LMFDB - Embedded newform 76.6.d.a.75.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.17
Character	$\chi$	$=$	76.75
Dual form			76.6.d.a.75.18

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99929 - 4.79628i) q^{2} -24.6139 q^{3} +(-14.0085 + 28.7708i) q^{4} +37.3653 q^{5} +(73.8243 + 118.055i) q^{6} +35.5589i q^{7} +(180.009 - 19.1033i) q^{8} +362.846 q^{9} +O(q^{10})$	\(q+(-2.99929 - 4.79628i) q^{2} -24.6139 q^{3} +(-14.0085 + 28.7708i) q^{4} +37.3653 q^{5} +(73.8243 + 118.055i) q^{6} +35.5589i q^{7} +(180.009 - 19.1033i) q^{8} +362.846 q^{9} +(-112.069 - 179.214i) q^{10} +184.937i q^{11} +(344.805 - 708.163i) q^{12} +119.283i q^{13} +(170.551 - 106.652i) q^{14} -919.707 q^{15} +(-631.522 - 806.074i) q^{16} +152.741 q^{17} +(-1088.28 - 1740.31i) q^{18} +(-1458.65 - 590.280i) q^{19} +(-523.433 + 1075.03i) q^{20} -875.246i q^{21} +(887.008 - 554.679i) q^{22} -1580.72i q^{23} +(-4430.72 + 470.206i) q^{24} -1728.83 q^{25} +(572.115 - 357.765i) q^{26} -2949.87 q^{27} +(-1023.06 - 498.129i) q^{28} +54.3855i q^{29} +(2758.47 + 4411.17i) q^{30} +4260.92 q^{31} +(-1972.04 + 5446.60i) q^{32} -4552.02i q^{33} +(-458.114 - 732.588i) q^{34} +1328.67i q^{35} +(-5082.94 + 10439.4i) q^{36} -12169.2i q^{37} +(1543.78 + 8766.52i) q^{38} -2936.03i q^{39} +(6726.07 - 713.799i) q^{40} -5665.34i q^{41} +(-4197.92 + 2625.11i) q^{42} -19239.7i q^{43} +(-5320.78 - 2590.69i) q^{44} +13557.8 q^{45} +(-7581.56 + 4741.03i) q^{46} -26623.3i q^{47} +(15544.2 + 19840.7i) q^{48} +15542.6 q^{49} +(5185.28 + 8291.97i) q^{50} -3759.56 q^{51} +(-3431.88 - 1670.98i) q^{52} +29445.2i q^{53} +(8847.53 + 14148.4i) q^{54} +6910.22i q^{55} +(679.292 + 6400.91i) q^{56} +(35903.2 + 14529.1i) q^{57} +(260.848 - 163.118i) q^{58} -22874.8 q^{59} +(12883.7 - 26460.7i) q^{60} -31754.3 q^{61} +(-12779.7 - 20436.6i) q^{62} +12902.4i q^{63} +(32038.1 - 6877.50i) q^{64} +4457.05i q^{65} +(-21832.7 + 13652.8i) q^{66} +21754.5 q^{67} +(-2139.68 + 4394.49i) q^{68} +38907.7i q^{69} +(6372.67 - 3985.07i) q^{70} -12897.9 q^{71} +(65315.3 - 6931.54i) q^{72} +33382.4 q^{73} +(-58366.7 + 36498.8i) q^{74} +42553.4 q^{75} +(37416.4 - 33697.7i) q^{76} -6576.16 q^{77} +(-14082.0 + 8805.99i) q^{78} -57062.3 q^{79} +(-23597.0 - 30119.2i) q^{80} -15563.5 q^{81} +(-27172.5 + 16992.0i) q^{82} -14789.3i q^{83} +(25181.5 + 12260.9i) q^{84} +5707.21 q^{85} +(-92278.8 + 57705.3i) q^{86} -1338.64i q^{87} +(3532.90 + 33290.2i) q^{88} -138076. i q^{89} +(-40663.9 - 65027.1i) q^{90} -4241.58 q^{91} +(45478.6 + 22143.5i) q^{92} -104878. q^{93} +(-127693. + 79851.0i) q^{94} +(-54503.0 - 22056.0i) q^{95} +(48539.6 - 134062. i) q^{96} +34257.8i q^{97} +(-46616.6 - 74546.4i) q^{98} +67103.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.99929	−	4.79628i	−0.530204	−	0.847870i
$2$	−2.99929	−	4.79628i	−0.530204	−	0.847870i
$3$	−24.6139			−1.57898			−0.789492	−	0.613760i	$-0.789656\pi$
$3$	−24.6139			−1.57898			−0.789492	+	0.613760i	$0.789656\pi$
$4$	−14.0085	+	28.7708i	−0.437767	+	0.899089i
$5$	37.3653			0.668411			0.334205	−	0.942500i	$-0.391532\pi$
$5$	37.3653			0.668411			0.334205	+	0.942500i	$0.391532\pi$
$6$	73.8243	+	118.055i	0.837185	+	1.33877i
$7$			35.5589i			0.274286i	0.990551	+	0.137143i	$0.0437920\pi$
$7$			35.5589i			0.274286i	−0.990551	+	0.137143i	$0.956208\pi$
$8$	180.009	−	19.1033i	0.994416	−	0.105532i
$9$	362.846			1.49319
$10$	−112.069	−	179.214i	−0.354394	−	0.566725i
$11$			184.937i			0.460831i	0.973092	+	0.230415i	$0.0740085\pi$
$11$			184.937i			0.460831i	−0.973092	+	0.230415i	$0.925992\pi$
$12$	344.805	−	708.163i	0.691227	−	1.41965i
$13$			119.283i			0.195759i	0.995198	+	0.0978793i	$0.0312059\pi$
$13$			119.283i			0.195759i	−0.995198	+	0.0978793i	$0.968794\pi$
$14$	170.551	−	106.652i	0.232559	−	0.145428i
$15$	−919.707			−1.05541
$16$	−631.522	−	806.074i	−0.616721	−	0.787182i
$17$	152.741			0.128184			0.0640919	−	0.997944i	$-0.479585\pi$
$17$	152.741			0.128184			0.0640919	+	0.997944i	$0.479585\pi$
$18$	−1088.28	−	1740.31i	−0.791697	−	1.26603i
$19$	−1458.65	−	590.280i	−0.926975	−	0.375123i
$19$	−1458.65	−	590.280i	−0.926975	−	0.375123i
$20$	−523.433	+	1075.03i	−0.292608	+	0.600960i
$21$		−	875.246i		−	0.433093i
$22$	887.008	−	554.679i	0.390725	−	0.244335i
$23$		−	1580.72i		−	0.623067i	−0.950235	−	0.311534i	$-0.899157\pi$
$23$		−	1580.72i		−	0.623067i	0.950235	−	0.311534i	$-0.100843\pi$
$24$	−4430.72	+	470.206i	−1.57017	+	0.166633i
$25$	−1728.83			−0.553227
$26$	572.115	−	357.765i	0.165978	−	0.103792i
$27$	−2949.87			−0.778743
$28$	−1023.06	−	498.129i	−0.246607	−	0.120073i
$29$			54.3855i			0.0120085i	0.999982	+	0.00600425i	$0.00191122\pi$
$29$			54.3855i			0.0120085i	−0.999982	+	0.00600425i	$0.998089\pi$
$30$	2758.47	+	4411.17i	0.559583	+	0.894850i
$31$	4260.92			0.796342			0.398171	−	0.917311i	$-0.369645\pi$
$31$	4260.92			0.796342			0.398171	+	0.917311i	$0.369645\pi$
$32$	−1972.04	+	5446.60i	−0.340440	+	0.940266i
$33$		−	4552.02i		−	0.727645i
$34$	−458.114	−	732.588i	−0.0679636	−	0.108683i
$35$			1328.67i			0.183336i
$36$	−5082.94	+	10439.4i	−0.653670	+	1.34251i
$37$		−	12169.2i		−	1.46136i	−0.682722	−	0.730678i	$-0.739204\pi$
$37$		−	12169.2i		−	1.46136i	0.682722	−	0.730678i	$-0.260796\pi$
$38$	1543.78	+	8766.52i	0.173431	+	0.984846i
$39$		−	2936.03i		−	0.309100i
$40$	6726.07	−	713.799i	0.664678	−	0.0705385i
$41$		−	5665.34i		−	0.526340i	−0.964749	−	0.263170i	$-0.915232\pi$
$41$		−	5665.34i		−	0.526340i	0.964749	−	0.263170i	$-0.0847680\pi$
$42$	−4197.92	+	2625.11i	−0.367207	+	0.229628i
$43$		−	19239.7i		−	1.58682i	−0.608690	−	0.793408i	$-0.708305\pi$
$43$		−	19239.7i		−	1.58682i	0.608690	−	0.793408i	$-0.291695\pi$
$44$	−5320.78	−	2590.69i	−0.414328	−	0.201736i
$45$	13557.8			0.998066
$46$	−7581.56	+	4741.03i	−0.528280	+	0.330353i
$47$		−	26623.3i		−	1.75799i	−0.476828	−	0.878997i	$-0.658213\pi$
$47$		−	26623.3i		−	1.75799i	0.476828	−	0.878997i	$-0.341787\pi$
$48$	15544.2	+	19840.7i	0.973793	+	1.24295i
$49$	15542.6			0.924767
$50$	5185.28	+	8291.97i	0.293323	+	0.469065i
$51$	−3759.56			−0.202400
$52$	−3431.88	−	1670.98i	−0.176004	−	0.0856965i
$53$			29445.2i			1.43988i	0.694038	+	0.719938i	$0.255830\pi$
$53$			29445.2i			1.43988i	−0.694038	+	0.719938i	$0.744170\pi$
$54$	8847.53	+	14148.4i	0.412893	+	0.660273i
$55$			6910.22i			0.308024i
$56$	679.292	+	6400.91i	0.0289459	+	0.272754i
$57$	35903.2	+	14529.1i	1.46368	+	0.592314i
$58$	260.848	−	163.118i	0.0101816	−	0.00636695i
$59$	−22874.8			−0.855516			−0.427758	−	0.903893i	$-0.640696\pi$
$59$	−22874.8			−0.855516			−0.427758	+	0.903893i	$0.640696\pi$
$60$	12883.7	−	26460.7i	0.462023	−	0.948907i
$61$	−31754.3			−1.09264			−0.546320	−	0.837576i	$-0.683972\pi$
$61$	−31754.3			−1.09264			−0.546320	+	0.837576i	$0.683972\pi$
$62$	−12779.7	−	20436.6i	−0.422224	−	0.675194i
$63$			12902.4i			0.409562i
$64$	32038.1	−	6877.50i	0.977726	−	0.209885i
$65$			4457.05i			0.130847i
$66$	−21832.7	+	13652.8i	−0.616948	+	0.385800i
$67$	21754.5			0.592055			0.296028	−	0.955179i	$-0.404338\pi$
$67$	21754.5			0.592055			0.296028	+	0.955179i	$0.404338\pi$
$68$	−2139.68	+	4394.49i	−0.0561146	+	0.115249i
$69$			38907.7i			0.983813i
$70$	6372.67	−	3985.07i	0.155445	−	0.0972054i
$71$	−12897.9			−0.303651			−0.151825	−	0.988407i	$-0.548515\pi$
$71$	−12897.9			−0.303651			−0.151825	+	0.988407i	$0.548515\pi$
$72$	65315.3	−	6931.54i	1.48485	−	0.157579i
$73$	33382.4			0.733181			0.366590	−	0.930382i	$-0.380525\pi$
$73$	33382.4			0.733181			0.366590	+	0.930382i	$0.380525\pi$
$74$	−58366.7	+	36498.8i	−1.23904	+	0.774818i
$75$	42553.4			0.873537
$76$	37416.4	−	33697.7i	0.743068	−	0.669216i
$77$	−6576.16			−0.126399
$78$	−14082.0	+	8805.99i	−0.262076	+	0.163886i
$79$	−57062.3			−1.02868			−0.514342	−	0.857585i	$-0.671964\pi$
$79$	−57062.3			−1.02868			−0.514342	+	0.857585i	$0.671964\pi$
