LMFDB - Embedded newform 722.6.a.q.1.8

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			1.8
Root			$-1.51331$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -1.16601 q^{3} +16.0000 q^{4} -65.1319 q^{5} +4.66404 q^{6} +94.5243 q^{7} -64.0000 q^{8} -241.640 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -1.16601 q^{3} +16.0000 q^{4} -65.1319 q^{5} +4.66404 q^{6} +94.5243 q^{7} -64.0000 q^{8} -241.640 q^{9} +260.528 q^{10} -458.262 q^{11} -18.6562 q^{12} +984.374 q^{13} -378.097 q^{14} +75.9445 q^{15} +256.000 q^{16} +2124.68 q^{17} +966.562 q^{18} -1042.11 q^{20} -110.216 q^{21} +1833.05 q^{22} -3844.87 q^{23} +74.6247 q^{24} +1117.16 q^{25} -3937.50 q^{26} +565.096 q^{27} +1512.39 q^{28} -7336.37 q^{29} -303.778 q^{30} +1177.06 q^{31} -1024.00 q^{32} +534.338 q^{33} -8498.70 q^{34} -6156.55 q^{35} -3866.25 q^{36} -1760.46 q^{37} -1147.79 q^{39} +4168.44 q^{40} -2450.34 q^{41} +440.865 q^{42} +2125.30 q^{43} -7332.19 q^{44} +15738.5 q^{45} +15379.5 q^{46} +12732.9 q^{47} -298.499 q^{48} -7872.16 q^{49} -4468.65 q^{50} -2477.39 q^{51} +15750.0 q^{52} -33120.3 q^{53} -2260.38 q^{54} +29847.5 q^{55} -6049.55 q^{56} +29345.5 q^{58} -9236.15 q^{59} +1215.11 q^{60} +10296.4 q^{61} -4708.23 q^{62} -22840.9 q^{63} +4096.00 q^{64} -64114.1 q^{65} -2137.35 q^{66} -28631.3 q^{67} +33994.8 q^{68} +4483.16 q^{69} +24626.2 q^{70} +68701.6 q^{71} +15465.0 q^{72} +36251.3 q^{73} +7041.85 q^{74} -1302.62 q^{75} -43316.9 q^{77} +4591.16 q^{78} -21981.5 q^{79} -16673.8 q^{80} +58059.7 q^{81} +9801.34 q^{82} -102618. q^{83} -1763.46 q^{84} -138384. q^{85} -8501.20 q^{86} +8554.29 q^{87} +29328.8 q^{88} -28261.5 q^{89} -62954.0 q^{90} +93047.3 q^{91} -61517.9 q^{92} -1372.46 q^{93} -50931.8 q^{94} +1193.99 q^{96} -80776.2 q^{97} +31488.6 q^{98} +110735. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.16601	−0.0747996	−0.0373998	−	0.999300i	$-0.511908\pi$
$3$	−1.16601	−0.0747996	−0.0373998	+	0.999300i	$0.511908\pi$
$4$	16.0000	0.500000
$5$	−65.1319	−1.16511	−0.582557	−	0.812790i	$-0.697948\pi$
$5$	−65.1319	−1.16511	−0.582557	+	0.812790i	$0.697948\pi$
$6$	4.66404	0.0528913
$7$	94.5243	0.729119	0.364559	−	0.931180i	$-0.381220\pi$
$7$	94.5243	0.729119	0.364559	+	0.931180i	$0.381220\pi$
$8$	−64.0000	−0.353553
$9$	−241.640	−0.994405
$10$	260.528	0.823860
$11$	−458.262	−1.14191	−0.570955	−	0.820981i	$-0.693427\pi$
$11$	−458.262	−1.14191	−0.570955	+	0.820981i	$0.693427\pi$
$12$	−18.6562	−0.0373998
$13$	984.374	1.61548	0.807740	−	0.589538i	$-0.200690\pi$
$13$	984.374	1.61548	0.807740	+	0.589538i	$0.200690\pi$
$14$	−378.097	−0.515565
$15$	75.9445	0.0871501
$16$	256.000	0.250000
$17$	2124.68	1.78308	0.891539	−	0.452944i	$-0.149626\pi$
$17$	2124.68	1.78308	0.891539	+	0.452944i	$0.149626\pi$
$18$	966.562	0.703151
$19$	0	0
$19$	0	0
$20$	−1042.11	−0.582557
$21$	−110.216	−0.0545378
$22$	1833.05	0.807453
$23$	−3844.87	−1.51552	−0.757761	−	0.652532i	$-0.773707\pi$
$23$	−3844.87	−1.51552	−0.757761	+	0.652532i	$0.773707\pi$
$24$	74.6247	0.0264457
$25$	1117.16	0.357492
$26$	−3937.50	−1.14232
$27$	565.096	0.149181
$28$	1512.39	0.364559
$29$	−7336.37	−1.61989	−0.809947	−	0.586503i	$-0.800504\pi$
$29$	−7336.37	−1.61989	−0.809947	+	0.586503i	$0.800504\pi$
$30$	−303.778	−0.0616244
$31$	1177.06	0.219985	0.109993	−	0.993932i	$-0.464917\pi$
$31$	1177.06	0.219985	0.109993	+	0.993932i	$0.464917\pi$
$32$	−1024.00	−0.176777
$33$	534.338	0.0854145
$34$	−8498.70	−1.26083
$35$	−6156.55	−0.849507
$36$	−3866.25	−0.497203
$37$	−1760.46	−0.211409	−0.105704	−	0.994398i	$-0.533710\pi$
$37$	−1760.46	−0.211409	−0.105704	+	0.994398i	$0.533710\pi$
$38$	0	0
$39$	−1147.79	−0.120837
$40$	4168.44	0.411930
$41$	−2450.34	−0.227649	−0.113825	−	0.993501i	$-0.536310\pi$
$41$	−2450.34	−0.227649	−0.113825	+	0.993501i	$0.536310\pi$
$42$	440.865	0.0385641
$43$	2125.30	0.175287	0.0876434	−	0.996152i	$-0.472066\pi$
$43$	2125.30	0.175287	0.0876434	+	0.996152i	$0.472066\pi$
$44$	−7332.19	−0.570955
$45$	15738.5	1.15860
$46$	15379.5	1.07164
$47$	12732.9	0.840784	0.420392	−	0.907343i	$-0.361893\pi$
$47$	12732.9	0.840784	0.420392	+	0.907343i	$0.361893\pi$
$48$	−298.499	−0.0186999
$49$	−7872.16	−0.468386
$50$	−4468.65	−0.252785
$51$	−2477.39	−0.133374
$52$	15750.0	0.807740
$53$	−33120.3	−1.61959	−0.809793	−	0.586715i	$-0.800421\pi$
$53$	−33120.3	−1.61959	−0.809793	+	0.586715i	$0.800421\pi$
$54$	−2260.38	−0.105487
$55$	29847.5	1.33046
$56$	−6049.55	−0.257782
$57$	0	0
$58$	29345.5	1.14544
$59$	−9236.15	−0.345431	−0.172715	−	0.984972i	$-0.555254\pi$
$59$	−9236.15	−0.345431	−0.172715	+	0.984972i	$0.555254\pi$
$60$	1215.11	0.0435751
$61$	10296.4	0.354293	0.177146	−	0.984185i	$-0.443313\pi$
$61$	10296.4	0.354293	0.177146	+	0.984185i	$0.443313\pi$
$62$	−4708.23	−0.155553
$63$	−22840.9	−0.725039
$64$	4096.00	0.125000
$65$	−64114.1	−1.88222
$66$	−2137.35	−0.0603972
$67$	−28631.3	−0.779209	−0.389605	−	0.920982i	$-0.627388\pi$
$67$	−28631.3	−0.779209	−0.389605	+	0.920982i	$0.627388\pi$
$68$	33994.8	0.891539
$69$	4483.16	0.113360
$70$	24626.2	0.600692
$71$	68701.6	1.61741	0.808707	−	0.588212i	$-0.200168\pi$
$71$	68701.6	1.61741	0.808707	+	0.588212i	$0.200168\pi$
$72$	15465.0	0.351575
$73$	36251.3	0.796189	0.398094	−	0.917345i	$-0.369672\pi$
$73$	36251.3	0.796189	0.398094	+	0.917345i	$0.369672\pi$
$74$	7041.85	0.149488
$75$	−1302.62	−0.0267403
$76$	0	0
$77$	−43316.9	−0.832589
$78$	4591.16	0.0854449
$79$	−21981.5	−0.396269	−0.198134	−	0.980175i	$-0.563488\pi$
$79$	−21981.5	−0.396269	−0.198134	+	0.980175i	$0.563488\pi$
$80$	−16673.8	−0.291279
$81$	58059.7	0.983246
$82$	9801.34	0.160972
