703$	0	0
$704$	2.45618e6	0.186779
$705$	8.18210e6	0.620000
$706$	−1.88662e6	−0.142454
$707$	6.67106e6	0.501934
$708$	−1.64876e7	−1.23616
$709$	−6.06043e6	−0.452781	−0.226390	−	0.974037i	$-0.572692\pi$
$709$	−6.06043e6	−0.452781	−0.226390	+	0.974037i	$0.572692\pi$
$710$	1.05673e7	0.786714
$711$	3.42167e6	0.253842
$712$	979486.	0.0724099
$713$	−3.23622e6	−0.238405
$714$	−1.42586e7	−1.04672
$715$	−1.15482e7	−0.844789
$716$	−3.04359e6	−0.221873
$717$	−7.39048e6	−0.536877
$718$	1.25648e6	0.0909587
$719$	−1.58569e7	−1.14392	−0.571962	−	0.820280i	$-0.693818\pi$
$719$	−1.58569e7	−1.14392	−0.571962	+	0.820280i	$0.693818\pi$
$720$	−5.15152e6	−0.370343
$721$	535821.	0.0383868
$722$	0	0
$723$	−2.29792e7	−1.63489
$724$	−1.57228e6	−0.111476
$725$	−191933.	−0.0135614
$726$	−2.26346e7	−1.59379
$727$	2.02139e7	1.41845	0.709227	−	0.704981i	$-0.249044\pi$
$727$	2.02139e7	1.41845	0.709227	+	0.704981i	$0.249044\pi$
$728$	2.99565e6	0.209490
$729$	7.76105e6	0.540881
$730$	8.34855e6	0.579834
$731$	−7.31176e6	−0.506091
$732$	−1.79517e7	−1.23830
$733$	−1.41871e7	−0.975287	−0.487643	−	0.873043i	$-0.662143\pi$
$733$	−1.41871e7	−0.975287	−0.487643	+	0.873043i	$0.662143\pi$
$734$	−6.85667e6	−0.469757
$735$	−9.49748e6	−0.648470
$736$	3.75877e6	0.255771
$737$	−8.21279e6	−0.556957
$738$	2.42828e7	1.64119
$739$	4.24386e6	0.285857	0.142929	−	0.989733i	$-0.454348\pi$
$739$	4.24386e6	0.285857	0.142929	+	0.989733i	$0.454348\pi$
$740$	4.89149e6	0.328369
$741$	0	0
$742$	8.89634e6	0.593200
$743$	1.25411e7	0.833421	0.416710	−	0.909039i	$-0.363183\pi$
$743$	1.25411e7	0.833421	0.416710	+	0.909039i	$0.363183\pi$
$744$	1.60825e6	0.106518
$745$	1.10506e7	0.729451
$746$	1.03041e7	0.677894
$747$	4.16590e7	2.73154
$748$	1.39692e7	0.912885
$749$	−1.27290e7	−0.829069
$750$	−2.01504e7	−1.30807
$751$	−1.91130e7	−1.23660	−0.618299	−	0.785943i	$-0.712178\pi$
$751$	−1.91130e7	−1.23660	−0.618299	+	0.785943i	$0.712178\pi$
$752$	2.07938e6	0.134088
$753$	2.72591e7	1.75196
$754$	223003.	0.0142851
$755$	1.57206e7	1.00369
$756$	−1.27856e7	−0.813608
$757$	−9.75141e6	−0.618483	−0.309241	−	0.950984i	$-0.600075\pi$
$757$	−9.75141e6	−0.618483	−0.309241	+	0.950984i	$0.600075\pi$
$758$	1.01477e7	0.641500
$759$	−6.27375e7	−3.95297
$760$	0	0
$761$	7.08784e6	0.443662	0.221831	−	0.975085i	$-0.428797\pi$
$761$	7.08784e6	0.443662	0.221831	+	0.975085i	$0.428797\pi$
$762$	−3.12083e7	−1.94707
$763$	1.15940e6	0.0720977
$764$	2.56857e6	0.159206
$765$	−2.92985e7	−1.81006
$766$	−1.41747e6	−0.0872856
$767$	1.97007e7	1.20919
$768$	−1.86793e6	−0.114277
$769$	2.06840e7	1.26130	0.630650	−	0.776068i	$-0.282789\pi$
$769$	2.06840e7	1.26130	0.630650	+	0.776068i	$0.282789\pi$
$770$	−7.28174e6	−0.442597
$771$	1.74206e7	1.05542
$772$	−2.04210e6	−0.123320