$80$	−23597.0	−	30119.2i	−0.412223	−	0.526161i
$81$	−15563.5			−0.263569
$82$	−27172.5	+	16992.0i	−0.446268	+	0.279068i
$83$		−	14789.3i		−	0.235641i	−0.993035	−	0.117821i	$-0.962409\pi$
$83$		−	14789.3i		−	0.235641i	0.993035	−	0.117821i	$-0.0375908\pi$
$84$	25181.5	+	12260.9i	0.389389	+	0.189594i
$85$	5707.21			0.0856794
$86$	−92278.8	+	57705.3i	−1.34541	+	0.841337i
$87$		−	1338.64i		−	0.0189612i
$88$	3532.90	+	33290.2i	0.0486322	+	0.458258i
$89$		−	138076.i		−	1.84775i	−0.382694	−	0.923875i	$-0.625004\pi$
$89$		−	138076.i		−	1.84775i	0.382694	−	0.923875i	$-0.374996\pi$
$90$	−40663.9	−	65027.1i	−0.529179	−	0.846230i
$91$	−4241.58			−0.0536938
$92$	45478.6	+	22143.5i	0.560193	+	0.272758i
$93$	−104878.			−1.25741
$94$	−127693.	+	79851.0i	−1.49055	+	0.932096i
$95$	−54503.0	−	22056.0i	−0.619600	−	0.250736i
$96$	48539.6	−	134062.i	0.537549	−	1.48467i
$97$			34257.8i			0.369684i	0.982768	+	0.184842i	$0.0591773\pi$
$97$			34257.8i			0.369684i	−0.982768	+	0.184842i	$0.940823\pi$
$98$	−46616.6	−	74546.4i	−0.490316	−	0.784082i
$99$			67103.5i			0.688109i
$100$	24218.4	−	49740.0i	0.242184	−	0.497400i
$101$	−112359.			−1.09598			−0.547992	−	0.836483i	$-0.684608\pi$
$101$	−112359.			−1.09598			−0.547992	+	0.836483i	$0.684608\pi$
$102$	11276.0	+	18031.9i	0.107314	+	0.171609i
$103$	116233.			1.07953			0.539765	−	0.841816i	$-0.318513\pi$
$103$	116233.			1.07953			0.539765	+	0.841816i	$0.318513\pi$
$104$	2278.70	+	21472.0i	0.0206587	+	0.194665i
$105$		−	32703.8i		−	0.289484i
$106$	141227.	−	88314.7i	1.22083	−	0.763429i
$107$	129398.			1.09262			0.546311	−	0.837583i	$-0.316032\pi$
$107$	129398.			1.09262			0.546311	+	0.837583i	$0.316032\pi$
$108$	41323.4	−	84870.4i	0.340908	−	0.700159i
$109$		−	123459.i		−	0.995303i	−0.867377	−	0.497652i	$-0.834196\pi$
$109$		−	123459.i		−	0.995303i	0.867377	−	0.497652i	$-0.165804\pi$
$110$	33143.3	−	20725.7i	0.261164	−	0.163316i
$111$			299531.i			2.30746i
$112$	28663.2	−	22456.3i	0.215913	−	0.169158i
$113$		−	200568.i		−	1.47763i	−0.673908	−	0.738815i	$-0.735386\pi$
$113$		−	200568.i		−	1.47763i	0.673908	−	0.738815i	$-0.264614\pi$
$114$	−37998.4	−	215779.i	−0.273844	−	1.55506i
$115$		−	59064.0i		−	0.416465i
$116$	−1564.72	−	761.862i	−0.0107967	−	0.00525692i
$117$			43281.4i			0.292305i
$118$	68608.3	+	109714.i	0.453598	+	0.725366i
$119$			5431.31i			0.0351590i
$120$	−165555.	+	17569.4i	−1.04952	+	0.111379i
$121$	126849.			0.787635
$122$	95240.2	+	152302.i	0.579323	+	0.926417i
$123$			139446.i			0.831083i
$124$	−59689.3	+	122590.i	−0.348612	+	0.715982i
$125$	−181365.			−1.03819
$126$	61883.5	−	38698.1i	0.347255	−	0.217151i
$127$	7707.66			0.0424046			0.0212023	−	0.999775i	$-0.493251\pi$
$127$	7707.66			0.0424046			0.0212023	+	0.999775i	$0.493251\pi$
$128$	−129078.	−	133036.i	−0.696350	−	0.717703i
$129$			473564.i			2.50556i
$130$	21377.2	−	13368.0i	0.110941	−	0.0693757i
$131$			64679.8i			0.329299i	0.986352	+	0.164650i	$0.0526493\pi$
$131$			64679.8i			0.329299i	−0.986352	+	0.164650i	$0.947351\pi$
$132$	130965.	+	63767.1i	0.654217	+	0.318539i
$133$	20989.7	−	51868.2i	0.102891	−	0.254256i
$134$	−65248.1	−	104341.i	−0.313910	−	0.501986i
$135$	−110223.			−0.520520
$136$	27494.7	−	2917.85i	0.127468	−	0.0135274i
$137$	183622.			0.835839			0.417919	−	0.908484i	$-0.362759\pi$
$137$	183622.			0.835839			0.417919	+	0.908484i	$0.362759\pi$
$138$	186612.	−	116695.i	0.834146	−	0.521622i
$139$		−	55030.4i		−	0.241582i	−0.992678	−	0.120791i	$-0.961457\pi$
$139$		−	55030.4i		−	0.241582i	0.992678	−	0.120791i	$-0.0385432\pi$
$140$	−38227.0	−	18612.7i	−0.164835	−	0.0802583i
$141$			655304.i			2.77584i
$142$	38684.6	+	61862.1i	0.160997	+	0.257456i
$143$	−22059.8			−0.0902115
$144$	−229145.	−	292481.i	−0.920883	−	1.17541i
$145$			2032.13i			0.00802660i
$146$	−100124.	−	160111.i	−0.388736	−	0.621642i
$147$	−382564.			−1.46019
$148$	350117.	+	170472.i	1.31389	+	0.639733i
$149$	−449359.			−1.65816			−0.829082	−	0.559127i	$-0.811136\pi$
$149$	−449359.			−1.65816			−0.829082	+	0.559127i	$0.811136\pi$
$150$	−127630.	−	204098.i	−0.463153	−	0.740646i
$151$	329534.			1.17614			0.588069	−	0.808811i	$-0.299888\pi$
$151$	329534.			1.17614			0.588069	+	0.808811i	$0.299888\pi$
$152$	−273846.	−	78390.4i	−0.961386	−	0.275203i
$153$	55421.4			0.191403
$154$	19723.8	+	31541.1i	0.0670176	+	0.107170i
$155$	159211.			0.532283
$156$	84472.0	+	41129.4i	0.277908	+	0.135314i
$157$	89868.3			0.290976			0.145488	−	0.989360i	$-0.453525\pi$
$157$	89868.3			0.290976			0.145488	+	0.989360i	$0.453525\pi$
$158$	171146.	+	273687.i	0.545412	+	0.872189i
$159$		−	724763.i		−	2.27354i
$160$	−73685.8	+	203514.i	−0.227554	+	0.628484i
$161$	56208.7			0.170899
$162$	46679.4	+	74646.8i	0.139746	+	0.223472i
$163$			331481.i			0.977215i	0.872504	+	0.488608i	$0.162495\pi$
$163$			331481.i			0.977215i	−0.872504	+	0.488608i	$0.837505\pi$
$164$	162997.	+	79363.1i	0.473226	+	0.230414i
$165$		−	170088.i		−	0.486365i
$166$	−70933.4	+	44357.3i	−0.199793	+	0.124938i
$167$	345101.			0.957535			0.478768	−	0.877942i	$-0.341084\pi$
$167$	345101.			0.957535			0.478768	+	0.877942i	$0.341084\pi$
$168$	−16720.0	−	157552.i	−0.0457051	−	0.430675i
$169$	357065.			0.961679
$170$	−17117.6	−	27373.4i	−0.0454276	−	0.0726450i
$171$	−529266.	−	214180.i	−1.38415	−	0.560131i
$172$	553541.	+	269520.i	1.42669	+	0.694655i
$173$		−	453340.i		−	1.15162i	−0.817584	−	0.575810i	$-0.804687\pi$
$173$		−	453340.i		−	1.15162i	0.817584	−	0.575810i	$-0.195313\pi$
$174$	−6420.50	+	4014.97i	−0.0160766	+	0.0100533i
$175$		−	61475.5i		−	0.151743i
$176$	149073.	−	116792.i	0.362758	−	0.284204i
$177$	563040.			1.35085
$178$	−662251.	+	414130.i	−1.56665	+	0.979685i
$179$	−351268.			−0.819418			−0.409709	−	0.912216i	$-0.634370\pi$
$179$	−351268.			−0.819418			−0.409709	+	0.912216i	$0.634370\pi$
$180$	−189925.	+	390070.i	−0.436920	+	0.897349i
$181$			328035.i			0.744258i	0.928181	+	0.372129i	$0.121372\pi$
$181$			328035.i			0.744258i	−0.928181	+	0.372129i	$0.878628\pi$
$182$	12721.7	+	20343.8i	0.0284687	+	0.0455254i
$183$	781597.			1.72526
$184$	−30196.9	−	284543.i	−0.0657533	−	0.619588i
$185$		−	454704.i		−	0.976787i
$186$	314560.	+	503024.i	0.666685	+	1.06612i
$187$			28247.4i			0.0590711i
$188$	765975.	+	372953.i	1.58059	+	0.769591i
$189$		−	104894.i		−	0.213598i
$190$	57683.7	+	327564.i	0.115923	+	0.658282i
$191$			896294.i			1.77774i	0.458164	+	0.888868i	$0.348507\pi$
$191$			896294.i			1.77774i	−0.458164	+	0.888868i	$0.651493\pi$
$192$	−788584.	+	169282.i	−1.54381	+	0.331405i
$193$		−	820690.i		−	1.58594i	−0.609262	−	0.792969i	$-0.708534\pi$
$193$		−	820690.i		−	1.58594i	0.609262	−	0.792969i	$-0.291466\pi$
$194$	164310.	−	102749.i	0.313444	−	0.196008i
$195$		−	109706.i		−	0.206606i
$196$	−217728.	+	447172.i	−0.404832	+	0.831448i
$197$	−25862.2			−0.0474788			−0.0237394	−	0.999718i	$-0.507557\pi$
$197$	−25862.2			−0.0474788			−0.0237394	+	0.999718i	$0.507557\pi$
$198$	321847.	−	201263.i	0.583427	−	0.364838i
$199$		−	957938.i		−	1.71477i	−0.514680	−	0.857383i	$-0.672089\pi$
$199$		−	957938.i		−	1.71477i	0.514680	−	0.857383i	$-0.327911\pi$
$200$	−311205.	+	33026.4i	−0.550138	+	0.0583830i
$201$	−535464.			−0.934846
$202$	336997.	+	538905.i	0.581096	+	0.929252i
$203$	−1933.89			−0.00329376
$204$	52665.9	−	108166.i	0.0886041	−	0.181976i
$205$		−	211687.i		−	0.351811i
$206$	−348615.	−	557484.i	−0.572372	−	0.915301i
$207$		−	573557.i		−	0.930359i
$208$	96151.1	−	75329.9i	0.154098	−	0.120728i
$209$	109164.	−	269759.i	0.172868	−	0.427179i
$210$	−156856.	+	98088.2i	−0.245445	+	0.153486i
$211$	−365052.			−0.564479			−0.282240	−	0.959344i	$-0.591077\pi$
$211$	−365052.			−0.564479			−0.282240	+	0.959344i	$0.591077\pi$
$212$	−847164.	−	412484.i	−1.29458	−	0.630330i
$213$	317469.			0.479460
$214$	−388103.	−	620631.i	−0.579313	−	0.926401i
$215$		−	718896.i		−	1.06064i