$83$	−102618.	−1.63505	−0.817524	−	0.575895i	$-0.804654\pi$
$83$	−102618.	−1.63505	−0.817524	+	0.575895i	$0.804654\pi$
$84$	−1763.46	−0.0272689
$85$	−138384.	−2.07749
$86$	−8501.20	−0.123946
$87$	8554.29	0.121167
$88$	29328.8	0.403726
$89$	−28261.5	−0.378199	−0.189100	−	0.981958i	$-0.560557\pi$
$89$	−28261.5	−0.378199	−0.189100	+	0.981958i	$0.560557\pi$
$90$	−62954.0	−0.819251
$91$	93047.3	1.17788
$92$	−61517.9	−0.757761
$93$	−1372.46	−0.0164548
$94$	−50931.8	−0.594524
$95$	0	0
$96$	1193.99	0.0132228
$97$	−80776.2	−0.871674	−0.435837	−	0.900026i	$-0.643548\pi$
$97$	−80776.2	−0.871674	−0.435837	+	0.900026i	$0.643548\pi$
$98$	31488.6	0.331199
$99$	110735.	1.13552
$100$	17874.6	0.178746
$101$	6404.65	0.0624730	0.0312365	−	0.999512i	$-0.490055\pi$
$101$	6404.65	0.0624730	0.0312365	+	0.999512i	$0.490055\pi$
$102$	9909.58	0.0943094
$103$	146931.	1.36465	0.682325	−	0.731049i	$-0.260969\pi$
$103$	146931.	1.36465	0.682325	+	0.731049i	$0.260969\pi$
$104$	−62999.9	−0.571159
$105$	7178.60	0.0635428
$106$	132481.	1.14522
$107$	−143484.	−1.21156	−0.605779	−	0.795633i	$-0.707138\pi$
$107$	−143484.	−1.21156	−0.605779	+	0.795633i	$0.707138\pi$
$108$	9041.53	0.0745904
$109$	−100557.	−0.810671	−0.405335	−	0.914168i	$-0.632845\pi$
$109$	−100557.	−0.810671	−0.405335	+	0.914168i	$0.632845\pi$
$110$	−119390.	−0.940775
$111$	2052.72	0.0158133
$112$	24198.2	0.182280
$113$	116363.	0.857272	0.428636	−	0.903477i	$-0.358994\pi$
$113$	116363.	0.857272	0.428636	+	0.903477i	$0.358994\pi$
$114$	0	0
$115$	250424.	1.76576
$116$	−117382.	−0.809947
$117$	−237865.	−1.60644
$118$	36944.6	0.244257
$119$	200833.	1.30008
$120$	−4860.45	−0.0308122
$121$	48953.1	0.303960
$122$	−41185.7	−0.250523
$123$	2857.12	0.0170281
$124$	18832.9	0.109993
$125$	130774.	0.748595
$126$	91363.6	0.512680
$127$	−482.007	−0.00265182	−0.00132591	−	0.999999i	$-0.500422\pi$
$127$	−482.007	−0.00265182	−0.00132591	+	0.999999i	$0.500422\pi$
$128$	−16384.0	−0.0883883
$129$	−2478.12	−0.0131114
$130$	256457.	1.33093
$131$	91708.9	0.466910	0.233455	−	0.972368i	$-0.424997\pi$
$131$	91708.9	0.466910	0.233455	+	0.972368i	$0.424997\pi$
$132$	8549.41	0.0427072
$133$	0	0
$134$	114525.	0.550984
$135$	−36805.8	−0.173813
$136$	−135979.	−0.630413
$137$	235112.	1.07022	0.535110	−	0.844783i	$-0.320270\pi$
$137$	235112.	1.07022	0.535110	+	0.844783i	$0.320270\pi$
$138$	−17932.6	−0.0801579
$139$	75845.7	0.332962	0.166481	−	0.986045i	$-0.446760\pi$
$139$	75845.7	0.332962	0.166481	+	0.986045i	$0.446760\pi$
$140$	−98504.7	−0.424754
$141$	−14846.8	−0.0628903
$142$	−274806.	−1.14368
$143$	−451101.	−1.84474
$144$	−61859.9	−0.248601
$145$	477832.	1.88736
$146$	−145005.	−0.562990
$147$	9179.02	0.0350351
$148$	−28167.4	−0.105704
$149$	137287.	0.506599	0.253299	−	0.967388i	$-0.418484\pi$
$149$	137287.	0.506599	0.253299	+	0.967388i	$0.418484\pi$
$150$	5210.49	0.0189082
$151$	85090.8	0.303697	0.151848	−	0.988404i	$-0.451477\pi$
$151$	85090.8	0.303697	0.151848	+	0.988404i	$0.451477\pi$
$152$	0	0
$153$	−513408.	−1.77310
$154$	173268.	0.588729
$155$	−76664.0	−0.256308
$156$	−18364.7	−0.0604187
$157$	−81098.1	−0.262580	−0.131290	−	0.991344i	$-0.541912\pi$
$157$	−81098.1	−0.262580	−0.131290	+	0.991344i	$0.541912\pi$
$158$	87926.0	0.280204
$159$	38618.6	0.121144
$160$	66695.1	0.205965
$161$	−363434.	−1.10500
$162$	−232239.	−0.695260
$163$	485148.	1.43023	0.715113	−	0.699009i	$-0.246375\pi$
$163$	485148.	1.43023	0.715113	+	0.699009i	$0.246375\pi$
$164$	−39205.4	−0.113825
$165$	−34802.5	−0.0995177
$166$	410474.	1.15615
$167$	−336511.	−0.933700	−0.466850	−	0.884336i	$-0.654611\pi$
$167$	−336511.	−0.933700	−0.466850	+	0.884336i	$0.654611\pi$
$168$	7053.84	0.0192820
$169$	597700.	1.60978
$170$	553537.	1.46901
$171$	0	0
$172$	34004.8	0.0876434
$173$	107309.	0.272598	0.136299	−	0.990668i	$-0.456479\pi$
$173$	107309.	0.272598	0.136299	+	0.990668i	$0.456479\pi$
$174$	−34217.2	−0.0856783
$175$	105599.	0.260654
$176$	−117315.	−0.285478
$177$	10769.5	0.0258381
$178$	113046.	0.267427
$179$	−266250.	−0.621095	−0.310547	−	0.950558i	$-0.600512\pi$
$179$	−266250.	−0.621095	−0.310547	+	0.950558i	$0.600512\pi$
$180$	251816.	0.579298
$181$	42455.8	0.0963253	0.0481626	−	0.998840i	$-0.484663\pi$
$181$	42455.8	0.0963253	0.0481626	+	0.998840i	$0.484663\pi$
$182$	−372189.	−0.832885
$183$	−12005.7	−0.0265009
$184$	246072.	0.535818
$185$	114662.	0.246315
$186$	5489.85	0.0116353
$187$	−973658.	−2.03612
$188$	203727.	0.420392
$189$	53415.3	0.108770
$190$	0	0
$191$	950028.	1.88431	0.942157	−	0.335172i	$-0.108795\pi$
$191$	950028.	1.88431	0.942157	+	0.335172i	$0.108795\pi$
$192$	−4775.98	−0.00934995
$193$	127823.	0.247010	0.123505	−	0.992344i	$-0.460587\pi$
$193$	127823.	0.247010	0.123505	+	0.992344i	$0.460587\pi$
$194$	323105.	0.616367
$195$	74757.8	0.140789
$196$	−125955.	−0.234193
$197$	−725481.	−1.33187	−0.665933	−	0.746012i	$-0.731966\pi$
$197$	−725481.	−1.33187	−0.665933	+	0.746012i	$0.731966\pi$
$198$	−442939.	−0.802935
$199$	−134661.	−0.241052	−0.120526	−	0.992710i	$-0.538458\pi$
$199$	−134661.	−0.241052	−0.120526	+	0.992710i	$0.538458\pi$
$200$	−71498.4	−0.126393
$201$	33384.4	0.0582846
$202$	−25618.6	−0.0441751
$203$	−693466.	−1.18110
$204$	−39638.3	−0.0666868
$205$	159595.	0.265237
$206$	−587725.	−0.964954
$207$	929076.	1.50704
$208$	252000.	0.403870
$209$	0	0
$210$	−28714.4	−0.0449315
$211$	968337.	1.49734	0.748670	−	0.662943i	$-0.230693\pi$
$211$	968337.	1.49734	0.748670	+	0.662943i	$0.230693\pi$
$212$	−529924.	−0.809793
$213$	−80106.8	−0.120982
$214$	573936.	0.856701
$215$	−138425.	−0.204229
$216$	−36166.1	−0.0527434
$217$	111261.	0.160395
$218$	402227.	0.573231
