LMFDB - Embedded newform 722.6.a.r.1.13

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			1.13
Root			$-23.5180$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +25.3974 q^{3} +16.0000 q^{4} -93.4251 q^{5} +101.589 q^{6} -182.176 q^{7} +64.0000 q^{8} +402.026 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +25.3974 q^{3} +16.0000 q^{4} -93.4251 q^{5} +101.589 q^{6} -182.176 q^{7} +64.0000 q^{8} +402.026 q^{9} -373.700 q^{10} +397.869 q^{11} +406.358 q^{12} -690.727 q^{13} -728.706 q^{14} -2372.75 q^{15} +256.000 q^{16} +1232.56 q^{17} +1608.11 q^{18} -1494.80 q^{20} -4626.80 q^{21} +1591.48 q^{22} +281.981 q^{23} +1625.43 q^{24} +5603.25 q^{25} -2762.91 q^{26} +4038.85 q^{27} -2914.82 q^{28} +4339.79 q^{29} -9491.01 q^{30} +2687.01 q^{31} +1024.00 q^{32} +10104.8 q^{33} +4930.26 q^{34} +17019.9 q^{35} +6432.42 q^{36} -3855.72 q^{37} -17542.7 q^{39} -5979.21 q^{40} +19559.5 q^{41} -18507.2 q^{42} -371.078 q^{43} +6365.91 q^{44} -37559.4 q^{45} +1127.92 q^{46} +13535.3 q^{47} +6501.73 q^{48} +16381.3 q^{49} +22413.0 q^{50} +31303.9 q^{51} -11051.6 q^{52} +5625.60 q^{53} +16155.4 q^{54} -37171.0 q^{55} -11659.3 q^{56} +17359.2 q^{58} -30093.5 q^{59} -37964.0 q^{60} +2211.30 q^{61} +10748.0 q^{62} -73239.8 q^{63} +4096.00 q^{64} +64531.3 q^{65} +40419.3 q^{66} +266.031 q^{67} +19721.0 q^{68} +7161.58 q^{69} +68079.4 q^{70} +22291.0 q^{71} +25729.7 q^{72} +55692.4 q^{73} -15422.9 q^{74} +142308. q^{75} -72482.4 q^{77} -70170.6 q^{78} -56558.7 q^{79} -23916.8 q^{80} +4883.80 q^{81} +78238.0 q^{82} +85155.3 q^{83} -74028.9 q^{84} -115152. q^{85} -1484.31 q^{86} +110219. q^{87} +25463.6 q^{88} +21699.8 q^{89} -150237. q^{90} +125834. q^{91} +4511.70 q^{92} +68243.0 q^{93} +54141.2 q^{94} +26006.9 q^{96} +111559. q^{97} +65525.1 q^{98} +159954. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	25.3974	1.62924	0.814621	−	0.579994i	$-0.196945\pi$
$3$	25.3974	1.62924	0.814621	+	0.579994i	$0.196945\pi$
$4$	16.0000	0.500000
$5$	−93.4251	−1.67124	−0.835620	−	0.549309i	$-0.814891\pi$
$5$	−93.4251	−1.67124	−0.835620	+	0.549309i	$0.814891\pi$
$6$	101.589	1.15205
$7$	−182.176	−1.40523	−0.702615	−	0.711571i	$-0.747984\pi$
$7$	−182.176	−1.40523	−0.702615	+	0.711571i	$0.747984\pi$
$8$	64.0000	0.353553
$9$	402.026	1.65443
$10$	−373.700	−1.18174
$11$	397.869	0.991422	0.495711	−	0.868488i	$-0.334908\pi$
$11$	397.869	0.991422	0.495711	+	0.868488i	$0.334908\pi$
$12$	406.358	0.814621
$13$	−690.727	−1.13357	−0.566785	−	0.823866i	$-0.691813\pi$
$13$	−690.727	−1.13357	−0.566785	+	0.823866i	$0.691813\pi$
$14$	−728.706	−0.993647
$15$	−2372.75	−2.72285
$16$	256.000	0.250000
$17$	1232.56	1.03440	0.517198	−	0.855866i	$-0.326975\pi$
$17$	1232.56	1.03440	0.517198	+	0.855866i	$0.326975\pi$
$18$	1608.11	1.16986
$19$	0	0
$19$	0	0
$20$	−1494.80	−0.835620
$21$	−4626.80	−2.28946
$22$	1591.48	0.701041
$23$	281.981	0.111148	0.0555739	−	0.998455i	$-0.482301\pi$
$23$	281.981	0.111148	0.0555739	+	0.998455i	$0.482301\pi$
$24$	1625.43	0.576024
$25$	5603.25	1.79304
$26$	−2762.91	−0.801555
$27$	4038.85	1.06622
$28$	−2914.82	−0.702615
$29$	4339.79	0.958240	0.479120	−	0.877750i	$-0.340956\pi$
$29$	4339.79	0.958240	0.479120	+	0.877750i	$0.340956\pi$
$30$	−9491.01	−1.92535
$31$	2687.01	0.502187	0.251093	−	0.967963i	$-0.419210\pi$
$31$	2687.01	0.502187	0.251093	+	0.967963i	$0.419210\pi$
$32$	1024.00	0.176777
$33$	10104.8	1.61527
$34$	4930.26	0.731429
$35$	17019.9	2.34847
$36$	6432.42	0.827215
$37$	−3855.72	−0.463021	−0.231511	−	0.972832i	$-0.574367\pi$
$37$	−3855.72	−0.463021	−0.231511	+	0.972832i	$0.574367\pi$
$38$	0	0
$39$	−17542.7	−1.84686
$40$	−5979.21	−0.590872
$41$	19559.5	1.81718	0.908590	−	0.417688i	$-0.137160\pi$
$41$	19559.5	1.81718	0.908590	+	0.417688i	$0.137160\pi$
$42$	−18507.2	−1.61889
$43$	−371.078	−0.0306051	−0.0153026	−	0.999883i	$-0.504871\pi$
$43$	−371.078	−0.0306051	−0.0153026	+	0.999883i	$0.504871\pi$
$44$	6365.91	0.495711
$45$	−37559.4	−2.76495
$46$	1127.92	0.0785933
$47$	13535.3	0.893765	0.446883	−	0.894593i	$-0.352534\pi$
$47$	13535.3	0.893765	0.446883	+	0.894593i	$0.352534\pi$
$48$	6501.73	0.407311
$49$	16381.3	0.974670
$50$	22413.0	1.26787
$51$	31303.9	1.68528
$52$	−11051.6	−0.566785
$53$	5625.60	0.275093	0.137546	−	0.990495i	$-0.456078\pi$
$53$	5625.60	0.275093	0.137546	+	0.990495i	$0.456078\pi$
$54$	16155.4	0.753934
$55$	−37171.0	−1.65690
$56$	−11659.3	−0.496824
$57$	0	0
$58$	17359.2	0.677578
$59$	−30093.5	−1.12549	−0.562746	−	0.826630i	$-0.690255\pi$
$59$	−30093.5	−1.12549	−0.562746	+	0.826630i	$0.690255\pi$
$60$	−37964.0	−1.36143
$61$	2211.30	0.0760893	0.0380446	−	0.999276i	$-0.487887\pi$
$61$	2211.30	0.0760893	0.0380446	+	0.999276i	$0.487887\pi$
$62$	10748.0	0.355100
$63$	−73239.8	−2.32485
$64$	4096.00	0.125000
$65$	64531.3	1.89447
$66$	40419.3	1.14217
$67$	266.031	0.00724011	0.00362006	−	0.999993i	$-0.498848\pi$
$67$	266.031	0.00724011	0.00362006	+	0.999993i	$0.498848\pi$
$68$	19721.0	0.517198
$69$	7161.58	0.181087
$70$	68079.4	1.66062
$71$	22291.0	0.524788	0.262394	−	0.964961i	$-0.415488\pi$
$71$	22291.0	0.524788	0.262394	+	0.964961i	$0.415488\pi$
$72$	25729.7	0.584929
$73$	55692.4	1.22317	0.611587	−	0.791177i	$-0.290531\pi$
$73$	55692.4	1.22317	0.611587	+	0.791177i	$0.290531\pi$
$74$	−15422.9	−0.327405
$75$	142308.	2.92130
$76$	0	0
$77$	−72482.4	−1.39318
$78$	−70170.6	−1.30593
$79$	−56558.7	−1.01960	−0.509802	−	0.860292i	$-0.670281\pi$
$79$	−56558.7	−1.01960	−0.509802	+	0.860292i	$0.670281\pi$
$80$	−23916.8	−0.417810
$81$	4883.80	0.0827076
$82$	78238.0	1.28494
$83$	85155.3	1.35680	0.678401	−	0.734692i	$-0.262673\pi$