$216$	−531003.	+	56352.2i	−0.774394	+	0.0821820i
$217$			151514.i			0.218425i
$218$	−592142.	+	370288.i	−0.843888	+	0.527714i
$219$	−821673.			−1.15768
$220$	−198813.	−	96802.0i	−0.276941	−	0.134843i
$221$			18219.4i			0.0250931i
$222$	1.43663e6	−	898380.i	1.95643	−	1.22343i
$223$	−390919.			−0.526411			−0.263205	−	0.964740i	$-0.584780\pi$
$223$	−390919.			−0.526411			−0.263205	+	0.964740i	$0.584780\pi$
$224$	−193675.	−	70123.6i	−0.257902	−	0.0933779i
$225$	−627300.			−0.826075
$226$	−961980.	+	601562.i	−1.25284	+	0.783446i
$227$	−1.08573e6			−1.39848			−0.699239	−	0.714888i	$-0.746478\pi$
$227$	−1.08573e6			−1.39848			−0.699239	+	0.714888i	$0.746478\pi$
$228$	−920966.	+	829433.i	−1.17329	+	1.05668i
$229$	−300421.			−0.378566			−0.189283	−	0.981923i	$-0.560616\pi$
$229$	−300421.			−0.378566			−0.189283	+	0.981923i	$0.560616\pi$
$230$	−283287.	+	177150.i	−0.353108	+	0.220811i
$231$	161865.			0.199583
$232$	1038.94	+	9789.86i	0.00126728	+	0.0119414i
$233$	−790652.			−0.954104			−0.477052	−	0.878875i	$-0.658295\pi$
$233$	−790652.			−0.954104			−0.477052	+	0.878875i	$0.658295\pi$
$234$	207589.	−	129813.i	0.247837	−	0.154981i
$235$		−	994787.i		−	1.17506i
$236$	320443.	−	658128.i	0.374516	−	0.769185i
$237$	1.40453e6			1.62427
$238$	26050.1	−	16290.1i	0.0298103	−	0.0186415i
$239$			663704.i			0.751588i	0.926703	+	0.375794i	$0.122630\pi$
$239$			663704.i			0.751588i	−0.926703	+	0.375794i	$0.877370\pi$
$240$	580815.	+	741352.i	0.650893	+	0.830800i
$241$			1.16859e6i			1.29604i	0.761622	+	0.648021i	$0.224403\pi$
$241$			1.16859e6i			1.29604i	−0.761622	+	0.648021i	$0.775597\pi$
$242$	−380458.	−	608405.i	−0.417608	−	0.667812i
$243$	1.09990e6			1.19491
$244$	444831.	−	913597.i	0.478322	−	0.982381i
$245$	580752.			0.618124
$246$	668823.	−	418240.i	0.704650	−	0.440644i
$247$	70410.4	−	173993.i	0.0734336	−	0.181463i
$248$	767003.	−	81397.6i	0.791895	−	0.0840392i
$249$			364022.i			0.372074i
$250$	543966.	+	869876.i	0.550455	+	0.880253i
$251$			789035.i			0.790518i	0.918570	+	0.395259i	$0.129345\pi$
$251$			789035.i			0.790518i	−0.918570	+	0.395259i	$0.870655\pi$
$252$	−371213.	−	180744.i	−0.368232	−	0.179293i
$253$	292333.			0.287129
$254$	−23117.5	−	36968.1i	−0.0224831	−	0.0359536i
$255$	−140477.			−0.135287
$256$	−250936.	+	1.01811e6i	−0.239311	+	0.970943i
$257$			712224.i			0.672642i	0.941747	+	0.336321i	$0.109183\pi$
$257$			712224.i			0.672642i	−0.941747	+	0.336321i	$0.890817\pi$
$258$	2.27134e6	−	1.42036e6i	2.12439	−	1.32846i
$259$	432723.			0.400830
$260$	−128233.	−	62436.7i	−0.117643	−	0.0572805i
$261$			19733.6i			0.0179310i
$262$	310222.	−	193993.i	0.279203	−	0.174596i
$263$			1.57887e6i			1.40752i	0.710436	+	0.703762i	$0.248498\pi$
$263$			1.57887e6i			1.40752i	−0.710436	+	0.703762i	$0.751502\pi$
$264$	−86958.4	−	819403.i	−0.0767895	−	0.723582i
$265$			1.10023e6i			0.962428i
$266$	−311728.	+	54895.1i	−0.270130	+	0.0475696i
$267$			3.39859e6i			2.91757i
$268$	−304749.	+	625895.i	−0.259182	+	0.532310i
$269$		−	431584.i		−	0.363651i	−0.983331	−	0.181825i	$-0.941799\pi$
$269$		−	431584.i		−	0.363651i	0.983331	−	0.181825i	$-0.0582005\pi$
$270$	330590.	+	528660.i	0.275982	+	0.441333i
$271$		−	69307.9i		−	0.0573270i	−0.999589	−	0.0286635i	$-0.990875\pi$
$271$		−	69307.9i		−	0.0573270i	0.999589	−	0.0286635i	$-0.00912513\pi$
$272$	−96459.3	−	123121.i	−0.0790536	−	0.100904i
$273$	104402.			0.0847817
$274$	−550734.	−	880700.i	−0.443165	−	0.708683i
$275$		−	319725.i		−	0.254944i
$276$	−1.11941e6	−	545040.i	−0.884535	−	0.430681i
$277$	−559473.			−0.438107			−0.219053	−	0.975713i	$-0.570297\pi$
$277$	−559473.			−0.438107			−0.219053	+	0.975713i	$0.570297\pi$
$278$	−263941.	+	165052.i	−0.204831	+	0.128088i
$279$	1.54606e6			1.18909
$280$	25381.9	+	239172.i	0.0193477	+	0.182312i
$281$		−	1.35111e6i		−	1.02076i	−0.859949	−	0.510381i	$-0.829505\pi$
$281$		−	1.35111e6i		−	1.02076i	0.859949	−	0.510381i	$-0.170495\pi$
$282$	3.14302e6	−	1.96545e6i	2.35356	−	1.47177i
$283$		−	1.88088e6i		−	1.39603i	−0.716084	−	0.698014i	$-0.754067\pi$
$283$		−	1.88088e6i		−	1.39603i	0.716084	−	0.698014i	$-0.245933\pi$
$284$	180681.	−	371084.i	0.132928	−	0.273009i
$285$	1.34153e6	+	542884.i	0.978339	+	0.395909i
$286$	66163.8	+	105805.i	0.0478306	+	0.0764877i
$287$	201454.			0.144368
$288$	−715546.	+	1.97628e6i	−0.508342	+	1.40400i
$289$	−1.39653e6			−0.983569
$290$	9746.66	−	6094.95i	0.00680552	−	0.00425574i
$291$		−	843219.i		−	0.583725i
$292$	−467639.	+	960441.i	−0.320962	+	0.659194i
$293$		−	132314.i		−	0.0900404i	−0.998986	−	0.0450202i	$-0.985665\pi$
$293$		−	132314.i		−	0.0900404i	0.998986	−	0.0450202i	$-0.0143352\pi$
$294$	1.14742e6	+	1.83488e6i	0.774201	+	1.23805i
$295$	−854725.			−0.571836
$296$	−232471.	−	2.19055e6i	−0.154219	−	1.45320i
$297$		−	545540.i		−	0.358869i
$298$	1.34776e6	+	2.15525e6i	0.879166	+	1.40591i
$299$	188553.			0.121971
$300$	−596111.	+	1.22430e6i	−0.382405	+	0.785387i
$301$	684142.			0.435242
$302$	−988368.	−	1.58054e6i	−0.623593	−	0.997212i
$303$	2.76560e6			1.73054
$304$	445362.	+	1.54856e6i	0.276395	+	0.961044i
$305$	−1.18651e6			−0.730333
$306$	−166225.	−	265816.i	−0.101483	−	0.162285i
$307$	888116.			0.537804			0.268902	−	0.963168i	$-0.413339\pi$
$307$	888116.			0.537804			0.268902	+	0.963168i	$0.413339\pi$
$308$	92122.3	−	189201.i	0.0553335	−	0.113644i
$309$	−2.86094e6			−1.70456
$310$	−477519.	−	763618.i	−0.282219	−	0.451307i
$311$		−	2.69154e6i		−	1.57798i	−0.614409	−	0.788988i	$-0.710606\pi$
$311$		−	2.69154e6i		−	1.57798i	0.614409	−	0.788988i	$-0.289394\pi$
$312$	−56087.7	−	528510.i	−0.0326198	−	0.307374i
$313$	1.10940e6			0.640070			0.320035	−	0.947406i	$-0.396305\pi$
$313$	1.10940e6			0.640070			0.320035	+	0.947406i	$0.396305\pi$
$314$	−269541.	−	431033.i	−0.154277	−	0.246710i
$315$			482102.i			0.273756i
$316$	799359.	−	1.64173e6i	0.450323	−	0.924877i
$317$			1.48050e6i			0.827484i	0.910394	+	0.413742i	$0.135778\pi$
$317$			1.48050e6i			0.827484i	−0.910394	+	0.413742i	$0.864222\pi$
$318$	−3.47616e6	+	2.17377e6i	−1.92767	+	1.20544i
$319$	−10057.9			−0.00553388
$320$	1.19711e6	−	256980.i	0.653523	−	0.140289i
$321$	−3.18500e6			−1.72523
$322$	−168586.	−	269592.i	−0.0906112	−	0.144900i
$323$	−222796.	−	90159.9i	−0.118823	−	0.0480847i
$324$	218022.	−	447775.i	0.115382	−	0.236972i
$325$		−	206221.i		−	0.108299i
$326$	1.58988e6	−	994209.i	0.828551	−	0.518124i
$327$			3.03880e6i			1.57157i
$328$	−108226.	−	1.01981e6i	−0.0555455	−	0.523401i
$329$	946697.			0.482193
$330$	−815787.	+	510142.i	−0.412375	+	0.257873i
$331$	−2.75880e6			−1.38404			−0.692022	−	0.721877i	$-0.743280\pi$
$331$	−2.75880e6			−1.38404			−0.692022	+	0.721877i	$0.743280\pi$
$332$	425499.	+	207176.i	0.211862	+	0.103156i
$333$		−	4.41553e6i		−	2.18209i
$334$	−1.03506e6	−	1.65520e6i	−0.507690	−	0.811865i
$335$	812864.			0.395736
$336$	−705513.	+	552737.i	−0.340923	+	0.267098i
$337$			2.02688e6i			0.972193i	0.873905	+	0.486097i	$0.161580\pi$
$337$			2.02688e6i			0.972193i	−0.873905	+	0.486097i	$0.838420\pi$
$338$	−1.07094e6	−	1.71258e6i	−0.509886	−	0.815378i
$339$			4.93677e6i			2.33315i
$340$	−79949.6	+	164201.i	−0.0375076	+	0.0770334i
$341$			788001.i			0.366979i
$342$	560153.	+	3.18090e6i	0.258965	+	1.47056i
$343$			1.15032e6i			0.527937i
$344$	−367541.	−	3.46330e6i	−0.167459	−	1.57796i
$345$			1.45380e6i			0.657591i
$346$	−2.17435e6	+	1.35970e6i	−0.976424	+	0.610594i
$347$			1.96009e6i			0.873879i	0.899491	+	0.436940i	$0.143938\pi$
$347$			1.96009e6i			0.873879i	−0.899491	+	0.436940i	$0.856062\pi$
$348$	38513.9	+	18752.4i	0.0170478	+	0.00830059i
$349$	2.81538e6			1.23730			0.618648	−	0.785668i	$-0.287681\pi$
$349$	2.81538e6			1.23730			0.618648	+	0.785668i	$0.287681\pi$
$350$	−294854.	+	184383.i	−0.128658	+	0.0804545i
$351$		−	351870.i		−	0.152446i
$352$	−1.00728e6	−	364702.i	−0.433304	−	0.156885i