$219$	−42269.3	−0.0595546
$220$	477560.	0.665228
$221$	2.09148e6	2.88053
$222$	−8210.87	−0.0111817
$223$	−843800.	−1.13626	−0.568130	−	0.822939i	$-0.692333\pi$
$223$	−843800.	−1.13626	−0.568130	+	0.822939i	$0.692333\pi$
$224$	−96792.9	−0.128891
$225$	−269952.	−0.355492
$226$	−465452.	−0.606183
$227$	1.22573e6	1.57881	0.789406	−	0.613872i	$-0.210389\pi$
$227$	1.22573e6	1.57881	0.789406	+	0.613872i	$0.210389\pi$
$228$	0	0
$229$	887407.	1.11824	0.559119	−	0.829087i	$-0.311140\pi$
$229$	887407.	1.11824	0.559119	+	0.829087i	$0.311140\pi$
$230$	−1.00169e6	−1.24858
$231$	50508.0	0.0622773
$232$	469528.	0.572719
$233$	453440.	0.547180	0.273590	−	0.961846i	$-0.411789\pi$
$233$	453440.	0.547180	0.273590	+	0.961846i	$0.411789\pi$
$234$	951458.	1.13593
$235$	−829321.	−0.979610
$236$	−147778.	−0.172715
$237$	25630.7	0.0296407
$238$	−803334.	−0.919293
$239$	−170897.	−0.193526	−0.0967629	−	0.995307i	$-0.530849\pi$
$239$	−170897.	−0.193526	−0.0967629	+	0.995307i	$0.530849\pi$
$240$	19441.8	0.0217875
$241$	−184308.	−0.204409	−0.102205	−	0.994763i	$-0.532590\pi$
$241$	−184308.	−0.204409	−0.102205	+	0.994763i	$0.532590\pi$
$242$	−195812.	−0.214932
$243$	−205017.	−0.222727
$244$	164743.	0.177146
$245$	512728.	0.545723
$246$	−11428.5	−0.0120407
$247$	0	0
$248$	−75331.7	−0.0777765
$249$	119654.	0.122301
$250$	−523097.	−0.529337
$251$	−403050.	−0.403808	−0.201904	−	0.979405i	$-0.564713\pi$
$251$	−403050.	−0.403808	−0.201904	+	0.979405i	$0.564713\pi$
$252$	−365454.	−0.362520
$253$	1.76196e6	1.73059
$254$	1928.03	0.00187512
$255$	161357.	0.155395
$256$	65536.0	0.0625000
$257$	123088.	0.116247	0.0581236	−	0.998309i	$-0.481488\pi$
$257$	123088.	0.116247	0.0581236	+	0.998309i	$0.481488\pi$
$258$	9912.49	0.00927115
$259$	−166406.	−0.154142
$260$	−1.02583e6	−0.941110
$261$	1.77276e6	1.61083
$262$	−366836.	−0.330155
$263$	816728.	0.728095	0.364047	−	0.931380i	$-0.381395\pi$
$263$	816728.	0.728095	0.364047	+	0.931380i	$0.381395\pi$
$264$	−34197.7	−0.0301986
$265$	2.15719e6	1.88700
$266$	0	0
$267$	32953.2	0.0282892
$268$	−458101.	−0.389605
$269$	1.26180e6	1.06319	0.531595	−	0.846999i	$-0.321593\pi$
$269$	1.26180e6	1.06319	0.531595	+	0.846999i	$0.321593\pi$
$270$	147223.	0.122904
$271$	1.16608e6	0.964502	0.482251	−	0.876033i	$-0.339819\pi$
$271$	1.16608e6	0.964502	0.482251	+	0.876033i	$0.339819\pi$
$272$	543917.	0.445770
$273$	−108494.	−0.0881048
$274$	−940447.	−0.756759
$275$	−511953.	−0.408224
$276$	71730.6	0.0566802
$277$	1.67477e6	1.31146	0.655730	−	0.754996i	$-0.272361\pi$
$277$	1.67477e6	1.31146	0.655730	+	0.754996i	$0.272361\pi$
$278$	−303383.	−0.235439
$279$	−284425.	−0.218754
$280$	394019.	0.300346
$281$	1.61515e6	1.22025	0.610124	−	0.792306i	$-0.291120\pi$
$281$	1.61515e6	1.22025	0.610124	+	0.792306i	$0.291120\pi$
$282$	59387.0	0.0444702
$283$	2.34442e6	1.74008	0.870039	−	0.492983i	$-0.164093\pi$
$283$	2.34442e6	1.74008	0.870039	+	0.492983i	$0.164093\pi$
$284$	1.09923e6	0.808707
$285$	0	0
$286$	1.80441e6	1.30442
$287$	−231616.	−0.165983
$288$	247440.	0.175788
$289$	3.09439e6	2.17937
$290$	−1.91133e6	−1.33457
$291$	94185.9	0.0652009
$292$	580020.	0.398094
$293$	41797.8	0.0284436	0.0142218	−	0.999899i	$-0.495473\pi$
$293$	41797.8	0.0284436	0.0142218	+	0.999899i	$0.495473\pi$
$294$	−36716.1	−0.0247735
$295$	601568.	0.402467
$296$	112670.	0.0747442
$297$	−258962.	−0.170351
$298$	−549148.	−0.358219
$299$	−3.78479e6	−2.44830
$300$	−20842.0	−0.0133701
$301$	200893.	0.127805
$302$	−340363.	−0.214746
$303$	−7467.89	−0.00467295
$304$	0	0
$305$	−670626.	−0.412791
$306$	2.05363e6	1.25377
$307$	−1.43037e6	−0.866166	−0.433083	−	0.901354i	$-0.642574\pi$
$307$	−1.43037e6	−0.866166	−0.433083	+	0.901354i	$0.642574\pi$
$308$	−693070.	−0.416294
$309$	−171324.	−0.102075
$310$	306656.	0.181237
$311$	−914782.	−0.536311	−0.268155	−	0.963376i	$-0.586414\pi$
$311$	−914782.	−0.536311	−0.268155	+	0.963376i	$0.586414\pi$
$312$	73458.6	0.0427225
$313$	1.81979e6	1.04993	0.524965	−	0.851124i	$-0.324078\pi$
$313$	1.81979e6	1.04993	0.524965	+	0.851124i	$0.324078\pi$
$314$	324392.	0.185672
$315$	1.48767e6	0.844754
$316$	−351704.	−0.198134
$317$	606362.	0.338910	0.169455	−	0.985538i	$-0.445799\pi$
$317$	606362.	0.338910	0.169455	+	0.985538i	$0.445799\pi$
$318$	−154474.	−0.0856621
$319$	3.36198e6	1.84977
$320$	−266780.	−0.145639
$321$	167304.	0.0906241
$322$	1.45373e6	0.781350
$323$	0	0
$324$	928955.	0.491623
$325$	1.09971e6	0.577522
$326$	−1.94059e6	−1.01132
$327$	117250.	0.0606379
$328$	156822.	0.0804861
$329$	1.20357e6	0.613031
$330$	139210.	0.0703696
$331$	579109.	0.290529	0.145265	−	0.989393i	$-0.453597\pi$
$331$	579109.	0.290529	0.145265	+	0.989393i	$0.453597\pi$
$332$	−1.64190e6	−0.817524
$333$	425399.	0.210226
$334$	1.34604e6	0.660226
$335$	1.86481e6	0.907868
$336$	−28215.4	−0.0136345
$337$	846958.	0.406244	0.203122	−	0.979153i	$-0.434891\pi$
$337$	846958.	0.406244	0.203122	+	0.979153i	$0.434891\pi$
$338$	−2.39080e6	−1.13829
$339$	−135681.	−0.0641236
$340$	−2.21415e6	−1.03875
$341$	−539401.	−0.251204
$342$	0	0
$343$	−2.33278e6	−1.07063
$344$	−136019.	−0.0619732
$345$	−291997.	−0.132078
$346$	−429238.	−0.192756
$347$	359108.	0.160104	0.0800519	−	0.996791i	$-0.474491\pi$
$347$	359108.	0.160104	0.0800519	+	0.996791i	$0.474491\pi$
$348$	136869.	0.0605837
$349$	400158.	0.175860	0.0879301	−	0.996127i	$-0.471975\pi$
$349$	400158.	0.175860	0.0879301	+	0.996127i	$0.471975\pi$
$350$	−422396.	−0.184310
$351$	556266.	0.240999
$352$	469260.	0.201863
$353$	−2.22449e6	−0.950152	−0.475076	−	0.879945i	$-0.657579\pi$
$353$	−2.22449e6	−0.950152	−0.475076	+	0.879945i	$0.657579\pi$