$83$	85155.3	1.35680	0.678401	+	0.734692i	$0.262673\pi$
$84$	−74028.9	−1.14473
$85$	−115152.	−1.72872
$86$	−1484.31	−0.0216411
$87$	110219.	1.56120
$88$	25463.6	0.350521
$89$	21699.8	0.290390	0.145195	−	0.989403i	$-0.453619\pi$
$89$	21699.8	0.290390	0.145195	+	0.989403i	$0.453619\pi$
$90$	−150237.	−1.95511
$91$	125834.	1.59293
$92$	4511.70	0.0555739
$93$	68243.0	0.818183
$94$	54141.2	0.631988
$95$	0	0
$96$	26006.9	0.288012
$97$	111559.	1.20386	0.601928	−	0.798550i	$-0.294399\pi$
$97$	111559.	1.20386	0.601928	+	0.798550i	$0.294399\pi$
$98$	65525.1	0.689196
$99$	159954.	1.64024
$100$	89652.0	0.896520
$101$	153551.	1.49779	0.748893	−	0.662691i	$-0.230586\pi$
$101$	153551.	1.49779	0.748893	+	0.662691i	$0.230586\pi$
$102$	125216.	1.19167
$103$	−18009.1	−0.167262	−0.0836312	−	0.996497i	$-0.526652\pi$
$103$	−18009.1	−0.167262	−0.0836312	+	0.996497i	$0.526652\pi$
$104$	−44206.5	−0.400777
$105$	432260.	3.82623
$106$	22502.4	0.194520
$107$	38243.9	0.322926	0.161463	−	0.986879i	$-0.448379\pi$
$107$	38243.9	0.322926	0.161463	+	0.986879i	$0.448379\pi$
$108$	64621.6	0.533112
$109$	152059.	1.22587	0.612937	−	0.790132i	$-0.289988\pi$
$109$	152059.	1.22587	0.612937	+	0.790132i	$0.289988\pi$
$110$	−148684.	−1.17161
$111$	−97925.1	−0.754374
$112$	−46637.2	−0.351307
$113$	235307.	1.73356	0.866782	−	0.498688i	$-0.166185\pi$
$113$	235307.	1.73356	0.866782	+	0.498688i	$0.166185\pi$
$114$	0	0
$115$	−26344.1	−0.185754
$116$	69436.7	0.479120
$117$	−277691.	−1.87541
$118$	−120374.	−0.795843
$119$	−224544.	−1.45356
$120$	−151856.	−0.962674
$121$	−2751.16	−0.0170825
$122$	8845.21	0.0538032
$123$	496760.	2.96063
$124$	42992.2	0.251093
$125$	−231531.	−1.32536
$126$	−292959.	−1.64392
$127$	−104851.	−0.576852	−0.288426	−	0.957502i	$-0.593132\pi$
$127$	−104851.	−0.576852	−0.288426	+	0.957502i	$0.593132\pi$
$128$	16384.0	0.0883883
$129$	−9424.40	−0.0498631
$130$	258125.	1.33959
$131$	−272068.	−1.38516	−0.692579	−	0.721342i	$-0.743526\pi$
$131$	−272068.	−1.38516	−0.692579	+	0.721342i	$0.743526\pi$
$132$	161677.	0.807633
$133$	0	0
$134$	1064.12	0.00511953
$135$	−377330.	−1.78192
$136$	78884.1	0.365715
$137$	82901.9	0.377366	0.188683	−	0.982038i	$-0.439578\pi$
$137$	82901.9	0.377366	0.188683	+	0.982038i	$0.439578\pi$
$138$	28646.3	0.128047
$139$	−90062.4	−0.395373	−0.197686	−	0.980265i	$-0.563343\pi$
$139$	−90062.4	−0.395373	−0.197686	+	0.980265i	$0.563343\pi$
$140$	272318.	1.17424
$141$	343761.	1.45616
$142$	89164.0	0.371081
$143$	−274819.	−1.12385
$144$	102919.	0.413607
$145$	−405446.	−1.60145
$146$	222769.	0.864915
$147$	416041.	1.58797
$148$	−61691.5	−0.231511
$149$	75850.8	0.279895	0.139947	−	0.990159i	$-0.455307\pi$
$149$	75850.8	0.279895	0.139947	+	0.990159i	$0.455307\pi$
$150$	569231.	2.06567
$151$	−321781.	−1.14847	−0.574233	−	0.818692i	$-0.694700\pi$
$151$	−321781.	−1.14847	−0.574233	+	0.818692i	$0.694700\pi$
$152$	0	0
$153$	495523.	1.71134
$154$	−289930.	−0.985124
$155$	−251034.	−0.839274
$156$	−280682.	−0.923430
$157$	−166748.	−0.539899	−0.269949	−	0.962875i	$-0.587007\pi$
$157$	−166748.	−0.539899	−0.269949	+	0.962875i	$0.587007\pi$
$158$	−226235.	−0.720969
$159$	142875.	0.448192
$160$	−95667.3	−0.295436
$161$	−51370.3	−0.156188
$162$	19535.2	0.0584831
$163$	−610716.	−1.80041	−0.900203	−	0.435471i	$-0.856582\pi$
$163$	−610716.	−1.80041	−0.900203	+	0.435471i	$0.856582\pi$
$164$	312952.	0.908590
$165$	−944045.	−2.69950
$166$	340621.	0.959404
$167$	−30693.4	−0.0851635	−0.0425817	−	0.999093i	$-0.513558\pi$
$167$	−30693.4	−0.0851635	−0.0425817	+	0.999093i	$0.513558\pi$
$168$	−296115.	−0.809446
$169$	105811.	0.284980
$170$	−460610.	−1.22239
$171$	0	0
$172$	−5937.25	−0.0153026
$173$	−9606.39	−0.0244031	−0.0122016	−	0.999926i	$-0.503884\pi$
$173$	−9606.39	−0.0244031	−0.0122016	+	0.999926i	$0.503884\pi$
$174$	440877.	1.10394
$175$	−1.02078e6	−2.51963
$176$	101854.	0.247855
$177$	−764296.	−1.83370
$178$	86799.4	0.205337
$179$	520788.	1.21487	0.607433	−	0.794371i	$-0.292199\pi$
$179$	520788.	1.21487	0.607433	+	0.794371i	$0.292199\pi$
$180$	−600950.	−1.38247
$181$	258616.	0.586757	0.293379	−	0.955996i	$-0.405220\pi$
$181$	258616.	0.586757	0.293379	+	0.955996i	$0.405220\pi$
$182$	503337.	1.12637
$183$	56161.2	0.123968
$184$	18046.8	0.0392966
$185$	360221.	0.773819
$186$	272972.	0.578543
$187$	490399.	1.02552
$188$	216565.	0.446883
$189$	−735784.	−1.49829
$190$	0	0
$191$	423915.	0.840805	0.420402	−	0.907338i	$-0.361889\pi$
$191$	423915.	0.840805	0.420402	+	0.907338i	$0.361889\pi$
$192$	104028.	0.203655
$193$	−510755.	−0.987004	−0.493502	−	0.869745i	$-0.664283\pi$
$193$	−510755.	−0.987004	−0.493502	+	0.869745i	$0.664283\pi$
$194$	446235.	0.851255
$195$	1.63892e6	3.08654
$196$	262100.	0.487335
$197$	732799.	1.34530	0.672650	−	0.739961i	$-0.265156\pi$
$197$	732799.	1.34530	0.672650	+	0.739961i	$0.265156\pi$
$198$	639816.	1.15982
$199$	−367160.	−0.657238	−0.328619	−	0.944463i	$-0.606583\pi$
$199$	−367160.	−0.657238	−0.328619	+	0.944463i	$0.606583\pi$
$200$	358608.	0.633936
$201$	6756.49	0.0117959
$202$	614205.	1.05909
$203$	−790608.	−1.34655
$204$	500862.	0.842641
$205$	−1.82735e6	−3.03694
$206$	−72036.3	−0.118272
$207$	113364.	0.183886
$208$	−176826.	−0.283392
$209$	0	0
$210$	1.72904e6	2.70556
$211$	−980416.	−1.51602	−0.758009	−	0.652245i	$-0.773828\pi$
$211$	−980416.	−1.51602	−0.758009	+	0.652245i	$0.773828\pi$
$212$	90009.5	0.137546
$213$	566133.	0.855006
$214$	152976.	0.228343
$215$	34668.0	0.0511485
$216$	258487.	0.376967
$217$	−489510.	−0.705687
$218$	608236.	0.866824
$219$	1.41444e6	1.99285
$220$	−594735.	−0.828452
$221$	−851366.	−1.17256
$222$	−391700.	−0.533423