$353$	−3.68738e6			−1.57500			−0.787500	−	0.616314i	$-0.788625\pi$
$353$	−3.68738e6			−1.57500			−0.787500	+	0.616314i	$0.788625\pi$
$354$	−1.68872e6	−	2.70049e6i	−0.716225	−	1.14534i
$355$	−481935.			−0.202963
$356$	3.97256e6	+	1.93424e6i	1.66129	+	0.808883i
$357$		−	133686.i		−	0.0555156i
$358$	1.05355e6	+	1.68478e6i	0.434459	+	0.694760i
$359$		−	339534.i		−	0.139042i	−0.997580	−	0.0695211i	$-0.977853\pi$
$359$		−	339534.i		−	0.139042i	0.997580	−	0.0695211i	$-0.0221471\pi$
$360$	2.44053e6	−	258999.i	0.992492	−	0.105327i
$361$	1.77924e6	+	1.72203e6i	0.718565	+	0.695460i
$362$	1.57335e6	−	983871.i	0.631034	−	0.394609i
$363$	−3.12226e6			−1.24366
$364$	59418.3	−	122034.i	0.0235054	−	0.0482755i
$365$	1.24734e6			0.490066
$366$	−2.34424e6	−	3.74876e6i	−0.914742	−	1.46280i
$367$		−	4.11001e6i		−	1.59286i	−0.604731	−	0.796430i	$-0.706719\pi$
$367$		−	4.11001e6i		−	1.59286i	0.604731	−	0.796430i	$-0.293281\pi$
$368$	−1.27418e6	+	998258.i	−0.490467	+	0.384258i
$369$		−	2.05564e6i		−	0.785927i
$370$	−2.18089e6	+	1.36379e6i	−0.828188	+	0.517897i
$371$	−1.04704e6			−0.394938
$372$	1.46919e6	−	3.01743e6i	0.550453	−	1.13052i
$373$		−	1.45363e6i		−	0.540981i	−0.962723	−	0.270491i	$-0.912814\pi$
$373$		−	1.45363e6i		−	0.540981i	0.962723	−	0.270491i	$-0.0871859\pi$
$374$	135482.	−	84722.2i	0.0500846	−	0.0313197i
$375$	4.46411e6			1.63929
$376$	−508592.	−	4.79242e6i	−0.185524	−	1.74818i
$377$	−6487.28			−0.00235076
$378$	−503103.	+	314609.i	−0.181104	+	0.113251i
$379$	−2.73757e6			−0.978964			−0.489482	−	0.872013i	$-0.662814\pi$
$379$	−2.73757e6			−0.978964			−0.489482	+	0.872013i	$0.662814\pi$
$380$	1.39808e6	−	1.25912e6i	0.496674	−	0.447311i
$381$	−189716.			−0.0669563
$382$	4.29887e6	−	2.68825e6i	1.50729	−	0.942563i
$383$	−754121.			−0.262690			−0.131345	−	0.991337i	$-0.541930\pi$
$383$	−754121.			−0.262690			−0.131345	+	0.991337i	$0.541930\pi$
$384$	3.17712e6	+	3.27454e6i	1.09953	+	1.13324i
$385$	−245720.			−0.0844868
$386$	−3.93626e6	+	2.46149e6i	−1.34467	+	0.840871i
$387$		−	6.98103e6i		−	2.36942i
$388$	−985626.	−	479901.i	−0.332378	−	0.161835i
$389$	2.55373e6			0.855660			0.427830	−	0.903859i	$-0.359278\pi$
$389$	2.55373e6			0.855660			0.427830	+	0.903859i	$0.359278\pi$
$390$	−526178.	+	329039.i	−0.175175	+	0.109543i
$391$		−	241440.i		−	0.0798671i
$392$	2.79779e6	−	296914.i	0.919603	−	0.0975922i
$393$		−	1.59202e6i		−	0.519958i
$394$	77568.1	+	124042.i	0.0251735	+	0.0402558i
$395$	−2.13215e6			−0.687583
$396$	−1.93062e6	−	940022.i	−0.618671	−	0.301231i
$397$	3.10038e6			0.987275			0.493638	−	0.869668i	$-0.335667\pi$
$397$	3.10038e6			0.987275			0.493638	+	0.869668i	$0.335667\pi$
$398$	−4.59453e6	+	2.87313e6i	−1.45390	+	0.909176i
$399$	−516640.	+	1.27668e6i	−0.162463	+	0.401467i
$400$	1.09180e6	+	1.39357e6i	0.341187	+	0.435490i
$401$			4.01172e6i			1.24586i	0.782277	+	0.622931i	$0.214058\pi$
$401$			4.01172e6i			1.24586i	−0.782277	+	0.622931i	$0.785942\pi$
$402$	1.60601e6	+	2.56823e6i	0.495660	+	0.792628i
$403$			508256.i			0.155891i
$404$	1.57398e6	−	3.23266e6i	0.479785	−	0.985387i
$405$	−581535.			−0.176172
$406$	5800.30	+	9275.48i	0.00174637	+	0.00279268i
$407$	2.25053e6			0.673438
$408$	−676752.	+	71819.8i	−0.201270	+	0.0213596i
$409$		−	5.50569e6i		−	1.62743i	−0.581261	−	0.813717i	$-0.697440\pi$
$409$		−	5.50569e6i		−	1.62743i	0.581261	−	0.813717i	$-0.302560\pi$
$410$	−1.01531e6	+	634911.i	−0.298290	+	0.186532i
$411$	−4.51965e6			−1.31978
$412$	−1.62825e6	+	3.34411e6i	−0.472582	+	0.970594i
$413$		−	813405.i		−	0.234656i
$414$	−2.75094e6	+	1.72026e6i	−0.788823	+	0.493280i
$415$		−	552605.i		−	0.157505i
$416$	−649688.	−	235231.i	−0.184065	−	0.0666440i
$417$			1.35451e6i			0.381455i
$418$	−1.62125e6	+	285501.i	−0.453847	+	0.0799221i
$419$			3.74656e6i			1.04255i	0.853388	+	0.521276i	$0.174544\pi$
$419$			3.74656e6i			1.04255i	−0.853388	+	0.521276i	$0.825456\pi$
$420$	940916.	+	458132.i	0.260272	+	0.126727i
$421$			2.72843e6i			0.750254i	0.926974	+	0.375127i	$0.122401\pi$
$421$			2.72843e6i			0.750254i	−0.926974	+	0.375127i	$0.877599\pi$
$422$	1.09490e6	+	1.75089e6i	0.299289	+	0.478605i
$423$		−	9.66015e6i		−	2.62502i
$424$	562500.	+	5.30039e6i	0.151952	+	1.43184i
$425$	−264064.			−0.0709148
$426$	−952181.	−	1.52267e6i	−0.254212	−	0.406519i
$427$		−	1.12915e6i		−	0.299696i
$428$	−1.81268e6	+	3.72290e6i	−0.478313	+	0.982363i
$429$	542979.			0.142443
$430$	−3.44802e6	+	2.15618e6i	−0.899289	+	0.562358i
$431$	3.80201e6			0.985870			0.492935	−	0.870066i	$-0.335924\pi$
$431$	3.80201e6			0.985870			0.492935	+	0.870066i	$0.335924\pi$
$432$	1.86291e6	+	2.37782e6i	0.480267	+	0.613012i
$433$		−	4.66140e6i		−	1.19480i	−0.801942	−	0.597401i	$-0.796200\pi$
$433$		−	4.66140e6i		−	1.19480i	0.801942	−	0.597401i	$-0.203800\pi$
$434$	726703.	−	454434.i	0.185196	−	0.115810i
$435$		−	50018.8i		−	0.0126739i
$436$	3.55201e6	+	1.72947e6i	0.894866	+	0.435711i
$437$	−933066.	+	2.30572e6i	−0.233727	+	0.577568i
$438$	2.46444e6	+	3.94097e6i	0.613807	+	0.981563i
$439$	−2.23839e6			−0.554338			−0.277169	−	0.960821i	$-0.589396\pi$
$439$	−2.23839e6			−0.554338			−0.277169	+	0.960821i	$0.589396\pi$
$440$	132008.	+	1.24390e6i	0.0325063	+	0.306304i
$441$	5.63955e6			1.38086
$442$	87385.4	−	54645.3i	0.0212757	−	0.0133045i
$443$			354337.i			0.0857842i	0.999080	+	0.0428921i	$0.0136572\pi$
$443$			354337.i			0.0857842i	−0.999080	+	0.0428921i	$0.986343\pi$
$444$	−8.61775e6	−	4.19599e6i	−2.07461	−	1.01013i
$445$		−	5.15925e6i		−	1.23506i
$446$	1.17248e6	+	1.87496e6i	0.279105	+	0.446328i
$447$	1.10605e7			2.61822
$448$	244557.	+	1.13924e6i	0.0575684	+	0.268177i
$449$			3.20959e6i			0.751335i	0.926755	+	0.375667i	$0.122587\pi$
$449$			3.20959e6i			0.751335i	−0.926755	+	0.375667i	$0.877413\pi$
$450$	1.88146e6	+	3.00871e6i	0.437988	+	0.700404i
$451$	1.04773e6			0.242554
$452$	5.77051e6	+	2.80966e6i	1.32852	+	0.646857i
$453$	−8.11113e6			−1.85710
$454$	3.25641e6	+	5.20744e6i	0.741479	+	1.18573i
$455$	−158488.			−0.0358895
$456$	6.74043e6	+	1.92949e6i	1.51801	+	0.434542i
$457$	7.37437e6			1.65171			0.825857	−	0.563880i	$-0.190692\pi$
$457$	7.37437e6			1.65171			0.825857	+	0.563880i	$0.190692\pi$
$458$	901050.	+	1.44090e6i	0.200718	+	0.320975i
$459$	−450567.			−0.0998222
$460$	1.69932e6	+	827400.i	0.374439	+	0.182314i
$461$	−1.81438e6			−0.397626			−0.198813	−	0.980037i	$-0.563709\pi$
$461$	−1.81438e6			−0.397626			−0.198813	+	0.980037i	$0.563709\pi$
$462$	−485480.	−	776350.i	−0.105820	−	0.169220i
$463$		−	4.76937e6i		−	1.03397i	−0.855994	−	0.516985i	$-0.827054\pi$
$463$		−	4.76937e6i		−	1.03397i	0.855994	−	0.516985i	$-0.172946\pi$
$464$	43838.8	−	34345.7i	0.00945287	−	0.00740589i
$465$	−3.91880e6			−0.840467
$466$	2.37139e6	+	3.79218e6i	0.505870	+	0.808956i
$467$		−	545828.i		−	0.115815i	−0.998322	−	0.0579073i	$-0.981557\pi$
$467$		−	545828.i		−	0.115815i	0.998322	−	0.0579073i	$-0.0184428\pi$
$468$	−1.24524e6	−	606308.i	−0.262808	−	0.127961i
$469$			773567.i			0.162393i
$470$	−4.77128e6	+	2.98365e6i	−0.996299	+	0.623023i
$471$	−2.21201e6			−0.459447
$472$	−4.11767e6	+	436984.i	−0.850739	+	0.0902840i
$473$	3.55812e6			0.731254
$474$	−4.21259e6	−	6.73650e6i	−0.861198	−	1.37717i
$475$	2.52177e6	+	1.02050e6i	0.512828	+	0.207528i
$476$	−156263.	−	76084.6i	−0.0316111	−	0.0153915i
$477$			1.06841e7i			2.15001i
$478$	3.18331e6	−	1.99064e6i	0.637249	−	0.398495i
$479$			1.80069e6i			0.358591i	0.983795	+	0.179296i	$0.0573819\pi$
$479$			1.80069e6i			0.358591i	−0.983795	+	0.179296i	$0.942618\pi$
$480$	1.81370e6	−	5.00928e6i	0.359304	−	0.992367i
$481$	1.45158e6			0.286073
$482$	5.60488e6	−	3.50494e6i	1.09888	−	0.687168i
$483$	−1.38352e6			−0.269846
$484$	−1.77697e6	+	3.64956e6i	−0.344800	+	0.708154i
$485$			1.28005e6i			0.247100i
$486$	−3.29891e6	−	5.27542e6i	−0.633549	−	1.01313i