$354$	−43077.8	−0.0182703
$355$	−4.47466e6	−1.88447
$356$	−452184.	−0.189100
$357$	−234174.	−0.0972452
$358$	1.06500e6	0.439180
$359$	475655.	0.194785	0.0973927	−	0.995246i	$-0.468950\pi$
$359$	475655.	0.194785	0.0973927	+	0.995246i	$0.468950\pi$
$360$	−1.00726e6	−0.409625
$361$	0	0
$362$	−169823.	−0.0681123
$363$	−57079.8	−0.0227361
$364$	1.48876e6	0.588939
$365$	−2.36111e6	−0.927651
$366$	48023.0	0.0187390
$367$	−3.55083e6	−1.37615	−0.688073	−	0.725642i	$-0.741543\pi$
$367$	−3.55083e6	−1.37615	−0.688073	+	0.725642i	$0.741543\pi$
$368$	−984287.	−0.378880
$369$	592100.	0.226375
$370$	−458649.	−0.174171
$371$	−3.13067e6	−1.18087
$372$	−21959.4	−0.00822741
$373$	1.93944e6	0.721778	0.360889	−	0.932609i	$-0.382473\pi$
$373$	1.93944e6	0.721778	0.360889	+	0.932609i	$0.382473\pi$
$374$	3.89463e6	1.43975
$375$	−152484.	−0.0559946
$376$	−814909.	−0.297262
$377$	−7.22174e6	−2.61691
$378$	−213661.	−0.0769123
$379$	−2.12461e6	−0.759768	−0.379884	−	0.925034i	$-0.624036\pi$
$379$	−2.12461e6	−0.759768	−0.379884	+	0.925034i	$0.624036\pi$
$380$	0	0
$381$	562.025	0.000198355 0
$382$	−3.80011e6	−1.33241
$383$	4.63648e6	1.61507	0.807535	−	0.589820i	$-0.200801\pi$
$383$	4.63648e6	1.61507	0.807535	+	0.589820i	$0.200801\pi$
$384$	19103.9	0.00661141
$385$	2.82131e6	0.970061
$386$	−511290.	−0.174662
$387$	−513558.	−0.174306
$388$	−1.29242e6	−0.435837
$389$	−3.29250e6	−1.10319	−0.551597	−	0.834111i	$-0.685981\pi$
$389$	−3.29250e6	−1.10319	−0.551597	+	0.834111i	$0.685981\pi$
$390$	−299031.	−0.0995531
$391$	−8.16910e6	−2.70229
$392$	503818.	0.165599
$393$	−106934.	−0.0349247
$394$	2.90192e6	0.941771
$395$	1.43170e6	0.461698
$396$	1.77175e6	0.567761
$397$	1.60659e6	0.511598	0.255799	−	0.966730i	$-0.417661\pi$
$397$	1.60659e6	0.511598	0.255799	+	0.966730i	$0.417661\pi$
$398$	538646.	0.170449
$399$	0	0
$400$	285994.	0.0893730
$401$	1.18032e6	0.366556	0.183278	−	0.983061i	$-0.441329\pi$
$401$	1.18032e6	0.366556	0.183278	+	0.983061i	$0.441329\pi$
$402$	−133538.	−0.0412134
$403$	1.15867e6	0.355382
$404$	102474.	0.0312365
$405$	−3.78154e6	−1.14559
$406$	2.77386e6	0.835160
$407$	806753.	0.241410
$408$	158553.	0.0471547
$409$	1.68903e6	0.499264	0.249632	−	0.968341i	$-0.419690\pi$
$409$	1.68903e6	0.499264	0.249632	+	0.968341i	$0.419690\pi$
$410$	−638380.	−0.187551
$411$	−274143.	−0.0800520
$412$	2.35090e6	0.682325
$413$	−873041.	−0.251860
$414$	−3.71630e6	−1.06564
$415$	6.68374e6	1.90502
$416$	−1.00800e6	−0.285579
$417$	−88436.9	−0.0249054
$418$	0	0
$419$	1.08104e6	0.300821	0.150411	−	0.988624i	$-0.451940\pi$
$419$	1.08104e6	0.300821	0.150411	+	0.988624i	$0.451940\pi$
$420$	114858.	0.0317714
$421$	−5.58922e6	−1.53690	−0.768451	−	0.639909i	$-0.778972\pi$
$421$	−5.58922e6	−1.53690	−0.768451	+	0.639909i	$0.778972\pi$
$422$	−3.87335e6	−1.05878
$423$	−3.07680e6	−0.836080
$424$	2.11970e6	0.572610
$425$	2.37361e6	0.637436
$426$	320427.	0.0855471
$427$	973263.	0.258321
$428$	−2.29574e6	−0.605779
$429$	525989.	0.137985
$430$	553699.	0.144412
$431$	5.95712e6	1.54470	0.772348	−	0.635200i	$-0.219082\pi$
$431$	5.95712e6	1.54470	0.772348	+	0.635200i	$0.219082\pi$
$432$	144665.	0.0372952
$433$	−5.19586e6	−1.33180	−0.665898	−	0.746043i	$-0.731952\pi$
$433$	−5.19586e6	−1.33180	−0.665898	+	0.746043i	$0.731952\pi$
$434$	−445042.	−0.113417
$435$	−557157.	−0.141174
$436$	−1.60891e6	−0.405335
$437$	0	0
$438$	169077.	0.0421115
$439$	−251173.	−0.0622031	−0.0311016	−	0.999516i	$-0.509902\pi$
$439$	−251173.	−0.0622031	−0.0311016	+	0.999516i	$0.509902\pi$
$440$	−1.91024e6	−0.470388
$441$	1.90223e6	0.465765
$442$	−8.36591e6	−2.03684
$443$	−2.98401e6	−0.722422	−0.361211	−	0.932484i	$-0.617637\pi$
$443$	−2.98401e6	−0.722422	−0.361211	+	0.932484i	$0.617637\pi$
$444$	32843.5	0.00790664
$445$	1.84073e6	0.440645
$446$	3.37520e6	0.803457
$447$	−160078.	−0.0378934
$448$	387172.	0.0911399
$449$	−5.01310e6	−1.17352	−0.586760	−	0.809761i	$-0.699597\pi$
$449$	−5.01310e6	−1.17352	−0.586760	+	0.809761i	$0.699597\pi$
$450$	1.07981e6	0.251371
$451$	1.12290e6	0.259955
$452$	1.86181e6	0.428636
$453$	−99216.8	−0.0227164
$454$	−4.90292e6	−1.11639
$455$	−6.06034e6	−1.37236
$456$	0	0
$457$	−6.93647e6	−1.55363	−0.776816	−	0.629728i	$-0.783166\pi$
$457$	−6.93647e6	−1.55363	−0.776816	+	0.629728i	$0.783166\pi$
$458$	−3.54963e6	−0.790714
$459$	1.20065e6	0.266001
$460$	4.00678e6	0.882878
$461$	4.99252e6	1.09413	0.547063	−	0.837091i	$-0.315746\pi$
$461$	4.99252e6	1.09413	0.547063	+	0.837091i	$0.315746\pi$
$462$	−202032.	−0.0440367
$463$	−2.65065e6	−0.574645	−0.287323	−	0.957834i	$-0.592765\pi$
$463$	−2.65065e6	−0.574645	−0.287323	+	0.957834i	$0.592765\pi$
$464$	−1.87811e6	−0.404973
$465$	89391.0	0.0191717
$466$	−1.81376e6	−0.386915
$467$	7.68506e6	1.63063	0.815314	−	0.579019i	$-0.196564\pi$
$467$	7.68506e6	1.63063	0.815314	+	0.579019i	$0.196564\pi$
$468$	−3.80583e6	−0.803221
$469$	−2.70635e6	−0.568136
$470$	3.31728e6	0.692689
$471$	94561.2	0.0196409
$472$	591114.	0.122128
$473$	−973944.	−0.200162
$474$	−102523.	−0.0209592
$475$	0	0
$476$	3.21334e6	0.650038
$477$	8.00320e6	1.61053
$478$	683587.	0.136843
$479$	−6.72219e6	−1.33867	−0.669333	−	0.742963i	$-0.733420\pi$
$479$	−6.72219e6	−1.33867	−0.669333	+	0.742963i	$0.733420\pi$
$480$	−77767.1	−0.0154061
$481$	−1.73295e6	−0.341526
$482$	737230.	0.144539
$483$	423768.	0.0826532
$484$	783249.	0.151980
$485$	5.26111e6	1.01560
$486$	820066.	0.157492
$487$	−7.70276e6	−1.47172	−0.735858	−	0.677136i	$-0.763221\pi$
$487$	−7.70276e6	−1.47172	−0.735858	+	0.677136i	$0.763221\pi$
$488$	−658972.	−0.125261
$489$	−565687.	−0.106980
$490$	−2.05091e6	−0.385884
$491$	−2.05199e6	−0.384124	−0.192062	−	0.981383i	$-0.561517\pi$