$223$	−549125.	−0.739450	−0.369725	−	0.929141i	$-0.620548\pi$
$223$	−549125.	−0.739450	−0.369725	+	0.929141i	$0.620548\pi$
$224$	−186549.	−0.248412
$225$	2.25265e6	2.96646
$226$	941230.	1.22581
$227$	497072.	0.640257	0.320129	−	0.947374i	$-0.396274\pi$
$227$	497072.	0.640257	0.320129	+	0.947374i	$0.396274\pi$
$228$	0	0
$229$	352557.	0.444263	0.222132	−	0.975017i	$-0.428699\pi$
$229$	352557.	0.444263	0.222132	+	0.975017i	$0.428699\pi$
$230$	−105376.	−0.131348
$231$	−1.84086e6	−2.26982
$232$	277747.	0.338789
$233$	−823068.	−0.993221	−0.496611	−	0.867973i	$-0.665422\pi$
$233$	−823068.	−0.993221	−0.496611	+	0.867973i	$0.665422\pi$
$234$	−1.11076e6	−1.32612
$235$	−1.26454e6	−1.49370
$236$	−481496.	−0.562746
$237$	−1.43644e6	−1.66118
$238$	−898177.	−1.02783
$239$	1.16861e6	1.32335	0.661673	−	0.749792i	$-0.269847\pi$
$239$	1.16861e6	1.32335	0.661673	+	0.749792i	$0.269847\pi$
$240$	−607425.	−0.680713
$241$	−178085.	−0.197508	−0.0987539	−	0.995112i	$-0.531486\pi$
$241$	−178085.	−0.197508	−0.0987539	+	0.995112i	$0.531486\pi$
$242$	−11004.6	−0.0120792
$243$	−857405.	−0.931473
$244$	35380.8	0.0380446
$245$	−1.53042e6	−1.62891
$246$	1.98704e6	2.09348
$247$	0	0
$248$	171969.	0.177550
$249$	2.16272e6	2.21056
$250$	−926124.	−0.937171
$251$	−246738.	−0.247202	−0.123601	−	0.992332i	$-0.539444\pi$
$251$	−246738.	−0.247202	−0.123601	+	0.992332i	$0.539444\pi$
$252$	−1.17184e6	−1.16243
$253$	112192.	0.110194
$254$	−419405.	−0.407896
$255$	−2.92457e6	−2.81651
$256$	65536.0	0.0625000
$257$	−1.09643e6	−1.03549	−0.517746	−	0.855534i	$-0.673229\pi$
$257$	−1.09643e6	−1.03549	−0.517746	+	0.855534i	$0.673229\pi$
$258$	−37697.6	−0.0352586
$259$	702421.	0.650651
$260$	1.03250e6	0.947233
$261$	1.74471e6	1.58534
$262$	−1.08827e6	−0.979455
$263$	−751938.	−0.670336	−0.335168	−	0.942158i	$-0.608793\pi$
$263$	−751938.	−0.670336	−0.335168	+	0.942158i	$0.608793\pi$
$264$	646709.	0.571083
$265$	−525572.	−0.459745
$266$	0	0
$267$	551119.	0.473115
$268$	4256.50	0.00362006
$269$	1.61173e6	1.35804	0.679020	−	0.734119i	$-0.262405\pi$
$269$	1.61173e6	1.35804	0.679020	+	0.734119i	$0.262405\pi$
$270$	−1.50932e6	−1.26000
$271$	−1.56856e6	−1.29742	−0.648708	−	0.761038i	$-0.724690\pi$
$271$	−1.56856e6	−1.29742	−0.648708	+	0.761038i	$0.724690\pi$
$272$	315536.	0.258599
$273$	3.19586e6	2.59526
$274$	331607.	0.266838
$275$	2.22936e6	1.77766
$276$	114585.	0.0905433
$277$	183350.	0.143576	0.0717878	−	0.997420i	$-0.477130\pi$
$277$	183350.	0.143576	0.0717878	+	0.997420i	$0.477130\pi$
$278$	−360250.	−0.279571
$279$	1.08025e6	0.830832
$280$	1.08927e6	0.830311
$281$	2.30870e6	1.74422	0.872110	−	0.489310i	$-0.162751\pi$
$281$	2.30870e6	1.74422	0.872110	+	0.489310i	$0.162751\pi$
$282$	1.37504e6	1.02966
$283$	2.32342e6	1.72449	0.862245	−	0.506491i	$-0.169058\pi$
$283$	2.32342e6	1.72449	0.862245	+	0.506491i	$0.169058\pi$
$284$	356656.	0.262394
$285$	0	0
$286$	−1.09928e6	−0.794679
$287$	−3.56328e6	−2.55356
$288$	411675.	0.292465
$289$	99357.0	0.0699768
$290$	−1.62178e6	−1.13239
$291$	2.83330e6	1.96137
$292$	891078.	0.611587
$293$	1.03067e6	0.701378	0.350689	−	0.936492i	$-0.385947\pi$
$293$	1.03067e6	0.701378	0.350689	+	0.936492i	$0.385947\pi$
$294$	1.66416e6	1.12287
$295$	2.81149e6	1.88097
$296$	−246766.	−0.163703
$297$	1.60693e6	1.05708
$298$	303403.	0.197915
$299$	−194772.	−0.125994
$300$	2.27693e6	1.46065
$301$	67601.7	0.0430072
$302$	−1.28712e6	−0.812088
$303$	3.89980e6	2.44026
$304$	0	0
$305$	−206591.	−0.127163
$306$	1.98209e6	1.21010
$307$	1.68234e6	1.01875	0.509374	−	0.860545i	$-0.329877\pi$
$307$	1.68234e6	1.01875	0.509374	+	0.860545i	$0.329877\pi$
$308$	−1.15972e6	−0.696588
$309$	−457383.	−0.272511
$310$	−1.00414e6	−0.593456
$311$	−693660.	−0.406673	−0.203337	−	0.979109i	$-0.565179\pi$
$311$	−693660.	−0.406673	−0.203337	+	0.979109i	$0.565179\pi$
$312$	−1.12273e6	−0.652963
$313$	−1.52403e6	−0.879290	−0.439645	−	0.898172i	$-0.644896\pi$
$313$	−1.52403e6	−0.879290	−0.439645	+	0.898172i	$0.644896\pi$
$314$	−666993.	−0.381766
$315$	6.84243e6	3.88539
$316$	−904939.	−0.509802
$317$	1.49806e6	0.837303	0.418651	−	0.908147i	$-0.362503\pi$
$317$	1.49806e6	0.837303	0.418651	+	0.908147i	$0.362503\pi$
$318$	571501.	0.316920
$319$	1.72667e6	0.950020
$320$	−382669.	−0.208905
$321$	971295.	0.526124
$322$	−205481.	−0.110442
$323$	0	0
$324$	78140.8	0.0413538
$325$	−3.87032e6	−2.03254
$326$	−2.44286e6	−1.27308
$327$	3.86190e6	1.99725
$328$	1.25181e6	0.642470
$329$	−2.46581e6	−1.25595
$330$	−3.77618e6	−1.90883
$331$	511224.	0.256473	0.128236	−	0.991744i	$-0.459068\pi$
$331$	511224.	0.256473	0.128236	+	0.991744i	$0.459068\pi$
$332$	1.36249e6	0.678401
$333$	−1.55010e6	−0.766036
$334$	−122773.	−0.0602197
$335$	−24854.0	−0.0121000
$336$	−1.18446e6	−0.572365
$337$	−4.14406e6	−1.98770	−0.993851	−	0.110722i	$-0.964684\pi$
$337$	−4.14406e6	−1.98770	−0.993851	+	0.110722i	$0.964684\pi$
$338$	423245.	0.201511
$339$	5.97619e6	2.82439
$340$	−1.84244e6	−0.864362
$341$	1.06908e6	0.497879
$342$	0	0
$343$	77557.5	0.0355950
$344$	−23749.0	−0.0108205
$345$	−669071.	−0.302639
$346$	−38425.6	−0.0172556
$347$	−3.23795e6	−1.44360	−0.721799	−	0.692102i	$-0.756685\pi$
$347$	−3.23795e6	−1.44360	−0.721799	+	0.692102i	$0.756685\pi$
$348$	1.76351e6	0.780602
$349$	−2.22607e6	−0.978306	−0.489153	−	0.872198i	$-0.662694\pi$
$349$	−2.22607e6	−0.978306	−0.489153	+	0.872198i	$0.662694\pi$
$350$	−4.08312e6	−1.78165
$351$	−2.78975e6	−1.20864
$352$	407418.	0.175260
$353$	−1.06483e6	−0.454824	−0.227412	−	0.973799i	$-0.573026\pi$
$353$	−1.06483e6	−0.454824	−0.227412	+	0.973799i	$0.573026\pi$
$354$	−3.05718e6	−1.29662
$355$	−2.08254e6	−0.877046