$773$	1.79886e7	1.08280	0.541400	−	0.840765i	$-0.317895\pi$
$773$	1.79886e7	1.08280	0.541400	+	0.840765i	$0.317895\pi$
$774$	−1.14377e7	−0.686256
$775$	1.65392e6	0.0989147
$776$	−6.85773e6	−0.408815
$777$	2.11788e7	1.25848
$778$	9.20053e6	0.544959
$779$	0	0
$780$	8.78242e6	0.516866
$781$	−4.48244e7	−2.62958
$782$	2.13775e7	1.25008
$783$	−951787.	−0.0554799
$784$	−2.41367e6	−0.140245
$785$	−1.87790e7	−1.08767
$786$	−3.09126e7	−1.78476
$787$	−7.16861e6	−0.412571	−0.206285	−	0.978492i	$-0.566137\pi$
$787$	−7.16861e6	−0.412571	−0.206285	+	0.978492i	$0.566137\pi$
$788$	6.65707e6	0.381916
$789$	1.92887e7	1.10309
$790$	−849532.	−0.0484297
$791$	9.74603e6	0.553843
$792$	2.18518e7	1.23787
$793$	2.14501e7	1.21128
$794$	4.95730e6	0.279057
$795$	2.60816e7	1.46358
$796$	8.62899e6	0.482700
$797$	3.21068e7	1.79040	0.895202	−	0.445661i	$-0.147031\pi$
$797$	3.21068e7	1.79040	0.895202	+	0.445661i	$0.147031\pi$
$798$	0	0
$799$	1.18262e7	0.655357
$800$	−1.92098e6	−0.106120
$801$	8.71415e6	0.479892
$802$	−9.49706e6	−0.521379
$803$	−3.54130e7	−1.93809
$804$	6.24585e6	0.340762
$805$	−1.11435e7	−0.606083
$806$	−1.92166e6	−0.104193
$807$	−1.21921e7	−0.659011
$808$	4.97037e6	0.267830
$809$	2.62167e7	1.40834	0.704170	−	0.710032i	$-0.251320\pi$
$809$	2.62167e7	1.40834	0.704170	+	0.710032i	$0.251320\pi$
$810$	−1.79241e7	−0.959895
$811$	−1.40706e7	−0.751210	−0.375605	−	0.926780i	$-0.622565\pi$
$811$	−1.40706e7	−0.751210	−0.375605	+	0.926780i	$0.622565\pi$
$812$	140616.	0.00748417
$813$	−1.02706e7	−0.544967
$814$	−2.07488e7	−1.09757
$815$	4.76672e6	0.251377
$816$	−1.06236e7	−0.558529
$817$	0	0
$818$	−8.90723e6	−0.465436
$819$	2.66513e7	1.38838
$820$	−6.02894e6	−0.313117
$821$	2.78399e7	1.44148	0.720741	−	0.693204i	$-0.243802\pi$
$821$	2.78399e7	1.44148	0.720741	+	0.693204i	$0.243802\pi$
$822$	4.21902e7	2.17787
$823$	−2.20926e7	−1.13697	−0.568483	−	0.822695i	$-0.692469\pi$
$823$	−2.20926e7	−1.13697	−0.568483	+	0.822695i	$0.692469\pi$
$824$	399221.	0.0204831
$825$	3.20630e7	1.64010
$826$	1.24223e7	0.633510
$827$	3.52327e7	1.79136	0.895679	−	0.444702i	$-0.146690\pi$
$827$	3.52327e7	1.79136	0.895679	+	0.444702i	$0.146690\pi$
$828$	3.34405e7	1.69511
$829$	3.94718e7	1.99481	0.997404	−	0.0720139i	$-0.0229426\pi$
$829$	3.94718e7	1.99481	0.997404	+	0.0720139i	$0.0229426\pi$
$830$	−1.03431e7	−0.521142
$831$	−5.14252e7	−2.58329
$832$	2.23195e6	0.111783
$833$	−1.37274e7	−0.685451
$834$	3.12615e7	1.55630
$835$	−3.13037e6	−0.155374
$836$	0	0
$837$	8.20172e6	0.404661
$838$	1.45757e7	0.716999
$839$	−1.91447e7	−0.938951	−0.469476	−	0.882945i	$-0.655557\pi$
$839$	−1.91447e7	−0.938951	−0.469476	+	0.882945i	$0.655557\pi$
$840$	5.53779e6	0.270794
$841$	−2.05007e7	−0.999490
$842$	−1.19376e7	−0.580277
$843$	−2.29267e7	−1.11115
$844$	−4.77121e6	−0.230554