$491$	−2.05199e6	−0.384124	−0.192062	+	0.981383i	$0.561517\pi$
$492$	45713.9	0.00851403
$493$	−1.55874e7	−2.88840
$494$	0	0
$495$	−7.21236e6	−1.32301
$496$	301327.	0.0549963
$497$	6.49397e6	1.17929
$498$	−478617.	−0.0864798
$499$	6.20643e6	1.11581	0.557906	−	0.829904i	$-0.311605\pi$
$499$	6.20643e6	1.11581	0.557906	+	0.829904i	$0.311605\pi$
$500$	2.09239e6	0.374298
$501$	392375.	0.0698404
$502$	1.61220e6	0.285535
$503$	2.83149e6	0.498994	0.249497	−	0.968376i	$-0.419735\pi$
$503$	2.83149e6	0.498994	0.249497	+	0.968376i	$0.419735\pi$
$504$	1.46182e6	0.256340
$505$	−417147.	−0.0727882
$506$	−7.04783e6	−1.22371
$507$	−696924.	−0.120411
$508$	−7712.11	−0.00132591
$509$	6.63957e6	1.13591	0.567957	−	0.823058i	$-0.307734\pi$
$509$	6.63957e6	1.13591	0.567957	+	0.823058i	$0.307734\pi$
$510$	−645430.	−0.109881
$511$	3.42662e6	0.580516
$512$	−262144.	−0.0441942
$513$	0	0
$514$	−492351.	−0.0821991
$515$	−9.56992e6	−1.58997
$516$	−39650.0	−0.00655569
$517$	−5.83503e6	−0.960100
$518$	665626.	0.108995
$519$	−125124.	−0.0203902
$520$	4.10331e6	0.665465
$521$	9.81565e6	1.58425	0.792127	−	0.610357i	$-0.208974\pi$
$521$	9.81565e6	1.58425	0.792127	+	0.610357i	$0.208974\pi$
$522$	−7.09106e6	−1.13903
$523$	8.32979e6	1.33162	0.665809	−	0.746122i	$-0.268086\pi$
$523$	8.32979e6	1.33162	0.665809	+	0.746122i	$0.268086\pi$
$524$	1.46734e6	0.233455
$525$	−123130.	−0.0194968
$526$	−3.26691e6	−0.514841
$527$	2.50087e6	0.392251
$528$	136791.	0.0213536
$529$	8.34669e6	1.29681
$530$	−8.62874e6	−1.33431
$531$	2.23183e6	0.343498
$532$	0	0
$533$	−2.41205e6	−0.367763
$534$	−131813.	−0.0200035
$535$	9.34539e6	1.41160
$536$	1.83240e6	0.275492
$537$	310451.	0.0464576
$538$	−5.04721e6	−0.751788
$539$	3.60751e6	0.534855
$540$	−588892.	−0.0869063
$541$	−1.31845e6	−0.193673	−0.0968365	−	0.995300i	$-0.530872\pi$
$541$	−1.31845e6	−0.193673	−0.0968365	+	0.995300i	$0.530872\pi$
$542$	−4.66430e6	−0.682006
$543$	−49503.9	−0.00720509
$544$	−2.17567e6	−0.315207
$545$	6.54944e6	0.944524
$546$	433976.	0.0622995
$547$	3.41377e6	0.487827	0.243913	−	0.969797i	$-0.421569\pi$
$547$	3.41377e6	0.487827	0.243913	+	0.969797i	$0.421569\pi$
$548$	3.76179e6	0.535110
$549$	−2.48803e6	−0.352310
$550$	2.04781e6	0.288658
$551$	0	0
$552$	−286922.	−0.0400790
$553$	−2.07779e6	−0.288927
$554$	−6.69907e6	−0.927342
$555$	−133697.	−0.0184243
$556$	1.21353e6	0.166481
$557$	2.46992e6	0.337322	0.168661	−	0.985674i	$-0.446056\pi$
$557$	2.46992e6	0.337322	0.168661	+	0.985674i	$0.446056\pi$
$558$	1.13770e6	0.154683
$559$	2.09209e6	0.283172
$560$	−1.57608e6	−0.212377
$561$	1.13530e6	0.152301
$562$	−6.46061e6	−0.862845
$563$	8.34626e6	1.10974	0.554870	−	0.831937i	$-0.312768\pi$
$563$	8.34626e6	1.10974	0.554870	+	0.831937i	$0.312768\pi$
$564$	−237548.	−0.0314452
$565$	−7.57894e6	−0.998821
$566$	−9.37767e6	−1.23042
$567$	5.48805e6	0.716903
$568$	−4.39690e6	−0.571842
$569$	−6.16363e6	−0.798097	−0.399048	−	0.916930i	$-0.630659\pi$
$569$	−6.16363e6	−0.798097	−0.399048	+	0.916930i	$0.630659\pi$
$570$	0	0
$571$	8.79609e6	1.12901	0.564507	−	0.825428i	$-0.309066\pi$
$571$	8.79609e6	1.12901	0.564507	+	0.825428i	$0.309066\pi$
$572$	−7.21762e6	−0.922368
$573$	−1.10774e6	−0.140946
$574$	926465.	0.117368
$575$	−4.29535e6	−0.541787
$576$	−989759.	−0.124301
$577$	−2.25027e6	−0.281381	−0.140691	−	0.990054i	$-0.544932\pi$
$577$	−2.25027e6	−0.281381	−0.140691	+	0.990054i	$0.544932\pi$
$578$	−1.23776e7	−1.54105
$579$	−149043.	−0.0184762
$580$	7.64531e6	0.943681
$581$	−9.69994e6	−1.19214
$582$	−376744.	−0.0461040
$583$	1.51778e7	1.84942
$584$	−2.32008e6	−0.281495
$585$	1.54926e7	1.87169
$586$	−167191.	−0.0201126
$587$	−3.10442e6	−0.371865	−0.185933	−	0.982563i	$-0.559531\pi$
$587$	−3.10442e6	−0.371865	−0.185933	+	0.982563i	$0.559531\pi$
$588$	146864.	0.0175175
$589$	0	0
$590$	−2.40627e6	−0.284587
$591$	845919.	0.0996231
$592$	−450678.	−0.0528521
$593$	5.98086e6	0.698436	0.349218	−	0.937041i	$-0.386447\pi$
$593$	5.98086e6	0.698436	0.349218	+	0.937041i	$0.386447\pi$
$594$	1.03585e6	0.120456
$595$	−1.30807e7	−1.51474
$596$	2.19659e6	0.253299
$597$	157017.	0.0180306
$598$	1.51392e7	1.73121
$599$	6.92305e6	0.788370	0.394185	−	0.919031i	$-0.371027\pi$
$599$	6.92305e6	0.788370	0.394185	+	0.919031i	$0.371027\pi$
$600$	83367.9	0.00945411
$601$	4.63926e6	0.523917	0.261959	−	0.965079i	$-0.415632\pi$
$601$	4.63926e6	0.523917	0.261959	+	0.965079i	$0.415632\pi$
$602$	−803570.	−0.0903717
$603$	6.91848e6	0.774850
$604$	1.36145e6	0.151848
$605$	−3.18841e6	−0.354148
$606$	29871.6	0.00330428
$607$	−8.70257e6	−0.958685	−0.479343	−	0.877628i	$-0.659125\pi$
$607$	−8.70257e6	−0.958685	−0.479343	+	0.877628i	$0.659125\pi$
$608$	0	0
$609$	808588.	0.0883454
$610$	2.68250e6	0.291888
$611$	1.25340e7	1.35827
$612$	−8.21452e6	−0.886551
$613$	−5.42194e6	−0.582778	−0.291389	−	0.956605i	$-0.594117\pi$
$613$	−5.42194e6	−0.582778	−0.291389	+	0.956605i	$0.594117\pi$
$614$	5.72146e6	0.612472
$615$	−186089.	−0.0198396
$616$	2.77228e6	0.294365
$617$	4.64831e6	0.491566	0.245783	−	0.969325i	$-0.420955\pi$
$617$	4.64831e6	0.491566	0.245783	+	0.969325i	$0.420955\pi$
$618$	685294.	0.0721782
$619$	3.56785e6	0.374266	0.187133	−	0.982335i	$-0.440080\pi$
$619$	3.56785e6	0.374266	0.187133	+	0.982335i	$0.440080\pi$
$620$	−1.22662e6	−0.128154
$621$	−2.17272e6	−0.226087
$622$	3.65913e6	0.379229
$623$	−2.67140e6	−0.275752
$624$	−293834.	−0.0302093
$625$	−1.20087e7	−1.22969
$626$	−7.27916e6	−0.742413
$627$	0	0
$628$	−1.29757e6	−0.131290
$629$	−3.74041e6	−0.376958
$630$	−5.95068e6	−0.597331
$631$	−1.08645e7	−1.08627	−0.543134	−	0.839646i	$-0.682762\pi$