$356$	347197.	0.145195
$357$	−5.70283e6	−2.36821
$358$	2.08315e6	0.859040
$359$	789870.	0.323459	0.161730	−	0.986835i	$-0.448293\pi$
$359$	789870.	0.323459	0.161730	+	0.986835i	$0.448293\pi$
$360$	−2.40380e6	−0.977557
$361$	0	0
$362$	1.03446e6	0.414900
$363$	−69872.3	−0.0278316
$364$	2.01335e6	0.796463
$365$	−5.20306e6	−2.04422
$366$	224645.	0.0876585
$367$	3.60332e6	1.39649	0.698245	−	0.715859i	$-0.253965\pi$
$367$	3.60332e6	1.39649	0.698245	+	0.715859i	$0.253965\pi$
$368$	72187.2	0.0277869
$369$	7.86343e6	3.00640
$370$	1.44088e6	0.547173
$371$	−1.02485e6	−0.386568
$372$	1.09189e6	0.409092
$373$	1.72351e6	0.641418	0.320709	−	0.947178i	$-0.396079\pi$
$373$	1.72351e6	0.641418	0.320709	+	0.947178i	$0.396079\pi$
$374$	1.96160e6	0.725155
$375$	−5.88028e6	−2.15933
$376$	866260.	0.315994
$377$	−2.99761e6	−1.08623
$378$	−2.94314e6	−1.05945
$379$	1.34133e6	0.479666	0.239833	−	0.970814i	$-0.422907\pi$
$379$	1.34133e6	0.479666	0.239833	+	0.970814i	$0.422907\pi$
$380$	0	0
$381$	−2.66295e6	−0.939832
$382$	1.69566e6	0.594539
$383$	−1.05550e6	−0.367672	−0.183836	−	0.982957i	$-0.558852\pi$
$383$	−1.05550e6	−0.367672	−0.183836	+	0.982957i	$0.558852\pi$
$384$	416111.	0.144006
$385$	6.77168e6	2.32833
$386$	−2.04302e6	−0.697917
$387$	−149183.	−0.0506340
$388$	1.78494e6	0.601928
$389$	−3.24812e6	−1.08832	−0.544162	−	0.838980i	$-0.683152\pi$
$389$	−3.24812e6	−1.08832	−0.544162	+	0.838980i	$0.683152\pi$
$390$	6.55570e6	2.18252
$391$	347560.	0.114971
$392$	1.04840e6	0.344598
$393$	−6.90982e6	−2.25676
$394$	2.93120e6	0.951271
$395$	5.28400e6	1.70400
$396$	2.55926e6	0.820119
$397$	6.05532e6	1.92824	0.964119	−	0.265470i	$-0.0855272\pi$
$397$	6.05532e6	1.92824	0.964119	+	0.265470i	$0.0855272\pi$
$398$	−1.46864e6	−0.464737
$399$	0	0
$400$	1.43443e6	0.448260
$401$	758785.	0.235645	0.117822	−	0.993035i	$-0.462409\pi$
$401$	758785.	0.235645	0.117822	+	0.993035i	$0.462409\pi$
$402$	27026.0	0.00834096
$403$	−1.85599e6	−0.569263
$404$	2.45682e6	0.748893
$405$	−456270.	−0.138224
$406$	−3.16243e6	−0.952152
$407$	−1.53407e6	−0.459049
$408$	2.00345e6	0.595837
$409$	−2.98096e6	−0.881147	−0.440574	−	0.897717i	$-0.645225\pi$
$409$	−2.98096e6	−0.881147	−0.440574	+	0.897717i	$0.645225\pi$
$410$	−7.30939e6	−2.14744
$411$	2.10549e6	0.614821
$412$	−288145.	−0.0836312
$413$	5.48233e6	1.58158
$414$	453455.	0.130027
$415$	−7.95565e6	−2.26754
$416$	−707305.	−0.200389
$417$	−2.28735e6	−0.644158
$418$	0	0
$419$	−4.92084e6	−1.36932	−0.684658	−	0.728864i	$-0.740049\pi$
$419$	−4.92084e6	−1.36932	−0.684658	+	0.728864i	$0.740049\pi$
$420$	6.91615e6	1.91312
$421$	697907.	0.191908	0.0959539	−	0.995386i	$-0.469410\pi$
$421$	697907.	0.191908	0.0959539	+	0.995386i	$0.469410\pi$
$422$	−3.92166e6	−1.07199
$423$	5.44155e6	1.47867
$424$	360038.	0.0972599
$425$	6.90637e6	1.85472
$426$	2.26453e6	0.604581
$427$	−402847.	−0.106923
$428$	611903.	0.161463
$429$	−6.97968e6	−1.83102
$430$	138672.	0.0361674
$431$	3.45652e6	0.896285	0.448142	−	0.893962i	$-0.352086\pi$
$431$	3.45652e6	0.896285	0.448142	+	0.893962i	$0.352086\pi$
$432$	1.03395e6	0.266556
$433$	−5.65064e6	−1.44836	−0.724182	−	0.689609i	$-0.757782\pi$
$433$	−5.65064e6	−1.44836	−0.724182	+	0.689609i	$0.757782\pi$
$434$	−1.95804e6	−0.498996
$435$	−1.02973e7	−2.60915
$436$	2.43294e6	0.612937
$437$	0	0
$438$	5.65776e6	1.40916
$439$	−7.26821e6	−1.79997	−0.899987	−	0.435918i	$-0.856424\pi$
$439$	−7.26821e6	−1.79997	−0.899987	+	0.435918i	$0.856424\pi$
$440$	−2.37894e6	−0.585804
$441$	6.58570e6	1.61252
$442$	−3.40546e6	−0.829126
$443$	−1.81297e6	−0.438915	−0.219458	−	0.975622i	$-0.570429\pi$
$443$	−1.81297e6	−0.438915	−0.219458	+	0.975622i	$0.570429\pi$
$444$	−1.56680e6	−0.377187
$445$	−2.02731e6	−0.485311
$446$	−2.19650e6	−0.522870
$447$	1.92641e6	0.456016
$448$	−746195.	−0.175654
$449$	2.76069e6	0.646251	0.323126	−	0.946356i	$-0.395266\pi$
$449$	2.76069e6	0.646251	0.323126	+	0.946356i	$0.395266\pi$
$450$	9.01062e6	2.09760
$451$	7.78212e6	1.80159
$452$	3.76492e6	0.866782
$453$	−8.17239e6	−1.87113
$454$	1.98829e6	0.452730
$455$	−1.17561e7	−2.66216
$456$	0	0
$457$	7.69236e6	1.72294	0.861468	−	0.507812i	$-0.169546\pi$
$457$	7.69236e6	1.72294	0.861468	+	0.507812i	$0.169546\pi$
$458$	1.41023e6	0.314142
$459$	4.97814e6	1.10290
$460$	−421506.	−0.0928772
$461$	−5.81116e6	−1.27353	−0.636766	−	0.771057i	$-0.719728\pi$
$461$	−5.81116e6	−1.27353	−0.636766	+	0.771057i	$0.719728\pi$
$462$	−7.36345e6	−1.60500
$463$	4.05311e6	0.878691	0.439346	−	0.898318i	$-0.355210\pi$
$463$	4.05311e6	0.878691	0.439346	+	0.898318i	$0.355210\pi$
$464$	1.11099e6	0.239560
$465$	−6.37561e6	−1.36738
$466$	−3.29227e6	−0.702314
$467$	6.05625e6	1.28503	0.642513	−	0.766275i	$-0.277892\pi$
$467$	6.05625e6	1.28503	0.642513	+	0.766275i	$0.277892\pi$
$468$	−4.44305e6	−0.937706
$469$	−48464.6	−0.0101740
$470$	−5.05815e6	−1.05620
$471$	−4.23497e6	−0.879625
$472$	−1.92598e6	−0.397922
$473$	−147640.	−0.0303426
$474$	−5.74577e6	−1.17463
$475$	0	0
$476$	−3.59271e6	−0.726782
$477$	2.26164e6	0.455121
$478$	4.67443e6	0.935747
$479$	3.99007e6	0.794588	0.397294	−	0.917691i	$-0.369949\pi$
$479$	3.99007e6	0.794588	0.397294	+	0.917691i	$0.369949\pi$
$480$	−2.42970e6	−0.481337
$481$	2.66325e6	0.524867
$482$	−712339.	−0.139659
$483$	−1.30467e6	−0.254468
$484$	−44018.6	−0.00854127
$485$	−1.04224e7	−2.01193
$486$	−3.42962e6	−0.658651
$487$	7.57377e6	1.44707	0.723535	−	0.690287i	$-0.242516\pi$
$487$	7.57377e6	1.44707	0.723535	+	0.690287i	$0.242516\pi$
$488$	141523.	0.0269016
$489$	−1.55106e7	−2.93330
$490$	−6.12169e6	−1.15181
$491$	−1.52699e6	−0.285845	−0.142923	−	0.989734i	$-0.545650\pi$