$845$	2.62825e6	0.126627
$846$	1.84996e7	0.888660
$847$	1.70537e7	0.816790
$848$	6.62834e6	0.316530
$849$	2.54572e7	1.21211
$850$	−1.09253e7	−0.518663
$851$	−3.17526e7	−1.50299
$852$	3.40891e7	1.60885
$853$	−2.13209e7	−1.00330	−0.501652	−	0.865069i	$-0.667274\pi$
$853$	−2.13209e7	−1.00330	−0.501652	+	0.865069i	$0.667274\pi$
$854$	1.35254e7	0.634608
$855$	0	0
$856$	−9.48394e6	−0.442389
$857$	1.36472e7	0.634733	0.317366	−	0.948303i	$-0.397202\pi$
$857$	1.36472e7	0.634733	0.317366	+	0.948303i	$0.397202\pi$
$858$	−3.72534e7	−1.72762
$859$	8.94646e6	0.413683	0.206842	−	0.978374i	$-0.433681\pi$
$859$	8.94646e6	0.413683	0.206842	+	0.978374i	$0.433681\pi$
$860$	2.83975e6	0.130929
$861$	−2.61036e7	−1.20003
$862$	1.70484e7	0.781476
$863$	2.93169e7	1.33996	0.669979	−	0.742380i	$-0.266303\pi$
$863$	2.93169e7	1.33996	0.669979	+	0.742380i	$0.266303\pi$
$864$	−9.52605e6	−0.434139
$865$	−1.56575e7	−0.711510
$866$	815296.	0.0369420
$867$	−1.99508e7	−0.901389
$868$	−1.21171e6	−0.0545883
$869$	3.60355e6	0.161876
$870$	412246.	0.0184654
$871$	−7.46303e6	−0.333326
$872$	863825.	0.0384711
$873$	−6.10109e7	−2.70939
$874$	0	0
$875$	1.51820e7	0.670360
$876$	2.69317e7	1.18578
$877$	3.73450e7	1.63958	0.819792	−	0.572661i	$-0.194089\pi$
$877$	3.73450e7	1.63958	0.819792	+	0.572661i	$0.194089\pi$
$878$	3.21312e6	0.140667
$879$	4.16727e7	1.81920
$880$	−5.42536e6	−0.236169
$881$	−5.23343e6	−0.227168	−0.113584	−	0.993528i	$-0.536233\pi$
$881$	−5.23343e6	−0.227168	−0.113584	+	0.993528i	$0.536233\pi$
$882$	−2.14736e7	−0.929467
$883$	−7.64635e6	−0.330029	−0.165015	−	0.986291i	$-0.552767\pi$
$883$	−7.64635e6	−0.330029	−0.165015	+	0.986291i	$0.552767\pi$
$884$	1.26939e7	0.546341
$885$	3.64189e7	1.56304
$886$	−9.05097e6	−0.387356
$887$	2.96241e7	1.26426	0.632130	−	0.774862i	$-0.282181\pi$
$887$	2.96241e7	1.26426	0.632130	+	0.774862i	$0.282181\pi$
$888$	1.57795e7	0.671524
$889$	2.35134e7	0.997840
$890$	−2.16355e6	−0.0915571
$891$	7.60305e7	3.20844
$892$	−8.34487e6	−0.351162
$893$	0	0
$894$	3.56483e7	1.49175
$895$	6.72288e6	0.280542
$896$	1.40736e6	0.0585648
$897$	−5.70101e7	−2.36576
$898$	−3.11174e6	−0.128769
$899$	−90202.6	−0.00372237
$900$	−1.70903e7	−0.703305
$901$	3.76977e7	1.54704
$902$	2.55736e7	1.04659
$903$	1.22953e7	0.501788
$904$	7.26142e6	0.295529
$905$	3.47294e6	0.140954
$906$	5.07132e7	2.05258
$907$	3.74124e7	1.51007	0.755035	−	0.655684i	$-0.227620\pi$
$907$	3.74124e7	1.51007	0.755035	+	0.655684i	$0.227620\pi$
$908$	251377.	0.0101184
$909$	4.42196e7	1.77503
$910$	−6.61698e6	−0.264884
$911$	3.03078e6	0.120993	0.0604963	−	0.998168i	$-0.480732\pi$
$911$	3.03078e6	0.120993	0.0604963	+	0.998168i	$0.480732\pi$
$912$	0	0
$913$	4.38735e7	1.74191
$914$	2.77099e7	1.09716
$915$	3.96528e7	1.56575