$487$	−5.50150e6			−1.05113			−0.525567	−	0.850752i	$-0.676147\pi$
$487$	−5.50150e6			−1.05113			−0.525567	+	0.850752i	$0.676147\pi$
$488$	−5.71604e6	+	606610.i	−1.08654	+	0.115308i
$489$		−	8.15906e6i		−	1.54301i
$490$	−1.74184e6	−	2.78545e6i	−0.327732	−	0.524089i
$491$			3.27324e6i			0.612737i	0.951913	+	0.306369i	$0.0991140\pi$
$491$			3.27324e6i			0.612737i	−0.951913	+	0.306369i	$0.900886\pi$
$492$	−4.01199e6	−	1.95344e6i	−0.747217	−	0.363820i
$493$			8306.90i			0.00153929i
$494$	−1.04570e6	+	184147.i	−0.192792	+	0.0339505i
$495$			2.50734e6i			0.459939i
$496$	−2.69087e6	−	3.43462e6i	−0.491121	−	0.626866i
$497$		−	458637.i		−	0.0832872i
$498$	1.74595e6	−	1.09181e6i	0.315470	−	0.197275i
$499$		−	7.04077e6i		−	1.26581i	−0.774229	−	0.632905i	$-0.781862\pi$
$499$		−	7.04077e6i		−	1.26581i	0.774229	−	0.632905i	$-0.218138\pi$
$500$	2.54066e6	−	5.21802e6i	0.454487	−	0.933428i
$501$	−8.49429e6			−1.51193
$502$	3.78443e6	−	2.36654e6i	0.670257	−	0.419136i
$503$			2.17610e6i			0.383494i	0.981444	+	0.191747i	$0.0614153\pi$
$503$			2.17610e6i			0.383494i	−0.981444	+	0.191747i	$0.938585\pi$
$504$	246478.	+	2.32254e6i	0.0432217	+	0.407275i
$505$	−4.19833e6			−0.732568
$506$	−876791.	−	1.40211e6i	−0.152237	−	0.243448i
$507$	−8.78876e6			−1.51848
$508$	−107973.	+	221756.i	−0.0185633	+	0.0381255i
$509$			1.87029e6i			0.319974i	0.987119	+	0.159987i	$0.0511453\pi$
$509$			1.87029e6i			0.319974i	−0.987119	+	0.159987i	$0.948855\pi$
$510$	421331.	+	673766.i	0.0717295	+	0.114705i
$511$			1.18704e6i			0.201101i
$512$	5.63575e6	−	1.85004e6i	0.950117	−	0.311894i
$513$	4.30284e6	+	1.74125e6i	0.721875	+	0.292125i
$514$	3.41602e6	−	2.13617e6i	0.570313	−	0.356638i
$515$	4.34307e6			0.721570
$516$	−1.36248e7	−	6.63394e6i	−2.25272	−	1.09685i
$517$	4.92363e6			0.810138
$518$	−1.29786e6	−	2.07546e6i	−0.212522	−	0.339852i
$519$			1.11585e7i			1.81839i
$520$	85144.2	+	802307.i	0.0138085	+	0.130116i
$521$			8.14120e6i			1.31400i	0.753892	+	0.656998i	$0.228174\pi$
$521$			8.14120e6i			1.31400i	−0.753892	+	0.656998i	$0.771826\pi$
$522$	94647.6	−	59186.6i	0.0152031	−	0.00950709i
$523$	465737.			0.0744538			0.0372269	−	0.999307i	$-0.488148\pi$
$523$	465737.			0.0744538			0.0372269	+	0.999307i	$0.488148\pi$
$524$	−1.86089e6	−	906069.i	−0.296069	−	0.144156i
$525$			1.51316e6i			0.239599i
$526$	7.57267e6	−	4.73547e6i	1.19340	−	0.746275i
$527$	650818.			0.102078
$528$	−3.66927e6	+	2.87470e6i	−0.572789	+	0.448754i
$529$	3.93767e6			0.611787
$530$	5.27700e6	−	3.29990e6i	0.816014	−	0.510284i
$531$	−8.30004e6			−1.27745
$532$	1.19826e6	+	1.33049e6i	0.183557	+	0.203813i
$533$	675780.			0.103036
$534$	1.63006e7	−	1.01934e7i	2.47372	−	1.54691i
$535$	4.83501e6			0.730320
$536$	3.91600e6	−	415582.i	0.588749	−	0.0624806i
$537$	8.64608e6			1.29385
$538$	−2.06999e6	+	1.29444e6i	−0.308328	+	0.192809i
$539$			2.87439e6i			0.426161i
$540$	1.54406e6	−	3.17121e6i	0.227866	−	0.467994i
$541$	4.56771e6			0.670974			0.335487	−	0.942045i	$-0.391099\pi$
$541$	4.56771e6			0.670974			0.335487	+	0.942045i	$0.391099\pi$
$542$	−332420.	+	207874.i	−0.0486058	+	0.0303950i
$543$		−	8.07423e6i		−	1.17517i
$544$	−301211.	+	831920.i	−0.0436389	+	0.120527i
$545$		−	4.61307e6i		−	0.665271i
$546$	−313132.	−	500741.i	−0.0449516	−	0.0718839i
$547$	−499953.			−0.0714431			−0.0357216	−	0.999362i	$-0.511373\pi$
$547$	−499953.			−0.0714431			−0.0357216	+	0.999362i	$0.511373\pi$
$548$	−2.57227e6	+	5.28295e6i	−0.365902	+	0.751493i
$549$	−1.15219e7			−1.63152
$550$	−1.53349e6	+	958948.i	−0.216159	+	0.135172i
$551$	32102.7	−	79329.6i	0.00450466	−	0.0111316i
$552$	743264.	+	7.00372e6i	0.103823	+	0.978320i
$553$		−	2.02908e6i		−	0.282153i
$554$	1.67802e6	+	2.68339e6i	0.232286	+	0.371458i
$555$			1.11921e7i			1.54233i
$556$	1.58327e6	+	770895.i	0.217204	+	0.105757i
$557$	−9.53980e6			−1.30287			−0.651435	−	0.758704i	$-0.725833\pi$
$557$	−9.53980e6			−1.30287			−0.651435	+	0.758704i	$0.725833\pi$
$558$	−4.63707e6	−	7.41532e6i	−0.630462	−	1.00819i
$559$	2.29497e6			0.310633
$560$	1.07101e6	−	839085.i	0.144319	−	0.113067i
$561$		−	695280.i		−	0.0932723i
$562$	−6.48028e6	+	4.05236e6i	−0.865473	+	0.541212i
$563$	5.85980e6			0.779133			0.389567	−	0.920998i	$-0.372625\pi$
$563$	5.85980e6			0.779133			0.389567	+	0.920998i	$0.372625\pi$
$564$	−1.88536e7	−	9.17985e6i	−2.49573	−	1.21517i
$565$		−	7.49428e6i		−	0.987664i
$566$	−9.02120e6	+	5.64129e6i	−1.18365	+	0.740180i
$567$		−	553421.i		−	0.0722933i
$568$	−2.32174e6	+	246393.i	−0.301955	+	0.0320447i
$569$			1.27882e6i			0.165588i	0.996567	+	0.0827940i	$0.0263844\pi$
$569$			1.27882e6i			0.165588i	−0.996567	+	0.0827940i	$0.973616\pi$
$570$	−1.41982e6	−	8.06263e6i	−0.183040	−	1.03942i
$571$			3.42245e6i			0.439285i	0.975580	+	0.219642i	$0.0704891\pi$
$571$			3.42245e6i			0.439285i	−0.975580	+	0.219642i	$0.929511\pi$
$572$	309026.	−	634680.i	0.0394916	−	0.0811082i
$573$		−	2.20613e7i		−	2.80702i
$574$	−604217.	−	966227.i	−0.0765444	−	0.122405i
$575$			2.73280e6i			0.344698i
$576$	1.16249e7	−	2.49547e6i	1.45993	−	0.313398i
$577$	−9.67549e6			−1.20985			−0.604927	−	0.796281i	$-0.706798\pi$
$577$	−9.67549e6			−1.20985			−0.604927	+	0.796281i	$0.706798\pi$
$578$	4.18859e6	+	6.69813e6i	0.521493	+	0.833938i
$579$			2.02004e7i			2.50417i
$580$	−58466.1	−	28467.2i	−0.00721663	−	0.00351378i
$581$	525891.			0.0646331
$582$	−4.04431e6	+	2.52906e6i	−0.494923	+	0.309493i
$583$	−5.44550e6			−0.663539
$584$	6.00912e6	−	637714.i	0.729086	−	0.0773737i
$585$			1.61722e6i			0.195380i
$586$	−634616.	+	396849.i	−0.0763426	+	0.0477398i
$587$		−	8.70606e6i		−	1.04286i	−0.853294	−	0.521430i	$-0.825399\pi$
$587$		−	8.70606e6i		−	1.04286i	0.853294	−	0.521430i	$-0.174601\pi$
$588$	5.35915e6	−	1.10067e7i	0.639224	−	1.31284i
$589$	−6.21521e6	−	2.51514e6i	−0.738189	−	0.298726i
$590$	2.56357e6	+	4.09950e6i	0.303190	+	0.484843i
$591$	636570.			0.0749683
$592$	−9.80925e6	+	7.68509e6i	−1.15035	+	0.901249i
$593$	−1.31815e7			−1.53932			−0.769660	−	0.638453i	$-0.779574\pi$
$593$	−1.31815e7			−1.53932			−0.769660	+	0.638453i	$0.779574\pi$
$594$	−2.61656e6	+	1.63623e6i	−0.304274	+	0.190274i
$595$			202942.i			0.0235007i
$596$	6.29486e6	−	1.29284e7i	0.725889	−	1.49084i
$597$			2.35786e7i			2.70759i
$598$	−565525.	−	904352.i	−0.0646694	−	0.103415i
$599$	1.39991e7			1.59416			0.797082	−	0.603871i	$-0.206376\pi$
$599$	1.39991e7			1.59416			0.797082	+	0.603871i	$0.206376\pi$
$600$	7.65998e6	−	812909.i	0.868659	−	0.0921858i
$601$		−	3.23278e6i		−	0.365081i	−0.983198	−	0.182541i	$-0.941568\pi$
$601$		−	3.23278e6i		−	0.365081i	0.983198	−	0.182541i	$-0.0584321\pi$
$602$	−2.05194e6	−	3.28134e6i	−0.230767	−	0.369028i
$603$	7.89353e6			0.884053
$604$	−4.61629e6	+	9.48098e6i	−0.514874	+	1.05745i
$605$	4.73976e6			0.526464
$606$	−8.29482e6	−	1.32646e7i	−0.917541	−	1.46728i
$607$	−3.71893e6			−0.409681			−0.204841	−	0.978795i	$-0.565668\pi$
$607$	−3.71893e6			−0.409681			−0.204841	+	0.978795i	$0.565668\pi$
$608$	6.09154e6	−	6.78065e6i	0.668295	−	0.743896i
$609$	47600.7			0.00520080
$610$	3.55868e6	+	5.69082e6i	0.387226	+	0.619227i
$611$	3.17571e6			0.344142
$612$	−776373.	+	1.59452e6i	−0.0837899	+	0.172088i
$613$	−1.26975e7			−1.36479			−0.682395	−	0.730984i	$-0.739061\pi$
$613$	−1.26975e7			−1.36479			−0.682395	+	0.730984i	$0.739061\pi$
$614$	−2.66372e6	−	4.25965e6i	−0.285146	−	0.455988i
$615$			5.21045e6i			0.555505i
$616$	−1.18376e6	+	125626.i	−0.125694	+	0.0133391i
$617$	−1.09244e6			−0.115527			−0.0577635	−	0.998330i	$-0.518397\pi$
$617$	−1.09244e6			−0.115527			−0.0577635	+	0.998330i	$0.518397\pi$
$618$	8.58079e6	+	1.37219e7i	0.903766	+	1.44525i
$619$		−	1.38672e7i		−	1.45466i	−0.686285	−	0.727332i	$-0.740760\pi$
$619$		−	1.38672e7i		−	1.45466i	0.686285	−	0.727332i	$-0.259240\pi$
$620$	−2.23031e6	+	4.58062e6i	−0.233016	+	0.478570i
$621$			4.66292e6i			0.485209i