$631$	−1.08645e7	−1.08627	−0.543134	+	0.839646i	$0.682762\pi$
$632$	1.40682e6	0.140102
$633$	−1.12909e6	−0.112000
$634$	−2.42545e6	−0.239645
$635$	31394.0	0.00308967
$636$	617897.	0.0605722
$637$	−7.74915e6	−0.756668
$638$	−1.34479e7	−1.30799
$639$	−1.66011e7	−1.60836
$640$	1.06712e6	0.102983
$641$	−7.19318e6	−0.691474	−0.345737	−	0.938331i	$-0.612371\pi$
$641$	−7.19318e6	−0.691474	−0.345737	+	0.938331i	$0.612371\pi$
$642$	−669216.	−0.0640809
$643$	−1.59363e7	−1.52006	−0.760030	−	0.649888i	$-0.774816\pi$
$643$	−1.59363e7	−1.52006	−0.760030	+	0.649888i	$0.774816\pi$
$644$	−5.81494e6	−0.552498
$645$	161405.	0.0152763
$646$	0	0
$647$	−9.77399e6	−0.917934	−0.458967	−	0.888453i	$-0.651780\pi$
$647$	−9.77399e6	−0.917934	−0.458967	+	0.888453i	$0.651780\pi$
$648$	−3.71582e6	−0.347630
$649$	4.23258e6	0.394451
$650$	−4.39882e6	−0.408369
$651$	−129731.	−0.0119975
$652$	7.76236e6	0.715113
$653$	−5.52435e6	−0.506989	−0.253494	−	0.967337i	$-0.581580\pi$
$653$	−5.52435e6	−0.506989	−0.253494	+	0.967337i	$0.581580\pi$
$654$	−469000.	−0.0428774
$655$	−5.97317e6	−0.544004
$656$	−627286.	−0.0569123
$657$	−8.75977e6	−0.791734
$658$	−4.81429e6	−0.433479
$659$	−1.22620e7	−1.09989	−0.549943	−	0.835202i	$-0.685350\pi$
$659$	−1.22620e7	−1.09989	−0.549943	+	0.835202i	$0.685350\pi$
$660$	−556839.	−0.0497588
$661$	−1.65710e7	−1.47518	−0.737589	−	0.675250i	$-0.764036\pi$
$661$	−1.65710e7	−1.47518	−0.737589	+	0.675250i	$0.764036\pi$
$662$	−2.31644e6	−0.205435
$663$	−2.43868e6	−0.215462
$664$	6.56758e6	0.578077
$665$	0	0
$666$	−1.70160e6	−0.148652
$667$	2.82074e7	2.45498
$668$	−5.38417e6	−0.466850
$669$	983880.	0.0849918
$670$	−7.45924e6	−0.641960
$671$	−4.71846e6	−0.404571
$672$	112862.	0.00964101
$673$	−644074.	−0.0548148	−0.0274074	−	0.999624i	$-0.508725\pi$
$673$	−644074.	−0.0548148	−0.0274074	+	0.999624i	$0.508725\pi$
$674$	−3.38783e6	−0.287258
$675$	631304.	0.0533309
$676$	9.56319e6	0.804889
$677$	−9.78531e6	−0.820546	−0.410273	−	0.911963i	$-0.634567\pi$
$677$	−9.78531e6	−0.820546	−0.410273	+	0.911963i	$0.634567\pi$
$678$	542722.	0.0453423
$679$	−7.63531e6	−0.635554
$680$	8.85659e6	0.734504
$681$	−1.42921e6	−0.118094
$682$	2.15760e6	0.177628
$683$	3.75534e6	0.308033	0.154017	−	0.988068i	$-0.450779\pi$
$683$	3.75534e6	0.308033	0.154017	+	0.988068i	$0.450779\pi$
$684$	0	0
$685$	−1.53133e7	−1.24693
$686$	9.33112e6	0.757048
$687$	−1.03473e6	−0.0836438
$688$	544077.	0.0438217
$689$	−3.26027e7	−2.61641
$690$	1.16799e6	0.0933932
$691$	2.10376e7	1.67610	0.838051	−	0.545593i	$-0.183695\pi$
$691$	2.10376e7	1.67610	0.838051	+	0.545593i	$0.183695\pi$
$692$	1.71695e6	0.136299
$693$	1.04671e7	0.827930
$694$	−1.43643e6	−0.113211
$695$	−4.93997e6	−0.387938
$696$	−547475.	−0.0428392
$697$	−5.20617e6	−0.405916
$698$	−1.60063e6	−0.124352
$699$	−528716.	−0.0409289
$700$	1.68958e6	0.130327
$701$	9.56329e6	0.735043	0.367521	−	0.930015i	$-0.380207\pi$
$701$	9.56329e6	0.735043	0.367521	+	0.930015i	$0.380207\pi$
$702$	−2.22506e6	−0.170412
$703$	0	0
$704$	−1.87704e6	−0.142739
$705$	966997.	0.0732744
$706$	8.89794e6	0.671859
$707$	605395.	0.0455502
$708$	172311.	0.0129190
$709$	−5.73053e6	−0.428133	−0.214067	−	0.976819i	$-0.568671\pi$
$709$	−5.73053e6	−0.428133	−0.214067	+	0.976819i	$0.568671\pi$
$710$	1.78987e7	1.33252
$711$	5.31162e6	0.394051
$712$	1.80874e6	0.133714
$713$	−4.52564e6	−0.333392
$714$	936696.	0.0687627
$715$	2.93811e7	2.14933
$716$	−4.26001e6	−0.310547
$717$	199267.	0.0144757
$718$	−1.90262e6	−0.137734
$719$	858188.	0.0619099	0.0309550	−	0.999521i	$-0.490145\pi$
$719$	858188.	0.0619099	0.0309550	+	0.999521i	$0.490145\pi$
$720$	4.02906e6	0.289649
$721$	1.38886e7	0.994992
$722$	0	0
$723$	214905.	0.0152897
$724$	679292.	0.0481626
$725$	−8.19592e6	−0.579099
$726$	228319.	0.0160768
$727$	1.15990e7	0.813923	0.406962	−	0.913445i	$-0.366588\pi$
$727$	1.15990e7	0.813923	0.406962	+	0.913445i	$0.366588\pi$
$728$	−5.95503e6	−0.416443
$729$	−1.38695e7	−0.966586
$730$	9.44445e6	0.655948
$731$	4.51557e6	0.312550
$732$	−192092.	−0.0132505
$733$	−1.13392e7	−0.779511	−0.389756	−	0.920918i	$-0.627441\pi$
$733$	−1.13392e7	−0.779511	−0.389756	+	0.920918i	$0.627441\pi$
$734$	1.42033e7	0.973082
$735$	−597847.	−0.0408199
$736$	3.93715e6	0.267909
$737$	1.31206e7	0.889787
$738$	−2.36840e6	−0.160072
$739$	2.06956e7	1.39402	0.697008	−	0.717063i	$-0.254514\pi$
$739$	2.06956e7	1.39402	0.697008	+	0.717063i	$0.254514\pi$
$740$	1.83460e6	0.123158
$741$	0	0
$742$	1.25227e7	0.835002
$743$	1.77897e7	1.18221	0.591107	−	0.806593i	$-0.298691\pi$
$743$	1.77897e7	1.18221	0.591107	+	0.806593i	$0.298691\pi$
$744$	87837.6	0.00581765
$745$	−8.94177e6	−0.590245
$746$	−7.75775e6	−0.510374
$747$	2.47968e7	1.62590
$748$	−1.55785e7	−1.01806
$749$	−1.35627e7	−0.883370
$750$	609937.	0.0395942
$751$	2.41833e7	1.56465	0.782324	−	0.622872i	$-0.214034\pi$
$751$	2.41833e7	1.56465	0.782324	+	0.622872i	$0.214034\pi$
$752$	3.25964e6	0.210196
$753$	469960.	0.0302047
$754$	2.88870e7	1.85043
$755$	−5.54213e6	−0.353842
$756$	854645.	0.0543852
$757$	1.89248e7	1.20030	0.600151	−	0.799887i	$-0.295107\pi$
$757$	1.89248e7	1.20030	0.600151	+	0.799887i	$0.295107\pi$
$758$	8.49843e6	0.537237
$759$	−2.05446e6	−0.129447
$760$	0	0
$761$	−1.72399e6	−0.107913	−0.0539565	−	0.998543i	$-0.517183\pi$
$761$	−1.72399e6	−0.107913	−0.0539565	+	0.998543i	$0.517183\pi$
$762$	−2248.10	−0.000140258 0
$763$	−9.50504e6	−0.591075
$764$	1.52005e7	0.942157
$765$	3.34392e7	2.06587
$766$	−1.85459e7	−1.14203
$767$	−9.09183e6	−0.558037
$768$	−76415.7	−0.00467498
$769$	3.08370e7	1.88043	0.940214	−	0.340585i	$-0.110625\pi$
$769$	3.08370e7	1.88043	0.940214	+	0.340585i	$0.110625\pi$