$916$	1.83872e7	0.724065
$917$	2.32906e7	0.914654
$918$	−5.41780e7	−2.12186
$919$	−4.04873e7	−1.58136	−0.790679	−	0.612231i	$-0.790272\pi$
$919$	−4.04873e7	−1.58136	−0.790679	+	0.612231i	$0.790272\pi$
$920$	−8.30261e6	−0.323404
$921$	−3.01277e7	−1.17035
$922$	−1.56228e7	−0.605244
$923$	−4.07323e7	−1.57374
$924$	−2.34903e7	−0.905124
$925$	1.62276e7	0.623593
$926$	2.61493e7	1.00215
$927$	3.55173e6	0.135750
$928$	104768.	0.00399353
$929$	1.84678e7	0.702063	0.351032	−	0.936364i	$-0.385831\pi$
$929$	1.84678e7	0.702063	0.351032	+	0.936364i	$0.385831\pi$
$930$	−3.55240e6	−0.134684
$931$	0	0
$932$	−4.48929e6	−0.169293
$933$	6.50071e7	2.44487
$934$	1.09879e7	0.412142
$935$	−3.08560e7	−1.15428
$936$	1.98569e7	0.740835
$937$	2.97245e7	1.10603	0.553014	−	0.833172i	$-0.313478\pi$
$937$	2.97245e7	1.10603	0.553014	+	0.833172i	$0.313478\pi$
$938$	−4.70584e6	−0.174635
$939$	−3.68431e6	−0.136362
$940$	−4.59307e6	−0.169545
$941$	2.23858e7	0.824134	0.412067	−	0.911154i	$-0.364807\pi$
$941$	2.23858e7	0.824134	0.412067	+	0.911154i	$0.364807\pi$
$942$	−6.05794e7	−2.22432
$943$	3.91362e7	1.43317
$944$	9.25544e6	0.338039
$945$	2.82415e7	1.02875
$946$	−1.20457e7	−0.437627
$947$	−2.25242e7	−0.816159	−0.408079	−	0.912946i	$-0.633801\pi$
$947$	−2.25242e7	−0.816159	−0.408079	+	0.912946i	$0.633801\pi$
$948$	−2.74051e6	−0.0990401
$949$	−3.21801e7	−1.15990
$950$	0	0
$951$	1.57964e7	0.566377
$952$	8.00418e6	0.286236
$953$	2.60905e7	0.930573	0.465287	−	0.885160i	$-0.345951\pi$
$953$	2.60905e7	0.930573	0.465287	+	0.885160i	$0.345951\pi$
$954$	5.89700e7	2.09778
$955$	−5.67363e6	−0.201304
$956$	4.14869e6	0.146814
$957$	−1.74867e6	−0.0617204
$958$	−2.89017e7	−1.01744
$959$	−3.17875e7	−1.11612
$960$	4.12601e6	0.144495
$961$	−2.78519e7	−0.972850
$962$	−1.88546e7	−0.656870
$963$	−8.43754e7	−2.93191
$964$	1.28995e7	0.447076
$965$	4.51072e6	0.155929
$966$	−3.59479e7	−1.23946
$967$	200902.	0.00690905	0.00345452	−	0.999994i	$-0.498900\pi$
$967$	200902.	0.00690905	0.00345452	+	0.999994i	$0.498900\pi$
$968$	1.27061e7	0.435837
$969$	0	0
$970$	1.51478e7	0.516916
$971$	−3.51779e7	−1.19735	−0.598677	−	0.800991i	$-0.704307\pi$
$971$	−3.51779e7	−1.19735	−0.598677	+	0.800991i	$0.704307\pi$
$972$	−2.16522e7	−0.735083
$973$	−2.35535e7	−0.797577
$974$	−1.80688e6	−0.0610282
$975$	2.91359e7	0.981560
$976$	1.00773e7	0.338625
$977$	2.22703e7	0.746430	0.373215	−	0.927745i	$-0.378255\pi$
$977$	2.22703e7	0.746430	0.373215	+	0.927745i	$0.378255\pi$
$978$	1.53770e7	0.514073
$979$	9.17737e6	0.306028
$980$	5.33147e6	0.177330
$981$	7.68516e6	0.254965
$982$	−3.34049e7	−1.10543
$983$	−5.97998e7	−1.97386	−0.986929	−	0.161158i	$-0.948477\pi$
$983$	−5.97998e7	−1.97386	−0.986929	+	0.161158i	$0.948477\pi$
$984$	−1.94488e7	−0.640333
$985$	−1.47046e7	−0.482905