$622$	−1.29094e7	+	8.07271e6i	−1.33792	+	0.836649i
$623$	4.90984e6			0.506812
$624$	−2.36666e6	+	1.85417e6i	−0.243318	+	0.190628i
$625$	−1.37415e6			−0.140712
$626$	−3.32741e6	−	5.32099e6i	−0.339368	−	0.542696i
$627$	−2.68697e6	+	6.63982e6i	−0.272956	+	0.674508i
$628$	−1.25892e6	+	2.58558e6i	−0.127380	+	0.261613i
$629$		−	1.85873e6i		−	0.187322i
$630$	2.31230e6	−	1.44596e6i	0.232109	−	0.145146i
$631$		−	8.68724e6i		−	0.868577i	−0.900774	−	0.434289i	$-0.857000\pi$
$631$		−	8.68724e6i		−	0.868577i	0.900774	−	0.434289i	$-0.143000\pi$
$632$	−1.02717e7	+	1.09008e6i	−1.02294	+	0.108559i
$633$	8.98536e6			0.891304
$634$	7.10087e6	−	4.44044e6i	0.701599	−	0.438736i
$635$	287999.			0.0283437
$636$	2.08520e7	+	1.01529e7i	2.04412	+	0.995281i
$637$			1.85397e6i			0.181031i
$638$	30166.5	+	48240.4i	0.00293409	+	0.00469201i
$639$	−4.67996e6			−0.453409
$640$	−4.82304e6	−	4.97093e6i	−0.465447	−	0.479720i
$641$		−	1.02590e7i		−	0.986187i	−0.869976	−	0.493094i	$-0.835866\pi$
$641$		−	1.02590e7i		−	0.986187i	0.869976	−	0.493094i	$-0.164134\pi$
$642$	9.55275e6	+	1.52762e7i	0.914726	+	1.46277i
$643$		−	1.81124e7i		−	1.72762i	−0.503816	−	0.863811i	$-0.668071\pi$
$643$		−	1.81124e7i		−	1.72762i	0.503816	−	0.863811i	$-0.331929\pi$
$644$	−787401.	+	1.61717e6i	−0.0748137	+	0.153653i
$645$			1.76949e7i			1.67474i
$646$	235798.	+	1.33901e6i	0.0222310	+	0.126241i
$647$			4.32480e6i			0.406167i	0.979161	+	0.203084i	$0.0650964\pi$
$647$			4.32480e6i			0.406167i	−0.979161	+	0.203084i	$0.934904\pi$
$648$	−2.80156e6	+	297314.i	−0.262097	+	0.0278149i
$649$		−	4.23040e6i		−	0.394248i
$650$	−989092.	+	618516.i	−0.0918234	+	0.0574206i
$651$		−	3.72935e6i		−	0.344890i
$652$	−9.53700e6	−	4.64357e6i	−0.878603	−	0.427792i
$653$	1.62050e7			1.48719			0.743594	−	0.668631i	$-0.233120\pi$
$653$	1.62050e7			1.48719			0.743594	+	0.668631i	$0.233120\pi$
$654$	1.45749e7	−	9.11425e6i	1.33249	−	0.833252i
$655$			2.41678e6i			0.220107i
$656$	−4.56669e6	+	3.57779e6i	−0.414325	+	0.324605i
$657$	1.21127e7			1.09478
$658$	−2.83942e6	−	4.54062e6i	−0.255661	−	0.408837i
$659$	−1.58461e7			−1.42137			−0.710687	−	0.703508i	$-0.751616\pi$
$659$	−1.58461e7			−1.42137			−0.710687	+	0.703508i	$0.751616\pi$
$660$	4.89356e6	+	2.38268e6i	0.437286	+	0.212915i
$661$		−	9.57271e6i		−	0.852180i	−0.904681	−	0.426090i	$-0.859891\pi$
$661$		−	9.57271e6i		−	0.852180i	0.904681	−	0.426090i	$-0.140109\pi$
$662$	8.27443e6	+	1.32320e7i	0.733826	+	1.17349i
$663$		−	448452.i		−	0.0396216i
$664$	−282523.	−	2.66219e6i	−0.0248676	−	0.234325i
$665$	784287.	−	1.93807e6i	0.0687735	−	0.169948i
$666$	−2.11781e7	+	1.32434e7i	−1.85013	+	1.15695i
$667$	85968.2			0.00748210
$668$	−4.83436e6	+	9.92884e6i	−0.419177	+	0.860909i
$669$	9.62206e6			0.831195
$670$	−2.43801e6	−	3.89872e6i	−0.209821	−	0.335533i
$671$		−	5.87253e6i		−	0.503523i
$672$	4.76712e6	+	1.72602e6i	0.407223	+	0.147442i
$673$			1.94503e7i			1.65535i	0.561208	+	0.827675i	$0.310337\pi$
$673$			1.94503e7i			1.65535i	−0.561208	+	0.827675i	$0.689663\pi$
$674$	9.72146e6	−	6.07919e6i	0.824293	−	0.515461i
$675$	5.09985e6			0.430822
$676$	−5.00195e6	+	1.02730e7i	−0.420991	+	0.864634i
$677$			2.59599e6i			0.217686i	0.994059	+	0.108843i	$0.0347146\pi$
$677$			2.59599e6i			0.217686i	−0.994059	+	0.108843i	$0.965285\pi$
$678$	2.36781e7	−	1.48068e7i	1.97821	−	1.23705i
$679$	−1.21817e6			−0.101399
$680$	1.02735e6	−	109026.i	0.0852010	−	0.00904189i
$681$	2.67240e7			2.20818
$682$	3.77947e6	−	2.36344e6i	0.311150	−	0.194574i
$683$	−5.32769e6			−0.437006			−0.218503	−	0.975836i	$-0.570117\pi$
$683$	−5.32769e6			−0.437006			−0.218503	+	0.975836i	$0.570117\pi$
$684$	1.35764e7	−	1.22271e7i	1.10954	−	0.999269i
$685$	6.86108e6			0.558684
$686$	5.51723e6	−	3.45013e6i	0.447622	−	0.279914i
$687$	7.39455e6			0.597751
$688$	−1.55086e7	+	1.21503e7i	−1.24911	+	0.978622i
$689$	−3.51232e6			−0.281868
$690$	6.97281e6	−	4.36036e6i	0.557552	−	0.348658i
$691$			1.58455e7i			1.26244i	0.775604	+	0.631220i	$0.217446\pi$
$691$			1.58455e7i			1.26244i	−0.775604	+	0.631220i	$0.782554\pi$
$692$	1.30430e7	+	6.35063e6i	1.03541	+	0.504141i
$693$	−2.38613e6			−0.188739
$694$	9.40111e6	−	5.87886e6i	0.740936	−	0.463335i
$695$		−	2.05623e6i		−	0.161476i
$696$	−25572.4	−	240967.i	−0.00200101	−	0.0188553i
$697$		−	865330.i		−	0.0674683i
$698$	−8.44415e6	−	1.35034e7i	−0.656020	−	1.04907i
$699$	1.94611e7			1.50651
$700$	1.76870e6	+	861182.i	0.136430	+	0.0664278i
$701$	2.64710e6			0.203458			0.101729	−	0.994812i	$-0.467563\pi$
$701$	2.64710e6			0.203458			0.101729	+	0.994812i	$0.467563\pi$
$702$	−1.68767e6	+	1.05536e6i	−0.129254	+	0.0808273i
$703$	−7.18321e6	+	1.77506e7i	−0.548189	+	1.35464i
$704$	1.27190e6	+	5.92503e6i	0.0967213	+	0.450566i
$705$			2.44856e7i			1.85540i
$706$	1.10595e7	+	1.76857e7i	0.835072	+	1.33540i
$707$		−	3.99537e6i		−	0.300613i
$708$	−7.88736e6	+	1.61991e7i	−0.591356	+	1.21453i
$709$	−9.79778e6			−0.732001			−0.366001	−	0.930615i	$-0.619273\pi$
$709$	−9.79778e6			−0.732001			−0.366001	+	0.930615i	$0.619273\pi$
$710$	1.44546e6	+	2.31149e6i	0.107612	+	0.172087i
$711$	−2.07048e7			−1.53602
$712$	−2.63770e6	−	2.48549e7i	−0.194996	−	1.83743i
$713$		−	6.73532e6i		−	0.496174i
$714$	−641194.	+	400962.i	−0.0470700	+	0.0294346i
$715$	−824272.			−0.0602984
$716$	4.92075e6	−	1.01063e7i	0.358714	−	0.736730i
$717$		−	1.63364e7i		−	1.18675i
$718$	−1.62850e6	+	1.01836e6i	−0.117890	+	0.0737208i
$719$		−	1.44832e7i		−	1.04483i	−0.852693	−	0.522413i	$-0.825032\pi$
$719$		−	1.44832e7i		−	1.04483i	0.852693	−	0.522413i	$-0.174968\pi$
$720$	−8.56207e6	−	1.09286e7i	−0.615528	−	0.785659i
$721$			4.13311e6i			0.296100i
$722$	2.92287e6	−	1.36986e7i	0.208673	−	0.977986i
$723$		−	2.87636e7i		−	2.04643i
$724$	−9.43784e6	−	4.59529e6i	−0.669154	−	0.325811i
$725$		−	94023.6i		−	0.00664342i
$726$	9.36457e6	+	1.49752e7i	0.659396	+	1.05446i
$727$		−	1.11083e7i		−	0.779489i	−0.920923	−	0.389745i	$-0.872563\pi$
$727$		−	1.11083e7i		−	0.779489i	0.920923	−	0.389745i	$-0.127437\pi$
$728$	−763521.	+	81028.1i	−0.0533940	+	0.00566640i
$729$	−2.32909e7			−1.62318
$730$	−3.74115e6	−	5.98261e6i	−0.259835	−	0.415512i
$731$		−	2.93869e6i		−	0.203404i
$732$	−1.09490e7	+	2.24872e7i	−0.755262	+	1.55116i
$733$	2.26383e7			1.55627			0.778133	−	0.628099i	$-0.216167\pi$
$733$	2.26383e7			1.55627			0.778133	+	0.628099i	$0.216167\pi$
$734$	−1.97127e7	+	1.23271e7i	−1.35054	+	0.844541i
$735$	−1.42946e7			−0.976009
$736$	8.60955e6	+	3.11724e6i	0.585849	+	0.212117i
$737$			4.02321e6i			0.272837i
$738$	−9.85944e6	+	6.16547e6i	−0.666364	+	0.416702i
$739$			1.18449e7i			0.797850i	0.916983	+	0.398925i	$0.130617\pi$
$739$			1.18449e7i			0.797850i	−0.916983	+	0.398925i	$0.869383\pi$
$740$	1.30822e7	+	6.36974e6i	0.878218	+	0.427605i
$741$	−1.73308e6	+	4.28264e6i	−0.115950	+	0.286528i
$742$	3.14038e6	+	5.02190e6i	0.209398	+	0.334856i
$743$	−2.25253e7			−1.49692			−0.748461	−	0.663179i	$-0.769207\pi$
$743$	−2.25253e7			−1.49692			−0.748461	+	0.663179i	$0.769207\pi$
$744$	−1.88790e7	+	2.00351e6i	−1.25039	+	0.132697i
$745$	−1.67904e7			−1.10833
$746$	−6.97202e6	+	4.35986e6i	−0.458682	+	0.286831i
$747$		−	5.36622e6i		−	0.351858i
$748$	−812702.	−	395705.i	−0.0531101	−	0.0258593i
$749$			4.60127e6i			0.299691i
$750$	−1.33891e7	−	2.14111e7i	−0.869160	−	1.38991i
$751$	4.38866e6			0.283944			0.141972	−	0.989871i	$-0.454656\pi$
$751$	4.38866e6			0.283944			0.141972	+	0.989871i	$0.454656\pi$
$752$	−2.14604e7	+	1.68132e7i	−1.38386	+	1.08419i
$753$		−	1.94213e7i		−	1.24822i
$754$	19457.2	+	31114.8i	0.00124639	+	0.00199314i
$755$	1.23131e7			0.786143
$756$	3.01790e6	+	1.46942e6i	0.192044	+	0.0935062i
$757$	7.77022e6			0.492826			0.246413	−	0.969165i	$-0.420748\pi$
$757$	7.77022e6			0.492826			0.246413	+	0.969165i	$0.420748\pi$
$758$	8.21075e6	+	1.31301e7i	0.519051	+	0.830034i
$759$	−7.19546e6			−0.453371