$770$	−1.12852e7	−0.685937
$771$	−143522.	−0.00869524
$772$	2.04516e6	0.123505
$773$	−1.21764e7	−0.732942	−0.366471	−	0.930429i	$-0.619434\pi$
$773$	−1.21764e7	−0.732942	−0.366471	+	0.930429i	$0.619434\pi$
$774$	2.05423e6	0.123253
$775$	1.31497e6	0.0786430
$776$	5.16968e6	0.308183
$777$	194032.	0.0115298
$778$	1.31700e7	0.780076
$779$	0	0
$780$	1.19612e6	0.0703947
$781$	−3.14833e7	−1.84694
$782$	3.26764e7	1.91081
$783$	−4.14575e6	−0.241657
$784$	−2.01527e6	−0.117096
$785$	5.28207e6	0.305936
$786$	427734.	0.0246955
$787$	−7.35704e6	−0.423415	−0.211708	−	0.977333i	$-0.567902\pi$
$787$	−7.35704e6	−0.423415	−0.211708	+	0.977333i	$0.567902\pi$
$788$	−1.16077e7	−0.665933
$789$	−952313.	−0.0544612
$790$	−5.72679e6	−0.326470
$791$	1.09991e7	0.625054
$792$	−7.08702e6	−0.401468
$793$	1.01355e7	0.572353
$794$	−6.42636e6	−0.361754
$795$	−2.51530e6	−0.141147
$796$	−2.15458e6	−0.120526
$797$	1.72232e7	0.960434	0.480217	−	0.877150i	$-0.340558\pi$
$797$	1.72232e7	0.960434	0.480217	+	0.877150i	$0.340558\pi$
$798$	0	0
$799$	2.70534e7	1.49918
$800$	−1.14397e6	−0.0631963
$801$	6.82913e6	0.376083
$802$	−4.72130e6	−0.259194
$803$	−1.66126e7	−0.909176
$804$	534150.	0.0291423
$805$	2.36711e7	1.28745
$806$	−4.63466e6	−0.251293
$807$	−1.47127e6	−0.0795261
$808$	−409898.	−0.0220875
$809$	2.01553e7	1.08272	0.541361	−	0.840790i	$-0.317909\pi$
$809$	2.01553e7	1.08272	0.541361	+	0.840790i	$0.317909\pi$
$810$	1.51262e7	0.810058
$811$	−4.12961e6	−0.220474	−0.110237	−	0.993905i	$-0.535161\pi$
$811$	−4.12961e6	−0.220474	−0.110237	+	0.993905i	$0.535161\pi$
$812$	−1.10954e7	−0.590548
$813$	−1.35966e6	−0.0721444
$814$	−3.22701e6	−0.170702
$815$	−3.15986e7	−1.66638
$816$	−634213.	−0.0333434
$817$	0	0
$818$	−6.75613e6	−0.353033
$819$	−2.24840e7	−1.17129
$820$	2.55352e6	0.132619
$821$	1.43194e7	0.741425	0.370712	−	0.928748i	$-0.379114\pi$
$821$	1.43194e7	0.741425	0.370712	+	0.928748i	$0.379114\pi$
$822$	1.09657e6	0.0566053
$823$	3.02457e7	1.55655	0.778276	−	0.627922i	$-0.216094\pi$
$823$	3.02457e7	1.55655	0.778276	+	0.627922i	$0.216094\pi$
$824$	−9.40361e6	−0.482477
$825$	596943.	0.0305350
$826$	3.49216e6	0.178092
$827$	−2.66650e7	−1.35575	−0.677873	−	0.735179i	$-0.737098\pi$
$827$	−2.66650e7	−1.35575	−0.677873	+	0.735179i	$0.737098\pi$
$828$	1.48652e7	0.753521
$829$	−2.83495e7	−1.43271	−0.716356	−	0.697735i	$-0.754191\pi$
$829$	−2.83495e7	−1.43271	−0.716356	+	0.697735i	$0.754191\pi$
$830$	−2.67349e7	−1.34705
$831$	−1.95280e6	−0.0980966
$832$	4.03200e6	0.201935
$833$	−1.67258e7	−0.835168
$834$	353748.	0.0176108
$835$	2.19176e7	1.08787
$836$	0	0
$837$	665151.	0.0328176
$838$	−4.32418e6	−0.212713
$839$	−3.44319e7	−1.68871	−0.844356	−	0.535782i	$-0.820017\pi$
$839$	−3.44319e7	−1.68871	−0.844356	+	0.535782i	$0.820017\pi$
$840$	−459430.	−0.0224658
$841$	3.33112e7	1.62406
$842$	2.23569e7	1.08675
$843$	−1.88329e6	−0.0912740
$844$	1.54934e7	0.748670
$845$	−3.89293e7	−1.87558
$846$	1.23072e7	0.591198
$847$	4.62726e6	0.221623
$848$	−8.47879e6	−0.404897
$849$	−2.73361e6	−0.130157
$850$	−9.49443e6	−0.450736
$851$	6.76875e6	0.320394
$852$	−1.28171e6	−0.0604909
$853$	2.18193e7	1.02676	0.513378	−	0.858162i	$-0.328394\pi$
$853$	2.18193e7	1.02676	0.513378	+	0.858162i	$0.328394\pi$
$854$	−3.89305e6	−0.182661
$855$	0	0
$856$	9.18298e6	0.428350
$857$	2.97380e6	0.138312	0.0691560	−	0.997606i	$-0.477969\pi$
$857$	2.97380e6	0.138312	0.0691560	+	0.997606i	$0.477969\pi$
$858$	−2.10396e6	−0.0975705
$859$	1.61719e7	0.747786	0.373893	−	0.927472i	$-0.378023\pi$
$859$	1.61719e7	0.747786	0.373893	+	0.927472i	$0.378023\pi$
$860$	−2.21480e6	−0.102115
$861$	270067.	0.0124155
$862$	−2.38285e7	−1.09226
$863$	2.36695e7	1.08184	0.540918	−	0.841075i	$-0.318077\pi$
$863$	2.36695e7	1.08184	0.540918	+	0.841075i	$0.318077\pi$
$864$	−578658.	−0.0263717
$865$	−6.98927e6	−0.317608
$866$	2.07834e7	0.941722
$867$	−3.60809e6	−0.163016
$868$	1.78017e6	0.0801977
$869$	1.00733e7	0.452503
$870$	2.22863e6	0.0998250
$871$	−2.81839e7	−1.25880
$872$	6.43562e6	0.286615
$873$	1.95188e7	0.866797
$874$	0	0
$875$	1.23613e7	0.545815
$876$	−676310.	−0.0297773
$877$	−2.13817e7	−0.938736	−0.469368	−	0.883003i	$-0.655518\pi$
$877$	−2.13817e7	−0.938736	−0.469368	+	0.883003i	$0.655518\pi$
$878$	1.00469e6	0.0439843
$879$	−48736.6	−0.00212757
$880$	7.64095e6	0.332614
$881$	−1.89553e7	−0.822794	−0.411397	−	0.911456i	$-0.634959\pi$
$881$	−1.89553e7	−0.822794	−0.411397	+	0.911456i	$0.634959\pi$
$882$	−7.60893e6	−0.329346
$883$	−2.85853e7	−1.23379	−0.616895	−	0.787045i	$-0.711610\pi$
$883$	−2.85853e7	−1.23379	−0.616895	+	0.787045i	$0.711610\pi$
$884$	3.34636e7	1.44026
$885$	−701435.	−0.0301043
$886$	1.19360e7	0.510830
$887$	473148.	0.0201924	0.0100962	−	0.999949i	$-0.496786\pi$
$887$	473148.	0.0201924	0.0100962	+	0.999949i	$0.496786\pi$
$888$	−131374.	−0.00559084
$889$	−45561.3	−0.00193349
$890$	−7.36291e6	−0.311583
$891$	−2.66066e7	−1.12278
$892$	−1.35008e7	−0.568130
$893$	0	0
$894$	640313.	0.0267947
$895$	1.73414e7	0.723646
$896$	−1.54869e6	−0.0644456
$897$	4.41311e6	0.183132
$898$	2.00524e7	0.829803
$899$	−8.63534e6	−0.356353
$900$	−4.31923e6	−0.177746
$901$	−7.03698e7	−2.88785
$902$	−4.49158e6	−0.183816
$903$	−234243.	−0.00955976
$904$	−7.44723e6	−0.303092
$905$	−2.76522e6	−0.112230
$906$	396867.	0.0160629
$907$	1.53315e7	0.618824	0.309412	−	0.950928i	$-0.399868\pi$
$907$	1.53315e7	0.618824	0.309412	+	0.950928i	$0.399868\pi$
$908$	1.96117e7	0.789406
$909$	−1.54762e6	−0.0621234
$910$	2.42414e7	0.970407
$911$	−1.73110e7	−0.691076	−0.345538	−	0.938405i	$-0.612304\pi$
$911$	−1.73110e7	−0.691076	−0.345538	+	0.938405i	$0.612304\pi$