$491$	−1.52699e6	−0.285845	−0.142923	+	0.989734i	$0.545650\pi$
$492$	7.94816e6	1.48031
$493$	5.34907e6	0.991200
$494$	0	0
$495$	−1.49437e7	−2.74123
$496$	687875.	0.125547
$497$	−4.06089e6	−0.737447
$498$	8.65089e6	1.56310
$499$	1.46195e6	0.262833	0.131417	−	0.991327i	$-0.458047\pi$
$499$	1.46195e6	0.262833	0.131417	+	0.991327i	$0.458047\pi$
$500$	−3.70449e6	−0.662680
$501$	−779531.	−0.138752
$502$	−986952.	−0.174798
$503$	7.46220e6	1.31506	0.657532	−	0.753427i	$-0.271600\pi$
$503$	7.46220e6	1.31506	0.657532	+	0.753427i	$0.271600\pi$
$504$	−4.68734e6	−0.821960
$505$	−1.43455e7	−2.50316
$506$	448766.	0.0779191
$507$	2.68732e6	0.464302
$508$	−1.67762e6	−0.288426
$509$	−4.20401e6	−0.719232	−0.359616	−	0.933100i	$-0.617092\pi$
$509$	−4.20401e6	−0.719232	−0.359616	+	0.933100i	$0.617092\pi$
$510$	−1.16983e7	−1.99157
$511$	−1.01458e7	−1.71884
$512$	262144.	0.0441942
$513$	0	0
$514$	−4.38571e6	−0.732203
$515$	1.68250e6	0.279536
$516$	−150790.	−0.0249316
$517$	5.38528e6	0.886099
$518$	2.80968e6	0.460080
$519$	−243977.	−0.0397586
$520$	4.13000e6	0.669795
$521$	6.07744e6	0.980904	0.490452	−	0.871468i	$-0.336832\pi$
$521$	6.07744e6	0.980904	0.490452	+	0.871468i	$0.336832\pi$
$522$	6.97885e6	1.12100
$523$	4.82157e6	0.770786	0.385393	−	0.922752i	$-0.374066\pi$
$523$	4.82157e6	0.770786	0.385393	+	0.922752i	$0.374066\pi$
$524$	−4.35309e6	−0.692579
$525$	−2.59251e7	−4.10509
$526$	−3.00775e6	−0.473999
$527$	3.31191e6	0.519460
$528$	2.58684e6	0.403817
$529$	−6.35683e6	−0.987646
$530$	−2.10229e6	−0.325089
$531$	−1.20984e7	−1.86205
$532$	0	0
$533$	−1.35103e7	−2.05990
$534$	2.20448e6	0.334543
$535$	−3.57294e6	−0.539686
$536$	17026.0	0.00255977
$537$	1.32266e7	1.97931
$538$	6.44694e6	0.960280
$539$	6.51760e6	0.966309
$540$	−6.03728e6	−0.890958
$541$	1.08686e7	1.59654	0.798270	−	0.602300i	$-0.205749\pi$
$541$	1.08686e7	1.59654	0.798270	+	0.602300i	$0.205749\pi$
$542$	−6.27426e6	−0.917411
$543$	6.56816e6	0.955970
$544$	1.26215e6	0.182857
$545$	−1.42061e7	−2.04873
$546$	1.27834e7	1.83513
$547$	4.06366e6	0.580696	0.290348	−	0.956921i	$-0.406229\pi$
$547$	4.06366e6	0.580696	0.290348	+	0.956921i	$0.406229\pi$
$548$	1.32643e6	0.188683
$549$	889002.	0.125884
$550$	8.91744e6	1.25700
$551$	0	0
$552$	458341.	0.0640237
$553$	1.03037e7	1.43278
$554$	733398.	0.101523
$555$	9.14866e6	1.26074
$556$	−1.44100e6	−0.197686
$557$	1.03390e7	1.41202	0.706008	−	0.708204i	$-0.250494\pi$
$557$	1.03390e7	1.41202	0.706008	+	0.708204i	$0.250494\pi$
$558$	4.32100e6	0.587487
$559$	256314.	0.0346930
$560$	4.35708e6	0.587119
$561$	1.24548e7	1.67083
$562$	9.23479e6	1.23335
$563$	9.55594e6	1.27058	0.635291	−	0.772273i	$-0.280880\pi$
$563$	9.55594e6	1.27058	0.635291	+	0.772273i	$0.280880\pi$
$564$	5.50018e6	0.728080
$565$	−2.19836e7	−2.89720
$566$	9.29366e6	1.21940
$567$	−889714.	−0.116223
$568$	1.42662e6	0.185540
$569$	5.49168e6	0.711089	0.355545	−	0.934659i	$-0.384295\pi$
$569$	5.49168e6	0.711089	0.355545	+	0.934659i	$0.384295\pi$
$570$	0	0
$571$	7.79290e6	1.00025	0.500125	−	0.865953i	$-0.333287\pi$
$571$	7.79290e6	1.00025	0.500125	+	0.865953i	$0.333287\pi$
$572$	−4.39710e6	−0.561923
$573$	1.07663e7	1.36987
$574$	−1.42531e7	−1.80564
$575$	1.58001e6	0.199292
$576$	1.64670e6	0.206804
$577$	−3.74851e6	−0.468726	−0.234363	−	0.972149i	$-0.575300\pi$
$577$	−3.74851e6	−0.468726	−0.234363	+	0.972149i	$0.575300\pi$
$578$	397428.	0.0494811
$579$	−1.29718e7	−1.60807
$580$	−6.48713e6	−0.800724
$581$	−1.55133e7	−1.90662
$582$	1.13332e7	1.38690
$583$	2.23825e6	0.272733
$584$	3.56431e6	0.432457
$585$	2.59433e7	3.13426
$586$	4.12270e6	0.495949
$587$	−5.71829e6	−0.684968	−0.342484	−	0.939524i	$-0.611268\pi$
$587$	−5.71829e6	−0.684968	−0.342484	+	0.939524i	$0.611268\pi$
$588$	6.65666e6	0.793986
$589$	0	0
$590$	1.12460e7	1.33004
$591$	1.86112e7	2.19182
$592$	−987064.	−0.115755
$593$	4.98996e6	0.582721	0.291360	−	0.956613i	$-0.405892\pi$
$593$	4.98996e6	0.582721	0.291360	+	0.956613i	$0.405892\pi$
$594$	6.42774e6	0.747467
$595$	2.09781e7	2.42925
$596$	1.21361e6	0.139947
$597$	−9.32489e6	−1.07080
$598$	−779088.	−0.0890910
$599$	−1.24302e7	−1.41551	−0.707754	−	0.706459i	$-0.750291\pi$
$599$	−1.24302e7	−1.41551	−0.707754	+	0.706459i	$0.750291\pi$
$600$	9.10770e6	1.03283
$601$	−2.68175e6	−0.302854	−0.151427	−	0.988468i	$-0.548387\pi$
$601$	−2.68175e6	−0.302854	−0.151427	+	0.988468i	$0.548387\pi$
$602$	270407.	0.0304107
$603$	106951.	0.0119783
$604$	−5.14850e6	−0.574233
$605$	257028.	0.0285490
$606$	1.55992e7	1.72552
$607$	−4.21605e6	−0.464444	−0.232222	−	0.972663i	$-0.574600\pi$
$607$	−4.21605e6	−0.464444	−0.232222	+	0.972663i	$0.574600\pi$
$608$	0	0
$609$	−2.00794e7	−2.19385
$610$	−826364.	−0.0899181
$611$	−9.34921e6	−1.01315
$612$	7.92837e6	0.855668
$613$	−8.96978e6	−0.964119	−0.482059	−	0.876138i	$-0.660111\pi$
$613$	−8.96978e6	−0.964119	−0.482059	+	0.876138i	$0.660111\pi$
$614$	6.72934e6	0.720364
$615$	−4.64098e7	−4.94792
$616$	−4.63887e6	−0.492562
$617$	−1.36972e7	−1.44850	−0.724250	−	0.689537i	$-0.757814\pi$
$617$	−1.36972e7	−1.44850	−0.724250	+	0.689537i	$0.757814\pi$
$618$	−1.82953e6	−0.192694
$619$	1.36744e6	0.143444	0.0717219	−	0.997425i	$-0.477151\pi$
$619$	1.36744e6	0.143444	0.0717219	+	0.997425i	$0.477151\pi$
$620$	−4.01655e6	−0.419637
$621$	1.13888e6	0.118508
$622$	−2.77464e6	−0.287562
$623$	−3.95320e6	−0.408064
$624$	−4.49092e6	−0.461715
$625$	4.12064e6	0.421954
$626$	−6.09611e6	−0.621752
$627$	0	0
$628$	−2.66797e6	−0.269949
$629$	−4.75242e6	−0.478948
$630$	2.73697e7	2.74738
$631$	7.38513e6	0.738389	0.369194	−	0.929352i	$-0.379634\pi$
$631$	7.38513e6	0.738389	0.369194	+	0.929352i	$0.379634\pi$
$632$	−3.61976e6	−0.360485