$760$	−1.02323e7	−	2.92908e6i	−0.642601	−	0.183949i
$761$	1.04389e7			0.653418			0.326709	−	0.945125i	$-0.394060\pi$
$761$	1.04389e7			0.653418			0.326709	+	0.945125i	$0.394060\pi$
$762$	569013.	+	909930.i	0.0355005	+	0.0567702i
$763$	4.39006e6			0.272998
$764$	−2.57871e7	−	1.25558e7i	−1.59834	−	0.778233i
$765$	2.07084e6			0.127936
$766$	2.26183e6	+	3.61697e6i	0.139280	+	0.222727i
$767$		−	2.72858e6i		−	0.167475i
$768$	6.17652e6	−	2.50596e7i	0.377868	−	1.53310i
$769$	−2.70798e7			−1.65131			−0.825656	−	0.564174i	$-0.809195\pi$
$769$	−2.70798e7			−1.65131			−0.825656	+	0.564174i	$0.809195\pi$
$770$	736985.	+	1.17854e6i	0.0447952	+	0.0716338i
$771$		−	1.75306e7i		−	1.06209i
$772$	2.36120e7	+	1.14967e7i	1.42590	+	0.694271i
$773$		−	1.19968e7i		−	0.722134i	−0.932540	−	0.361067i	$-0.882413\pi$
$773$		−	1.19968e7i		−	0.722134i	0.932540	−	0.361067i	$-0.117587\pi$
$774$	−3.34830e7	+	2.09381e7i	−2.00896	+	1.25628i
$775$	−7.36643e6			−0.440558
$776$	654436.	+	6.16670e6i	0.0390133	+	0.367619i
$777$	−1.06510e7			−0.632904
$778$	−7.65938e6	−	1.22484e7i	−0.453675	−	0.725488i
$779$	−3.34414e6	+	8.26377e6i	−0.197442	+	0.487904i
$780$	3.15632e6	+	1.53681e6i	0.185757	+	0.0904450i
$781$		−	2.38530e6i		−	0.139932i
$782$	−1.15801e6	+	724149.i	−0.0677169	+	0.0423459i
$783$		−	160431.i		−	0.00935153i
$784$	−9.81547e6	−	1.25285e7i	−0.570323	−	0.727960i
$785$	3.35795e6			0.194491
$786$	−7.63579e6	+	4.77494e6i	−0.440857	+	0.275684i
$787$	8.04857e6			0.463214			0.231607	−	0.972809i	$-0.425602\pi$
$787$	8.04857e6			0.463214			0.231607	+	0.972809i	$0.425602\pi$
$788$	362291.	−	744076.i	0.0207846	−	0.0426876i
$789$		−	3.88621e7i		−	2.22246i
$790$	6.39493e6	+	1.02264e7i	0.364559	+	0.582981i
$791$	7.13199e6			0.405293
$792$	1.28190e6	+	1.20792e7i	0.0726173	+	0.684267i
$793$		−	3.78775e6i		−	0.213894i
$794$	−9.29893e6	−	1.48703e7i	−0.523458	−	0.837081i
$795$		−	2.70810e7i		−	1.51966i
$796$	2.75607e7	+	1.34193e7i	1.54173	+	0.750667i
$797$		−	1.67184e7i		−	0.932286i	−0.884709	−	0.466143i	$-0.845643\pi$
$797$		−	1.67184e7i		−	0.932286i	0.884709	−	0.466143i	$-0.154357\pi$
$798$	7.67286e6	−	1.35118e6i	0.426530	−	0.0751116i
$799$		−	4.06647e6i		−	0.225346i
$800$	3.40933e6	−	9.41628e6i	0.188341	−	0.520181i
$801$		−	5.01003e7i		−	2.75905i
$802$	1.92413e7	−	1.20323e7i	1.05633	−	0.660562i
$803$			6.17364e6i			0.337872i
$804$	7.50107e6	−	1.54058e7i	0.409245	−	0.840510i
$805$	2.10025e6			0.114230
$806$	2.43774e6	−	1.52441e6i	0.132175	−	0.0826539i
$807$			1.06230e7i			0.574199i
$808$	−2.02256e7	+	2.14642e6i	−1.08986	+	0.115661i
$809$	−2.25763e7			−1.21278			−0.606390	−	0.795167i	$-0.707383\pi$
$809$	−2.25763e7			−1.21278			−0.606390	+	0.795167i	$0.707383\pi$
$810$	1.74419e6	+	2.78920e6i	0.0934074	+	0.149371i
$811$	3.15131e7			1.68244			0.841219	−	0.540694i	$-0.181838\pi$
$811$	3.15131e7			1.68244			0.841219	+	0.540694i	$0.181838\pi$
$812$	27091.0	−	55639.7i	0.00144190	−	0.00296138i
$813$			1.70594e6i			0.0905185i
$814$	−6.74997e6	−	1.07941e7i	−0.357060	−	0.570988i
$815$			1.23859e7i			0.653181i
$816$	2.37424e6	+	3.03048e6i	0.124824	+	0.159326i
$817$	−1.13568e7	+	2.80640e7i	−0.595251	+	1.47094i
$818$	−2.64068e7	+	1.65132e7i	−1.37985	+	0.862873i
$819$	−1.53904e6			−0.0801752
$820$	6.09041e6	+	2.96543e6i	0.316310	+	0.154011i
$821$	2.59036e7			1.34123			0.670614	−	0.741807i	$-0.266031\pi$
$821$	2.59036e7			1.34123			0.670614	+	0.741807i	$0.266031\pi$
$822$	1.35557e7	+	2.16775e7i	0.699751	+	1.11900i
$823$			2.62980e7i			1.35339i	0.736262	+	0.676696i	$0.236589\pi$
$823$			2.62980e7i			1.35339i	−0.736262	+	0.676696i	$0.763411\pi$
$824$	2.09229e7	−	2.22042e6i	1.07350	−	0.113925i
$825$			7.86969e6i			0.402553i
$826$	−3.90132e6	+	2.43964e6i	−0.198958	+	0.124416i
$827$	6.67461e6			0.339361			0.169681	−	0.985499i	$-0.445726\pi$
$827$	6.67461e6			0.339361			0.169681	+	0.985499i	$0.445726\pi$
$828$	1.65017e7	+	8.03469e6i	0.836475	+	0.407280i
$829$			1.20700e7i			0.609985i	0.952355	+	0.304993i	$0.0986540\pi$
$829$			1.20700e7i			0.609985i	−0.952355	+	0.304993i	$0.901346\pi$
$830$	−2.65045e6	+	1.65742e6i	−0.133544	+	0.0835099i
$831$	1.37708e7			0.691764
$832$	820370.	+	3.82161e6i	0.0410867	+	0.191398i
$833$	2.37399e6			0.118540
$834$	6.49662e6	−	4.06258e6i	0.323424	−	0.202249i
$835$	1.28948e7			0.640027
$836$	6.23195e6	+	6.91967e6i	0.308395	+	0.342428i
$837$	−1.25692e7			−0.620146
$838$	1.79695e7	−	1.12370e7i	0.883949	−	0.552766i
$839$	−1.45567e7			−0.713935			−0.356967	−	0.934117i	$-0.616189\pi$
$839$	−1.45567e7			−0.713935			−0.356967	+	0.934117i	$0.616189\pi$
$840$	−624749.	−	5.88696e6i	−0.0305497	−	0.287868i
$841$	2.05082e7			0.999856
$842$	1.30863e7	−	8.18336e6i	0.636117	−	0.397788i
$843$			3.32561e7i			1.61177i
$844$	5.11384e6	−	1.05028e7i	0.247110	−	0.507517i
$845$	1.33418e7			0.642796
$846$	−4.63328e7	+	2.89736e7i	−2.22568	+	1.39180i
$847$			4.51063e6i			0.216037i
$848$	2.37350e7	−	1.85953e7i	1.13344	−	0.888001i
$849$			4.62958e7i			2.20431i
$850$	792004.	+	1.26652e6i	0.0375993	+	0.0601265i
$851$	−1.92360e7			−0.910523
$852$	−4.44727e6	+	9.13385e6i	−0.209891	+	0.431077i
$853$	2.79860e7			1.31695			0.658474	−	0.752604i	$-0.271202\pi$
$853$	2.79860e7			1.31695			0.658474	+	0.752604i	$0.271202\pi$
$854$	−5.41571e6	+	3.38664e6i	−0.254103	+	0.158900i
$855$	−1.97762e7	−	8.00292e6i	−0.925182	−	0.374398i
$856$	2.32928e7	−	2.47193e6i	1.08652	−	0.115306i
$857$			6.77607e6i			0.315156i	0.987507	+	0.157578i	$0.0503686\pi$
$857$			6.77607e6i			0.315156i	−0.987507	+	0.157578i	$0.949631\pi$
$858$	−1.62855e6	−	2.60428e6i	−0.0755237	−	0.120773i
$859$			7.42658e6i			0.343405i	0.985149	+	0.171702i	$0.0549267\pi$
$859$			7.42658e6i			0.343405i	−0.985149	+	0.171702i	$0.945073\pi$
$860$	2.06832e7	+	1.00707e7i	0.953614	+	0.464315i
$861$	−4.95856e6			−0.227954
$862$	−1.14033e7	−	1.82355e7i	−0.522713	−	0.835890i
$863$	−3.81986e7			−1.74591			−0.872953	−	0.487805i	$-0.837798\pi$
$863$	−3.81986e7			−1.74591			−0.872953	+	0.487805i	$0.837798\pi$
$864$	5.81727e6	−	1.60668e7i	0.265115	−	0.732226i
$865$		−	1.69392e7i		−	0.769755i
$866$	−2.23573e7	+	1.39809e7i	−1.01304	+	0.633490i
$867$	3.43740e7			1.55304
$868$	−4.35918e6	−	2.12249e6i	−0.196384	−	0.0956194i
$869$		−	1.05529e7i		−	0.474049i
$870$	−239904.	+	150021.i	−0.0107458	+	0.00671975i
$871$			2.59495e6i			0.115900i
$872$	−2.35846e6	−	2.22236e7i	−0.105036	−	0.989745i
$873$			1.24303e7i			0.552009i
$874$	1.38574e7	−	2.44028e6i	0.613625	−	0.108059i
$875$		−	6.44915e6i		−	0.284762i
$876$	1.15104e7	−	2.36402e7i	0.506794	−	1.04086i
$877$			2.75655e7i			1.21023i	0.796139	+	0.605114i	$0.206872\pi$
$877$			2.75655e7i			1.21023i	−0.796139	+	0.605114i	$0.793128\pi$
$878$	6.71358e6	+	1.07359e7i	0.293912	+	0.470007i
$879$			3.25677e6i			0.142172i
$880$	5.57015e6	−	4.36395e6i	0.242471	−	0.189965i
$881$	−2.02187e7			−0.877635			−0.438818	−	0.898576i	$-0.644603\pi$
$881$	−2.02187e7			−0.877635			−0.438818	+	0.898576i	$0.644603\pi$
$882$	−1.69146e7	−	2.70488e7i	−0.732135	−	1.17079i
$883$		−	9.86623e6i		−	0.425843i	−0.977069	−	0.212922i	$-0.931702\pi$
$883$		−	9.86623e6i		−	0.425843i	0.977069	−	0.212922i	$-0.0682979\pi$
$884$	−524188.	−	255227.i	−0.0225609	−	0.0109849i
$885$	2.10381e7			0.902920
$886$	1.69950e6	−	1.06276e6i	0.0727338	−	0.0454832i
$887$	1.02588e7			0.437812			0.218906	−	0.975746i	$-0.429751\pi$
$887$	1.02588e7			0.437812			0.218906	+	0.975746i	$0.429751\pi$
$888$	5.72202e6	+	5.39181e7i	0.243510	+	2.29458i
$889$			274076.i			0.0116310i
$890$	−2.47452e7	+	1.54741e7i	−1.04717	+	0.654832i
$891$		−	2.87826e6i		−	0.121461i
$892$	5.47620e6	−	1.12471e7i	0.230445	−	0.473290i
$893$	−1.57152e7	+	3.88342e7i	−0.659464	+	1.62962i
$894$	−3.31736e7	−	5.30492e7i	−1.38819	−	2.21991i
$895$	−1.31252e7			−0.547708
$896$	4.73062e6	−	4.58988e6i	0.196856	−	0.190999i
$897$	−4.64103e6			−0.192590