$986$	595850.	0.0195184
$987$	−1.98867e7	−0.649785
$988$	0	0
$989$	−1.84339e7	−0.599276
$990$	−4.82676e7	−1.56519
$991$	−4.53663e7	−1.46740	−0.733701	−	0.679472i	$-0.762209\pi$
$991$	−4.53663e7	−1.46740	−0.733701	+	0.679472i	$0.762209\pi$
$992$	−902801.	−0.0291282
$993$	4.25427e7	1.36915
$994$	−2.56839e7	−0.824508
$995$	−1.90603e7	−0.610339
$996$	−3.33660e7	−1.06575
$997$	−4.17159e7	−1.32912	−0.664560	−	0.747235i	$-0.731381\pi$
$997$	−4.17159e7	−1.32912	−0.664560	+	0.747235i	$0.731381\pi$
$998$	3.41138e7	1.08419
$999$	8.04721e7	2.55113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.r.1.2		15
19.6	even	9		38.6.e.b.17.1	yes	30
19.16	even	9		38.6.e.b.9.1	✓	30
19.18	odd	2		722.6.a.q.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.9.1	✓	30	19.16	even	9
38.6.e.b.17.1	yes	30	19.6	even	9
722.6.a.q.1.14		15	19.18	odd	2
722.6.a.r.1.2		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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -28.5024 q^{3} +16.0000 q^{4} -35.3418 q^{5} -114.010 q^{6} +85.8987 q^{7} +64.0000 q^{8} +569.386 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -28.5024 q^{3} +16.0000 q^{4} -35.3418 q^{5} -114.010 q^{6} +85.8987 q^{7} +64.0000 q^{8} +569.386 q^{9} -141.367 q^{10} +599.653 q^{11} -456.038 q^{12} +544.910 q^{13} +343.595 q^{14} +1007.33 q^{15} +256.000 q^{16} +1455.96 q^{17} +2277.54 q^{18} -565.469 q^{20} -2448.32 q^{21} +2398.61 q^{22} +3670.68 q^{23} -1824.15 q^{24} -1875.96 q^{25} +2179.64 q^{26} -9302.78 q^{27} +1374.38 q^{28} +102.312 q^{29} +4029.30 q^{30} -881.642 q^{31} +1024.00 q^{32} -17091.5 q^{33} +5823.85 q^{34} -3035.82 q^{35} +9110.18 q^{36} -8650.33 q^{37} -15531.2 q^{39} -2261.88 q^{40} +10661.8 q^{41} -9793.27 q^{42} -5021.94 q^{43} +9594.45 q^{44} -20123.1 q^{45} +14682.7 q^{46} +8122.59 q^{47} -7296.61 q^{48} -9428.41 q^{49} -7503.83 q^{50} -41498.4 q^{51} +8718.55 q^{52} +25891.9 q^{53} -37211.1 q^{54} -21192.8 q^{55} +5497.52 q^{56} +409.248 q^{58} +36154.1 q^{59} +16117.2 q^{60} +39364.4 q^{61} -3526.57 q^{62} +48909.5 q^{63} +4096.00 q^{64} -19258.1 q^{65} -68366.2 q^{66} -13695.9 q^{67} +23295.4 q^{68} -104623. q^{69} -12143.3 q^{70} -74750.5 q^{71} +36440.7 q^{72} -59055.8 q^{73} -34601.3 q^{74} +53469.2 q^{75} +51509.4 q^{77} -62124.9 q^{78} +6009.40 q^{79} -9047.50 q^{80} +126791. q^{81} +42647.4 q^{82} +73164.8 q^{83} -39173.1 q^{84} -51456.3 q^{85} -20087.8 q^{86} -2916.14 q^{87} +38377.8 q^{88} +15304.5 q^{89} -80492.5 q^{90} +46807.0 q^{91} +58730.8 q^{92} +25128.9 q^{93} +32490.4 q^{94} -29186.4 q^{96} -107152. q^{97} -37713.6 q^{98} +341434. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} + 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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