$912$	0	0
$913$	4.70262e7	1.86708
$914$	2.77459e7	1.09858
$915$	781957.	0.0308766
$916$	1.41985e7	0.559119
$917$	8.66872e6	0.340433
$918$	−4.80258e6	−0.188091
$919$	−2.77310e7	−1.08312	−0.541560	−	0.840662i	$-0.682166\pi$
$919$	−2.77310e7	−1.08312	−0.541560	+	0.840662i	$0.682166\pi$
$920$	−1.60271e7	−0.624289
$921$	1.66782e6	0.0647889
$922$	−1.99701e7	−0.773664
$923$	6.76281e7	2.61290
$924$	808127.	0.0311387
$925$	−1.96672e6	−0.0755769
$926$	1.06026e7	0.406336
$927$	−3.55046e7	−1.35702
$928$	7.51245e6	0.286359
$929$	5.06392e7	1.92508	0.962538	−	0.271148i	$-0.0874032\pi$
$929$	5.06392e7	1.92508	0.962538	+	0.271148i	$0.0874032\pi$
$930$	−357564.	−0.0135565
$931$	0	0
$932$	7.25505e6	0.273590
$933$	1.06665e6	0.0401158
$934$	−3.07402e7	−1.15303
$935$	6.34162e7	2.37231
$936$	1.52233e7	0.567963
$937$	7.26908e6	0.270477	0.135239	−	0.990813i	$-0.456820\pi$
$937$	7.26908e6	0.270477	0.135239	+	0.990813i	$0.456820\pi$
$938$	1.08254e7	0.401733
$939$	−2.12189e6	−0.0785343
$940$	−1.32691e7	−0.489805
$941$	−4.59306e7	−1.69094	−0.845469	−	0.534025i	$-0.820679\pi$
$941$	−4.59306e7	−1.69094	−0.845469	+	0.534025i	$0.820679\pi$
$942$	−378245.	−0.0138882
$943$	9.42123e6	0.345007
$944$	−2.36446e6	−0.0863577
$945$	−3.47904e6	−0.126730
$946$	3.89578e6	0.141536
$947$	3.02687e7	1.09678	0.548388	−	0.836224i	$-0.315242\pi$
$947$	3.02687e7	1.09678	0.548388	+	0.836224i	$0.315242\pi$
$948$	410091.	0.0148204
$949$	3.56848e7	1.28623
$950$	0	0
$951$	−707025.	−0.0253503
$952$	−1.28533e7	−0.459646
$953$	2.24045e7	0.799104	0.399552	−	0.916710i	$-0.369166\pi$
$953$	2.24045e7	0.799104	0.399552	+	0.916710i	$0.369166\pi$
$954$	−3.20128e7	−1.13881
$955$	−6.18771e7	−2.19544
$956$	−2.73435e6	−0.0967629
$957$	−3.92011e6	−0.138362
$958$	2.68888e7	0.946580
$959$	2.22238e7	0.780317
$960$	311069.	0.0108938
$961$	−2.72437e7	−0.951606
$962$	6.93182e6	0.241496
$963$	3.46715e7	1.20478
$964$	−2.94892e6	−0.102205
$965$	−8.32533e6	−0.287795
$966$	−1.69507e6	−0.0584447
$967$	1.23627e7	0.425153	0.212577	−	0.977144i	$-0.431814\pi$
$967$	1.23627e7	0.425153	0.212577	+	0.977144i	$0.431814\pi$
$968$	−3.13300e6	−0.107466
$969$	0	0
$970$	−2.10444e7	−0.718138
$971$	−4.47561e7	−1.52337	−0.761683	−	0.647950i	$-0.775627\pi$
$971$	−4.47561e7	−1.52337	−0.761683	+	0.647950i	$0.775627\pi$
$972$	−3.28026e6	−0.111364
$973$	7.16926e6	0.242769
$974$	3.08110e7	1.04066
$975$	−1.28227e6	−0.0431984
$976$	2.63589e6	0.0885731
$977$	−1.47843e7	−0.495524	−0.247762	−	0.968821i	$-0.579695\pi$
$977$	−1.47843e7	−0.495524	−0.247762	+	0.968821i	$0.579695\pi$
$978$	2.26275e6	0.0756466
$979$	1.29512e7	0.431870
$980$	8.20366e6	0.272861
$981$	2.42985e7	0.806135
$982$	8.20795e6	0.271616
$983$	1.47485e7	0.486814	0.243407	−	0.969924i	$-0.421735\pi$
$983$	1.47485e7	0.486814	0.243407	+	0.969924i	$0.421735\pi$
$984$	−182856.	−0.00602033
$985$	4.72520e7	1.55178
$986$	6.23497e7	2.04241
$987$	−1.40338e6	−0.0458545
$988$	0	0
$989$	−8.17150e6	−0.265651
$990$	2.88494e7	0.935511
$991$	−2.53843e7	−0.821072	−0.410536	−	0.911844i	$-0.634658\pi$
$991$	−2.53843e7	−0.821072	−0.410536	+	0.911844i	$0.634658\pi$
$992$	−1.20531e6	−0.0388883
$993$	−675247.	−0.0217315
$994$	−2.59759e7	−0.833881
$995$	8.77076e6	0.280853
$996$	1.91447e6	0.0611505
$997$	−2.62082e7	−0.835024	−0.417512	−	0.908671i	$-0.637098\pi$
$997$	−2.62082e7	−0.835024	−0.417512	+	0.908671i	$0.637098\pi$
$998$	−2.48257e7	−0.788998
$999$	−994830.	−0.0315381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.q.1.8		15
19.3	odd	18		38.6.e.b.9.3	✓	30
19.13	odd	18		38.6.e.b.17.3	yes	30
19.18	odd	2		722.6.a.r.1.8		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.9.3	✓	30	19.3	odd	18
38.6.e.b.17.3	yes	30	19.13	odd	18
722.6.a.q.1.8		15	1.1	even	1	trivial
722.6.a.r.1.8		15	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -1.16601 q^{3} +16.0000 q^{4} -65.1319 q^{5} +4.66404 q^{6} +94.5243 q^{7} -64.0000 q^{8} -241.640 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -1.16601 q^{3} +16.0000 q^{4} -65.1319 q^{5} +4.66404 q^{6} +94.5243 q^{7} -64.0000 q^{8} -241.640 q^{9} +260.528 q^{10} -458.262 q^{11} -18.6562 q^{12} +984.374 q^{13} -378.097 q^{14} +75.9445 q^{15} +256.000 q^{16} +2124.68 q^{17} +966.562 q^{18} -1042.11 q^{20} -110.216 q^{21} +1833.05 q^{22} -3844.87 q^{23} +74.6247 q^{24} +1117.16 q^{25} -3937.50 q^{26} +565.096 q^{27} +1512.39 q^{28} -7336.37 q^{29} -303.778 q^{30} +1177.06 q^{31} -1024.00 q^{32} +534.338 q^{33} -8498.70 q^{34} -6156.55 q^{35} -3866.25 q^{36} -1760.46 q^{37} -1147.79 q^{39} +4168.44 q^{40} -2450.34 q^{41} +440.865 q^{42} +2125.30 q^{43} -7332.19 q^{44} +15738.5 q^{45} +15379.5 q^{46} +12732.9 q^{47} -298.499 q^{48} -7872.16 q^{49} -4468.65 q^{50} -2477.39 q^{51} +15750.0 q^{52} -33120.3 q^{53} -2260.38 q^{54} +29847.5 q^{55} -6049.55 q^{56} +29345.5 q^{58} -9236.15 q^{59} +1215.11 q^{60} +10296.4 q^{61} -4708.23 q^{62} -22840.9 q^{63} +4096.00 q^{64} -64114.1 q^{65} -2137.35 q^{66} -28631.3 q^{67} +33994.8 q^{68} +4483.16 q^{69} +24626.2 q^{70} +68701.6 q^{71} +15465.0 q^{72} +36251.3 q^{73} +7041.85 q^{74} -1302.62 q^{75} -43316.9 q^{77} +4591.16 q^{78} -21981.5 q^{79} -16673.8 q^{80} +58059.7 q^{81} +9801.34 q^{82} -102618. q^{83} -1763.46 q^{84} -138384. q^{85} -8501.20 q^{86} +8554.29 q^{87} +29328.8 q^{88} -28261.5 q^{89} -62954.0 q^{90} +93047.3 q^{91} -61517.9 q^{92} -1372.46 q^{93} -50931.8 q^{94} +1193.99 q^{96} -80776.2 q^{97} +31488.6 q^{98} +110735. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} - 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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