$633$	−2.49000e7	−2.46996
$634$	5.99226e6	0.592062
$635$	9.79574e6	0.964058
$636$	2.28601e6	0.224096
$637$	−1.13150e7	−1.10486
$638$	6.90668e6	0.671765
$639$	8.96157e6	0.868224
$640$	−1.53068e6	−0.147718
$641$	−1.99105e6	−0.191398	−0.0956990	−	0.995410i	$-0.530509\pi$
$641$	−1.99105e6	−0.191398	−0.0956990	+	0.995410i	$0.530509\pi$
$642$	3.88518e6	0.372026
$643$	1.74701e7	1.66636	0.833178	−	0.553004i	$-0.186519\pi$
$643$	1.74701e7	1.66636	0.833178	+	0.553004i	$0.186519\pi$
$644$	−821925.	−0.0780940
$645$	880476.	0.0833332
$646$	0	0
$647$	1.46630e7	1.37709	0.688544	−	0.725195i	$-0.258250\pi$
$647$	1.46630e7	1.37709	0.688544	+	0.725195i	$0.258250\pi$
$648$	312563.	0.0292416
$649$	−1.19733e7	−1.11584
$650$	−1.54813e7	−1.43722
$651$	−1.24323e7	−1.14974
$652$	−9.77146e6	−0.900203
$653$	−9.33917e6	−0.857088	−0.428544	−	0.903521i	$-0.640973\pi$
$653$	−9.33917e6	−0.857088	−0.428544	+	0.903521i	$0.640973\pi$
$654$	1.54476e7	1.41227
$655$	2.54180e7	2.31493
$656$	5.00723e6	0.454295
$657$	2.23898e7	2.02366
$658$	−9.86326e6	−0.888087
$659$	3.12494e6	0.280303	0.140152	−	0.990130i	$-0.455241\pi$
$659$	3.12494e6	0.280303	0.140152	+	0.990130i	$0.455241\pi$
$660$	−1.51047e7	−1.34975
$661$	7.39771e6	0.658557	0.329279	−	0.944233i	$-0.393195\pi$
$661$	7.39771e6	0.658557	0.329279	+	0.944233i	$0.393195\pi$
$662$	2.04490e6	0.181354
$663$	−2.16224e7	−1.91039
$664$	5.44994e6	0.479702
$665$	0	0
$666$	−6.20040e6	−0.541669
$667$	1.22374e6	0.106506
$668$	−491094.	−0.0425817
$669$	−1.39463e7	−1.20474
$670$	−99415.9	−0.00855596
$671$	879809.	0.0754366
$672$	−4.73785e6	−0.404723
$673$	6.54208e6	0.556773	0.278386	−	0.960469i	$-0.410200\pi$
$673$	6.54208e6	0.556773	0.278386	+	0.960469i	$0.410200\pi$
$674$	−1.65762e7	−1.40552
$675$	2.26307e7	1.91178
$676$	1.69298e6	0.142490
$677$	8.02713e6	0.673114	0.336557	−	0.941663i	$-0.390738\pi$
$677$	8.02713e6	0.673114	0.336557	+	0.941663i	$0.390738\pi$
$678$	2.39048e7	1.99715
$679$	−2.03234e7	−1.69169
$680$	−7.36976e6	−0.611196
$681$	1.26243e7	1.04313
$682$	4.27631e6	0.352053
$683$	4.90962e6	0.402714	0.201357	−	0.979518i	$-0.435465\pi$
$683$	4.90962e6	0.402714	0.201357	+	0.979518i	$0.435465\pi$
$684$	0	0
$685$	−7.74511e6	−0.630669
$686$	310230.	0.0251694
$687$	8.95402e6	0.723813
$688$	−94995.9	−0.00765128
$689$	−3.88575e6	−0.311837
$690$	−2.67629e6	−0.213998
$691$	8.78347e6	0.699795	0.349897	−	0.936788i	$-0.386216\pi$
$691$	8.78347e6	0.699795	0.349897	+	0.936788i	$0.386216\pi$
$692$	−153702.	−0.0122016
$693$	−2.91398e7	−2.30491
$694$	−1.29518e7	−1.02078
$695$	8.41409e6	0.660762
$696$	7.05404e6	0.551969
$697$	2.41083e7	1.87969
$698$	−8.90427e6	−0.691767
$699$	−2.09038e7	−1.61820
$700$	−1.63325e7	−1.25982
$701$	−2.28545e7	−1.75661	−0.878307	−	0.478096i	$-0.841327\pi$
$701$	−2.28545e7	−1.75661	−0.878307	+	0.478096i	$0.841327\pi$
$702$	−1.11590e7	−0.854637
$703$	0	0
$704$	1.62967e6	0.123928
$705$	−3.21159e7	−2.43359
$706$	−4.25932e6	−0.321609
$707$	−2.79734e7	−2.10473
$708$	−1.22287e7	−0.916850
$709$	−8.07051e6	−0.602956	−0.301478	−	0.953473i	$-0.597480\pi$
$709$	−8.07051e6	−0.602956	−0.301478	+	0.953473i	$0.597480\pi$
$710$	−8.33015e6	−0.620165
$711$	−2.27381e7	−1.68686
$712$	1.38879e6	0.102668
$713$	757686.	0.0558169
$714$	−2.28113e7	−1.67458
$715$	2.56750e7	1.87822
$716$	8.33261e6	0.607433
$717$	2.96795e7	2.15605
$718$	3.15948e6	0.228720
$719$	−2.40450e7	−1.73462	−0.867308	−	0.497772i	$-0.834152\pi$
$719$	−2.40450e7	−1.73462	−0.867308	+	0.497772i	$0.834152\pi$
$720$	−9.61520e6	−0.691237
$721$	3.28083e6	0.235042
$722$	0	0
$723$	−4.52289e6	−0.321788
$724$	4.13785e6	0.293379
$725$	2.43170e7	1.71816
$726$	−279489.	−0.0196799
$727$	6.30121e6	0.442169	0.221084	−	0.975255i	$-0.429040\pi$
$727$	6.30121e6	0.442169	0.221084	+	0.975255i	$0.429040\pi$
$728$	8.05339e6	0.563184
$729$	−2.29626e7	−1.60030
$730$	−2.08123e7	−1.44548
$731$	−457377.	−0.0316578
$732$	898580.	0.0619839
$733$	1.84036e7	1.26515	0.632576	−	0.774498i	$-0.281998\pi$
$733$	1.84036e7	1.26515	0.632576	+	0.774498i	$0.281998\pi$
$734$	1.44133e7	0.987468
$735$	−3.88687e7	−2.65388
$736$	288749.	0.0196483
$737$	105846.	0.00717801
$738$	3.14537e7	2.12584
$739$	−2.04305e6	−0.137616	−0.0688079	−	0.997630i	$-0.521920\pi$
$739$	−2.04305e6	−0.137616	−0.0688079	+	0.997630i	$0.521920\pi$
$740$	5.76353e6	0.386910
$741$	0	0
$742$	−4.09940e6	−0.273345
$743$	−2.13550e7	−1.41915	−0.709574	−	0.704631i	$-0.751113\pi$
$743$	−2.13550e7	−1.41915	−0.709574	+	0.704631i	$0.751113\pi$
$744$	4.36755e6	0.289272
$745$	−7.08637e6	−0.467771
$746$	6.89404e6	0.453551
$747$	3.42347e7	2.24473
$748$	7.84639e6	0.512762
$749$	−6.96714e6	−0.453785
$750$	−2.35211e7	−1.52688
$751$	−8.37370e6	−0.541773	−0.270887	−	0.962611i	$-0.587317\pi$
$751$	−8.37370e6	−0.541773	−0.270887	+	0.962611i	$0.587317\pi$
$752$	3.46504e6	0.223441
$753$	−6.26650e6	−0.402752
$754$	−1.19905e7	−0.768082
$755$	3.00624e7	1.91936
$756$	−1.17725e7	−0.749145
$757$	−1.62582e6	−0.103118	−0.0515589	−	0.998670i	$-0.516419\pi$
$757$	−1.62582e6	−0.103118	−0.0515589	+	0.998670i	$0.516419\pi$
$758$	5.36533e6	0.339175
$759$	2.84937e6	0.179533
$760$	0	0
$761$	−5.87944e6	−0.368022	−0.184011	−	0.982924i	$-0.558908\pi$
$761$	−5.87944e6	−0.368022	−0.184011	+	0.982924i	$0.558908\pi$
$762$	−1.06518e7	−0.664561
$763$	−2.77016e7	−1.72263
$764$	6.78264e6	0.420402
$765$	−4.62943e7	−2.86005
$766$	−4.22199e6	−0.259983
$767$	2.07864e7	1.27582
$768$	1.66444e6	0.101828
$769$	−2.19280e6	−0.133716	−0.0668580	−	0.997762i	$-0.521297\pi$
$769$	−2.19280e6	−0.133716	−0.0668580	+	0.997762i	$0.521297\pi$
$770$	2.70867e7	1.64638
$771$	−2.78463e7	−1.68707
$772$	−8.17207e6	−0.493502
$773$	−1.50209e7	−0.904166	−0.452083	−	0.891976i	$-0.649319\pi$
$773$	−1.50209e7	−0.904166	−0.452083	+	0.891976i	$0.649319\pi$
$774$	−596732.	−0.0358036
$775$	1.50560e7	0.900441
$776$	7.13977e6	0.425628
$777$	1.78396e7	1.06007
$778$	−1.29925e7	−0.769562
$779$	0	0
$780$	2.62228e7	1.54327
$781$	8.86890e6	0.520286
$782$	1.39024e6	0.0812967
$783$	1.75278e7	1.02170
$784$	4.19361e6	0.243667
$785$	1.55785e7	0.902300
$786$	−2.76393e7	−1.59577
$787$	−2.21298e7	−1.27362	−0.636812	−	0.771019i	$-0.719747\pi$
$787$	−2.21298e7	−1.27362	−0.636812	+	0.771019i	$0.719747\pi$
$788$	1.17248e7	0.672650
$789$	−1.90972e7	−1.09214
$790$	2.11360e7	1.20491
$791$	−4.28675e7	−2.43605
$792$	1.02370e7	0.579912
$793$	−1.52741e6	−0.0862525
$794$	2.42213e7	1.36347
$795$	−1.33481e7	−0.749037
$796$	−5.87456e6	−0.328619
$797$	1.03614e6	0.0577791	0.0288895	−	0.999583i	$-0.490803\pi$
$797$	1.03614e6	0.0577791	0.0288895	+	0.999583i	$0.490803\pi$
$798$	0	0
$799$	1.66831e7	0.924508
$800$	5.73773e6	0.316968
$801$	8.72391e6	0.480430
$802$	3.03514e6	0.166626
$803$	2.21583e7	1.21268
$804$	108104.	0.00589795
$805$	4.79928e6	0.261028
$806$	−7.42396e6	−0.402530
$807$	4.09338e7	2.21258
$808$	9.82728e6	0.529547
$809$	−3.15192e7	−1.69319	−0.846593	−	0.532242i	$-0.821350\pi$
$809$	−3.15192e7	−1.69319	−0.846593	+	0.532242i	$0.821350\pi$
$810$	−1.82508e6	−0.0977393
$811$	−1.45695e7	−0.777846	−0.388923	−	0.921270i	$-0.627153\pi$
$811$	−1.45695e7	−0.777846	−0.388923	+	0.921270i	$0.627153\pi$
$812$	−1.26497e7	−0.673273
$813$	−3.98374e7	−2.11380
$814$	−6.13628e6	−0.324597
$815$	5.70562e7	3.00891
$816$	8.01379e6	0.421321
$817$	0	0
$818$	−1.19239e7	−0.623065
$819$	5.05887e7	2.63538
$820$	−2.92376e7	−1.51847
$821$	2.05675e7	1.06493	0.532467	−	0.846450i	$-0.321265\pi$
$821$	2.05675e7	1.06493	0.532467	+	0.846450i	$0.321265\pi$
$822$	8.42196e6	0.434744
$823$	−1.03183e7	−0.531016	−0.265508	−	0.964109i	$-0.585540\pi$
$823$	−1.03183e7	−0.531016	−0.265508	+	0.964109i	$0.585540\pi$
$824$	−1.15258e6	−0.0591362
$825$	5.66199e7	2.89624
$826$	2.19293e7	1.11834
$827$	−1.16402e7	−0.591832	−0.295916	−	0.955214i	$-0.595625\pi$
$827$	−1.16402e7	−0.591832	−0.295916	+	0.955214i	$0.595625\pi$
$828$	1.81382e6	0.0919430
$829$	−6.43177e6	−0.325045	−0.162523	−	0.986705i	$-0.551963\pi$
$829$	−6.43177e6	−0.325045	−0.162523	+	0.986705i	$0.551963\pi$
$830$	−3.18226e7	−1.60339
$831$	4.65660e6	0.233919
$832$	−2.82922e6	−0.141696
$833$	2.01910e7	1.00820
$834$	−9.14939e6	−0.455488
$835$	2.86753e6	0.142329
$836$	0	0
$837$	1.08524e7	0.535443
$838$	−1.96833e7	−0.968253
$839$	1.03920e7	0.509678	0.254839	−	0.966984i	$-0.417978\pi$
$839$	1.03920e7	0.509678	0.254839	+	0.966984i	$0.417978\pi$
$840$	2.76646e7	1.35278
$841$	−1.67734e6	−0.0817768
$842$	2.79163e6	0.135699
$843$	5.86348e7	2.84176
$844$	−1.56867e7	−0.758009
$845$	−9.88542e6	−0.476270
$846$	2.17662e7	1.04558
$847$	501197.	0.0240049
$848$	1.44015e6	0.0687731
$849$	5.90087e7	2.80961
$850$	2.76255e7	1.31148
$851$	−1.08724e6	−0.0514638
$852$	9.05812e6	0.427503
$853$	3.92571e7	1.84733	0.923666	−	0.383198i	$-0.125177\pi$
$853$	3.92571e7	1.84733	0.923666	+	0.383198i	$0.125177\pi$
$854$	−1.61139e6	−0.0756059
$855$	0	0
$856$	2.44761e6	0.114172
$857$	2.99794e7	1.39435	0.697175	−	0.716901i	$-0.254440\pi$
$857$	2.99794e7	1.39435	0.697175	+	0.716901i	$0.254440\pi$
$858$	−2.79187e7	−1.29472
$859$	1.84582e7	0.853506	0.426753	−	0.904368i	$-0.359657\pi$
$859$	1.84582e7	0.853506	0.426753	+	0.904368i	$0.359657\pi$
$860$	554688.	0.0255742
$861$	−9.04980e7	−4.16036
$862$	1.38261e7	0.633769
$863$	−2.82508e6	−0.129123	−0.0645614	−	0.997914i	$-0.520565\pi$
$863$	−2.82508e6	−0.129123	−0.0645614	+	0.997914i	$0.520565\pi$
$864$	4.13578e6	0.188484
$865$	897478.	0.0407834
$866$	−2.26025e7	−1.02415
$867$	2.52341e6	0.114009
$868$	−7.83216e6	−0.352844
$869$	−2.25030e7	−1.01086
$870$	−4.11890e7	−1.84494
$871$	−183755.	−0.00820717
$872$	9.73178e6	0.433412
$873$	4.48496e7	1.99170
$874$	0	0
$875$	4.21795e7	1.86244
$876$	2.26310e7	0.996424
$877$	−1.38877e7	−0.609721	−0.304861	−	0.952397i	$-0.598610\pi$
$877$	−1.38877e7	−0.609721	−0.304861	+	0.952397i	$0.598610\pi$
$878$	−2.90728e7	−1.27277
$879$	2.61764e7	1.14272
$880$	−9.51577e6	−0.414226
$881$	2.06379e7	0.895830	0.447915	−	0.894076i	$-0.352167\pi$
$881$	2.06379e7	0.895830	0.447915	+	0.894076i	$0.352167\pi$
$882$	2.63428e7	1.14023
$883$	−1.66653e7	−0.719304	−0.359652	−	0.933086i	$-0.617105\pi$
$883$	−1.66653e7	−0.719304	−0.359652	+	0.933086i	$0.617105\pi$
$884$	−1.36218e7	−0.586280
$885$	7.14044e7	3.06455
$886$	−7.25187e6	−0.310360
$887$	−2.42880e7	−1.03653	−0.518266	−	0.855220i	$-0.673422\pi$
$887$	−2.42880e7	−1.03653	−0.518266	+	0.855220i	$0.673422\pi$
$888$	−6.26721e6	−0.266711
$889$	1.91014e7	0.810609
$890$	−8.10924e6	−0.343167
$891$	1.94311e6	0.0819982
$892$	−8.78600e6	−0.369725
$893$	0	0
$894$	7.70564e6	0.322452
$895$	−4.86547e7	−2.03033
$896$	−2.98478e6	−0.124206
$897$	−4.94670e6	−0.205274
$898$	1.10427e7	0.456968
$899$	1.16611e7	0.481215
$900$	3.60425e7	1.48323
$901$	6.93391e6	0.284555
$902$	3.11285e7	1.27392
$903$	1.71690e6	0.0700691
$904$	1.50597e7	0.612907
$905$	−2.41612e7	−0.980612
$906$	−3.26896e7	−1.32309
$907$	3.73706e7	1.50838	0.754192	−	0.656654i	$-0.228029\pi$
$907$	3.73706e7	1.50838	0.754192	+	0.656654i	$0.228029\pi$
$908$	7.95315e6	0.320129
$909$	6.17316e7	2.47798
$910$	−4.70243e7	−1.88243
$911$	−2.05225e7	−0.819285	−0.409642	−	0.912246i	$-0.634347\pi$
$911$	−2.05225e7	−0.819285	−0.409642	+	0.912246i	$0.634347\pi$
$912$	0	0
$913$	3.38807e7	1.34516
$914$	3.07694e7	1.21830
$915$	−5.24687e6	−0.207180
$916$	5.64091e6	0.222132
$917$	4.95644e7	1.94647
$918$	1.99126e7	0.779867
$919$	9.70865e6	0.379201	0.189601	−	0.981861i	$-0.439281\pi$
$919$	9.70865e6	0.379201	0.189601	+	0.981861i	$0.439281\pi$
$920$	−1.68602e6	−0.0656741
$921$	4.27269e7	1.65979
$922$	−2.32446e7	−0.900524
$923$	−1.53970e7	−0.594883
$924$	−2.94538e7	−1.13491
$925$	−2.16046e7	−0.830216
$926$	1.62125e7	0.621329
$927$	−7.24013e6	−0.276724
$928$	4.44395e6	0.169394
$929$	2.38735e7	0.907562	0.453781	−	0.891113i	$-0.350075\pi$
$929$	2.38735e7	0.907562	0.453781	+	0.891113i	$0.350075\pi$
$930$	−2.55024e7	−0.966884
$931$	0	0
$932$	−1.31691e7	−0.496611
$933$	−1.76171e7	−0.662569
$934$	2.42250e7	0.908650
$935$	−4.58156e7	−1.71390
$936$	−1.77722e7	−0.663058
$937$	3.19106e7	1.18737	0.593685	−	0.804698i	$-0.297673\pi$
$937$	3.19106e7	1.18737	0.593685	+	0.804698i	$0.297673\pi$
$938$	−193858.	−0.00719412
$939$	−3.87063e7	−1.43258
$940$	−2.02326e7	−0.746848
$941$	1.74839e7	0.643673	0.321836	−	0.946795i	$-0.395700\pi$
$941$	1.74839e7	0.643673	0.321836	+	0.946795i	$0.395700\pi$
$942$	−1.69399e7	−0.621989
$943$	5.51541e6	0.201975
$944$	−7.70394e6	−0.281373
$945$	6.87407e7	2.50400
$946$	−590562.	−0.0214554
$947$	−884164.	−0.0320374	−0.0160187	−	0.999872i	$-0.505099\pi$
$947$	−884164.	−0.0320374	−0.0160187	+	0.999872i	$0.505099\pi$
$948$	−2.29831e7	−0.830591
$949$	−3.84682e7	−1.38655
$950$	0	0
$951$	3.80469e7	1.36417
$952$	−1.43708e7	−0.513913
$953$	724670.	0.0258469	0.0129234	−	0.999916i	$-0.495886\pi$
$953$	724670.	0.0258469	0.0129234	+	0.999916i	$0.495886\pi$
$954$	9.04655e6	0.321819
$955$	−3.96043e7	−1.40519
$956$	1.86977e7	0.661673
$957$	4.38529e7	1.54781
$958$	1.59603e7	0.561859
$959$	−1.51028e7	−0.530286
$960$	−9.71879e6	−0.340357
$961$	−2.14091e7	−0.747809
$962$	1.06530e7	0.371137
$963$	1.53751e7	0.534258
$964$	−2.84936e6	−0.0987539
$965$	4.77173e7	1.64952
$966$	−5.21869e6	−0.179936
$967$	−1.78219e7	−0.612897	−0.306448	−	0.951887i	$-0.599141\pi$
$967$	−1.78219e7	−0.612897	−0.306448	+	0.951887i	$0.599141\pi$
$968$	−176074.	−0.00603959
$969$	0	0
$970$	−4.16896e7	−1.42265
$971$	−1.43970e7	−0.490031	−0.245016	−	0.969519i	$-0.578793\pi$
$971$	−1.43970e7	−0.490031	−0.245016	+	0.969519i	$0.578793\pi$
$972$	−1.37185e7	−0.465737
$973$	1.64073e7	0.555589
$974$	3.02951e7	1.02323
$975$	−9.82959e7	−3.31149
$976$	566093.	0.0190223
$977$	−7.27121e6	−0.243708	−0.121854	−	0.992548i	$-0.538884\pi$
$977$	−7.27121e6	−0.243708	−0.121854	+	0.992548i	$0.538884\pi$
$978$	−6.20423e7	−2.07415
$979$	8.63370e6	0.287899
$980$	−2.44868e7	−0.814453
$981$	6.11317e7	2.02812
$982$	−6.10794e6	−0.202123
$983$	−3.03284e7	−1.00107	−0.500536	−	0.865716i	$-0.666864\pi$
$983$	−3.03284e7	−1.00107	−0.500536	+	0.865716i	$0.666864\pi$
$984$	3.17926e7	1.04674
$985$	−6.84618e7	−2.24832
$986$	2.13963e7	0.700884
$987$	−6.26252e7	−2.04624
$988$	0	0
$989$	−104637.	−0.00340169
$990$	−5.97748e7	−1.93834
$991$	−4.63530e7	−1.49932	−0.749659	−	0.661824i	$-0.769783\pi$
$991$	−4.63530e7	−1.49932	−0.749659	+	0.661824i	$0.769783\pi$
$992$	2.75150e6	0.0887749
$993$	1.29838e7	0.417856
$994$	−1.62436e7	−0.521454
$995$	3.43019e7	1.09840
$996$	3.46035e7	1.10528
$997$	8.59188e6	0.273748	0.136874	−	0.990588i	$-0.456295\pi$
$997$	8.59188e6	0.273748	0.136874	+	0.990588i	$0.456295\pi$
$998$	5.84779e6	0.185851
$999$	−1.55727e7	−0.493684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.6.a.r.1.13		15
19.9	even	9		38.6.e.b.5.5	✓	30
19.17	even	9		38.6.e.b.23.5	yes	30
19.18	odd	2		722.6.a.q.1.3		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.e.b.5.5	✓	30	19.9	even	9
38.6.e.b.23.5	yes	30	19.17	even	9
722.6.a.q.1.3		15	19.18	odd	2
722.6.a.r.1.13		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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +25.3974 q^{3} +16.0000 q^{4} -93.4251 q^{5} +101.589 q^{6} -182.176 q^{7} +64.0000 q^{8} +402.026 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +25.3974 q^{3} +16.0000 q^{4} -93.4251 q^{5} +101.589 q^{6} -182.176 q^{7} +64.0000 q^{8} +402.026 q^{9} -373.700 q^{10} +397.869 q^{11} +406.358 q^{12} -690.727 q^{13} -728.706 q^{14} -2372.75 q^{15} +256.000 q^{16} +1232.56 q^{17} +1608.11 q^{18} -1494.80 q^{20} -4626.80 q^{21} +1591.48 q^{22} +281.981 q^{23} +1625.43 q^{24} +5603.25 q^{25} -2762.91 q^{26} +4038.85 q^{27} -2914.82 q^{28} +4339.79 q^{29} -9491.01 q^{30} +2687.01 q^{31} +1024.00 q^{32} +10104.8 q^{33} +4930.26 q^{34} +17019.9 q^{35} +6432.42 q^{36} -3855.72 q^{37} -17542.7 q^{39} -5979.21 q^{40} +19559.5 q^{41} -18507.2 q^{42} -371.078 q^{43} +6365.91 q^{44} -37559.4 q^{45} +1127.92 q^{46} +13535.3 q^{47} +6501.73 q^{48} +16381.3 q^{49} +22413.0 q^{50} +31303.9 q^{51} -11051.6 q^{52} +5625.60 q^{53} +16155.4 q^{54} -37171.0 q^{55} -11659.3 q^{56} +17359.2 q^{58} -30093.5 q^{59} -37964.0 q^{60} +2211.30 q^{61} +10748.0 q^{62} -73239.8 q^{63} +4096.00 q^{64} +64531.3 q^{65} +40419.3 q^{66} +266.031 q^{67} +19721.0 q^{68} +7161.58 q^{69} +68079.4 q^{70} +22291.0 q^{71} +25729.7 q^{72} +55692.4 q^{73} -15422.9 q^{74} +142308. q^{75} -72482.4 q^{77} -70170.6 q^{78} -56558.7 q^{79} -23916.8 q^{80} +4883.80 q^{81} +78238.0 q^{82} +85155.3 q^{83} -74028.9 q^{84} -115152. q^{85} -1484.31 q^{86} +110219. q^{87} +25463.6 q^{88} +21699.8 q^{89} -150237. q^{90} +125834. q^{91} +4511.70 q^{92} +68243.0 q^{93} +54141.2 q^{94} +26006.9 q^{96} +111559. q^{97} +65525.1 q^{98} +159954. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 60 q^{2} + 240 q^{4} + 108 q^{5} + 84 q^{7} + 960 q^{8} + 2127 q^{9}+O(q^{10}) \) 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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