$898$	1.53941e7	−	9.62648e6i	0.637034	−	0.398361i
$899$			231733.i			0.00956287i
$900$	8.78756e6	−	1.80480e7i	0.361628	−	0.742714i
$901$			4.49749e6i			0.184569i
$902$	−3.14244e6	−	5.02520e6i	−0.128603	−	0.205654i
$903$	−1.68394e7			−0.687240
$904$	−3.83150e6	−	3.61040e7i	−0.155937	−	1.46938i
$905$			1.22571e7i			0.497470i
$906$	2.43276e7	+	3.89032e7i	0.984644	+	1.57458i
$907$	3.62275e6			0.146224			0.0731122	−	0.997324i	$-0.476707\pi$
$907$	3.62275e6			0.146224			0.0731122	+	0.997324i	$0.476707\pi$
$908$	1.52094e7	−	3.12373e7i	0.612207	−	1.25736i
$909$	−4.07690e7			−1.63652
$910$	475351.	+	760152.i	0.0190288	+	0.0304297i
$911$	3.77977e7			1.50893			0.754465	−	0.656340i	$-0.227896\pi$
$911$	3.77977e7			1.50893			0.754465	+	0.656340i	$0.227896\pi$
$912$	−1.09621e7	−	3.81161e7i	−0.436423	−	1.51747i
$913$	2.73508e6			0.108591
$914$	−2.21179e7	−	3.53695e7i	−0.875746	−	1.40044i
$915$	2.92046e7			1.15318
$916$	4.20846e6	−	8.64337e6i	0.165724	−	0.340365i
$917$	−2.29995e6			−0.0903222
$918$	1.35138e6	+	2.16104e6i	0.0529262	+	0.0846363i
$919$			4.62054e7i			1.80469i	0.431010	+	0.902347i	$0.358157\pi$
$919$			4.62054e7i			1.80469i	−0.431010	+	0.902347i	$0.641843\pi$
$920$	−1.12831e6	−	1.06320e7i	−0.0439502	−	0.414139i
$921$	−2.18600e7			−0.849184
$922$	5.44184e6	+	8.70225e6i	0.210823	+	0.337135i
$923$		−	1.53851e6i		−	0.0594422i
$924$	−2.26749e6	+	4.65699e6i	−0.0873707	+	0.179443i
$925$			2.10385e7i			0.808462i
$926$	−2.28752e7	+	1.43047e7i	−0.876673	+	0.548216i
$927$	4.21745e7			1.61195
$928$	−296217.	−	107250.i	−0.0112912	−	0.00408817i
$929$	1.29869e7			0.493702			0.246851	−	0.969053i	$-0.420604\pi$
$929$	1.29869e7			0.493702			0.246851	+	0.969053i	$0.420604\pi$
$930$	1.17536e7	+	1.87957e7i	0.445619	+	0.712607i
$931$	−2.26712e7	−	9.17446e6i	−0.857236	−	0.346902i
$932$	1.10759e7	−	2.27477e7i	0.417675	−	0.857824i
$933$			6.62494e7i			2.49160i
$934$	−2.61794e6	+	1.63709e6i	−0.0981957	+	0.0614054i
$935$			1.05547e6i			0.0394837i
$936$	826815.	+	7.79102e6i	0.0308474	+	0.290673i
$937$	−1.95487e7			−0.727392			−0.363696	−	0.931518i	$-0.618485\pi$
$937$	−1.95487e7			−0.727392			−0.363696	+	0.931518i	$0.618485\pi$
$938$	3.71024e6	−	2.32015e6i	0.137688	−	0.0861012i
$939$	−2.73067e7			−1.01066
$940$	2.86209e7	+	1.39355e7i	1.05648	+	0.514403i
$941$		−	4.73488e7i		−	1.74315i	−0.490263	−	0.871575i	$-0.663099\pi$
$941$		−	4.73488e7i		−	1.74315i	0.490263	−	0.871575i	$-0.336901\pi$
$942$	6.63446e6	+	1.06094e7i	0.243601	+	0.389551i
$943$	−8.95531e6			−0.327945
$944$	1.44460e7	+	1.84388e7i	0.527614	+	0.673447i
$945$		−	3.91941e6i		−	0.142771i
$946$	−1.06718e7	−	1.70657e7i	−0.387714	−	0.620008i
$947$			4.33759e7i			1.57172i	0.618407	+	0.785858i	$0.287778\pi$
$947$			4.33759e7i			1.57172i	−0.618407	+	0.785858i	$0.712222\pi$
$948$	−1.96754e7	+	4.04094e7i	−0.711053	+	1.46037i
$949$			3.98196e6i			0.143526i
$950$	−2.66894e6	−	1.51559e7i	−0.0959465	−	0.544844i
$951$		−	3.64409e7i		−	1.30658i
$952$	103756.	+	977682.i	0.00371039	+	0.0349627i
$953$			2.83056e7i			1.00958i	0.863242	+	0.504790i	$0.168430\pi$
$953$			2.83056e7i			1.00958i	−0.863242	+	0.504790i	$0.831570\pi$
$954$	5.12438e7	−	3.20446e7i	1.82293	−	1.13995i
$955$			3.34903e7i			1.18826i
$956$	−1.90953e7	−	9.29752e6i	−0.675744	−	0.329020i
$957$	247564.			0.00873792
$958$	8.63660e6	−	5.40078e6i	0.304039	−	0.190127i
$959$			6.52939e6i			0.229259i
$960$	−2.94657e7	+	6.32528e6i	−1.03190	+	0.221514i
$961$	−1.04737e7			−0.365840
$962$	−4.35369e6	−	6.96216e6i	−0.151677	−	0.242553i
$963$	4.69517e7			1.63149
$964$	−3.36213e7	−	1.63702e7i	−1.16526	−	0.567364i
$965$		−	3.06653e7i		−	1.06006i
$966$	4.14957e6	+	6.63573e6i	0.143074	+	0.228795i
$967$			1.08700e7i			0.373821i	0.982377	+	0.186911i	$0.0598475\pi$
$967$			1.08700e7i			0.373821i	−0.982377	+	0.186911i	$0.940153\pi$
$968$	2.28340e7	−	2.42324e6i	0.783237	−	0.0831204i
$969$	5.48389e6	+	2.21919e6i	0.187620	+	0.0759250i
$970$	6.13949e6	−	3.83925e6i	0.209509	−	0.131014i
$971$	−3.87606e7			−1.31929			−0.659647	−	0.751575i	$-0.729294\pi$
$971$	−3.87606e7			−1.31929			−0.659647	+	0.751575i	$0.729294\pi$
$972$	−1.54080e7	+	3.16450e7i	−0.523094	+	1.07433i
$973$	1.95682e6			0.0662627
$974$	1.65006e7	+	2.63867e7i	0.557316	+	0.891225i
$975$			5.07591e6i			0.171002i
$976$	2.00535e7	+	2.55963e7i	0.673854	+	0.860107i
$977$		−	3.23311e7i		−	1.08364i	−0.840496	−	0.541818i	$-0.817736\pi$
$977$		−	3.23311e7i		−	1.08364i	0.840496	−	0.541818i	$-0.182264\pi$
$978$	−3.91331e7	+	2.44714e7i	−1.30827	+	0.818110i
$979$	2.55353e7			0.851500
$980$	−8.13549e6	+	1.67087e7i	−0.270594	+	0.555748i
$981$		−	4.47965e7i		−	1.48618i
$982$	1.56994e7	−	9.81739e6i	0.519521	−	0.324876i
$983$	−2.85807e7			−0.943386			−0.471693	−	0.881763i	$-0.656357\pi$
$983$	−2.85807e7			−0.943386			−0.471693	+	0.881763i	$0.656357\pi$
$984$	2.66388e6	+	2.51015e7i	0.0877055	+	0.826442i
$985$	−966348.			−0.0317353
$986$	39842.2	−	24914.8i	0.00130512	−	0.000816141i
$987$	−2.33019e7			−0.761376
$988$	4.01957e6	+	4.46315e6i	0.131005	+	0.145462i
$989$	−3.04125e7			−0.988693
$990$	1.20259e7	−	7.52024e6i	0.389969	−	0.243862i
$991$	3.55974e7			1.15142			0.575711	−	0.817653i	$-0.304725\pi$
$991$	3.55974e7			1.15142			0.575711	+	0.817653i	$0.304725\pi$
$992$	−8.40271e6	+	2.32076e7i	−0.271107	+	0.748773i
$993$	6.79048e7			2.18538
$994$	−2.19975e6	+	1.37558e6i	−0.0706167	+	0.0441592i
$995$		−	3.57936e7i		−	1.14617i
$996$	−1.04732e7	−	5.09941e6i	−0.334527	−	0.162882i
$997$	1.29194e7			0.411627			0.205814	−	0.978591i	$-0.434016\pi$
$997$	1.29194e7			0.411627			0.205814	+	0.978591i	$0.434016\pi$
$998$	−3.37695e7	+	2.11173e7i	−1.07324	+	0.671138i
$999$			3.58975e7i			1.13802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.d.a.75.17	✓	48
4.3	odd	2	inner	76.6.d.a.75.31	yes	48
19.18	odd	2	inner	76.6.d.a.75.32	yes	48
76.75	even	2	inner	76.6.d.a.75.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.d.a.75.17	✓	48	1.1	even	1	trivial
76.6.d.a.75.18	yes	48	76.75	even	2	inner
76.6.d.a.75.31	yes	48	4.3	odd	2	inner
76.6.d.a.75.32	yes	48	19.18	odd	2	inner

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.99929 - 4.79628i) q^{2} -24.6139 q^{3} +(-14.0085 + 28.7708i) q^{4} +37.3653 q^{5} +(73.8243 + 118.055i) q^{6} +35.5589i q^{7} +(180.009 - 19.1033i) q^{8} +362.846 q^{9} +O(q^{10})\)	\(q+(-2.99929 - 4.79628i) q^{2} -24.6139 q^{3} +(-14.0085 + 28.7708i) q^{4} +37.3653 q^{5} +(73.8243 + 118.055i) q^{6} +35.5589i q^{7} +(180.009 - 19.1033i) q^{8} +362.846 q^{9} +(-112.069 - 179.214i) q^{10} +184.937i q^{11} +(344.805 - 708.163i) q^{12} +119.283i q^{13} +(170.551 - 106.652i) q^{14} -919.707 q^{15} +(-631.522 - 806.074i) q^{16} +152.741 q^{17} +(-1088.28 - 1740.31i) q^{18} +(-1458.65 - 590.280i) q^{19} +(-523.433 + 1075.03i) q^{20} -875.246i q^{21} +(887.008 - 554.679i) q^{22} -1580.72i q^{23} +(-4430.72 + 470.206i) q^{24} -1728.83 q^{25} +(572.115 - 357.765i) q^{26} -2949.87 q^{27} +(-1023.06 - 498.129i) q^{28} +54.3855i q^{29} +(2758.47 + 4411.17i) q^{30} +4260.92 q^{31} +(-1972.04 + 5446.60i) q^{32} -4552.02i q^{33} +(-458.114 - 732.588i) q^{34} +1328.67i q^{35} +(-5082.94 + 10439.4i) q^{36} -12169.2i q^{37} +(1543.78 + 8766.52i) q^{38} -2936.03i q^{39} +(6726.07 - 713.799i) q^{40} -5665.34i q^{41} +(-4197.92 + 2625.11i) q^{42} -19239.7i q^{43} +(-5320.78 - 2590.69i) q^{44} +13557.8 q^{45} +(-7581.56 + 4741.03i) q^{46} -26623.3i q^{47} +(15544.2 + 19840.7i) q^{48} +15542.6 q^{49} +(5185.28 + 8291.97i) q^{50} -3759.56 q^{51} +(-3431.88 - 1670.98i) q^{52} +29445.2i q^{53} +(8847.53 + 14148.4i) q^{54} +6910.22i q^{55} +(679.292 + 6400.91i) q^{56} +(35903.2 + 14529.1i) q^{57} +(260.848 - 163.118i) q^{58} -22874.8 q^{59} +(12883.7 - 26460.7i) q^{60} -31754.3 q^{61} +(-12779.7 - 20436.6i) q^{62} +12902.4i q^{63} +(32038.1 - 6877.50i) q^{64} +4457.05i q^{65} +(-21832.7 + 13652.8i) q^{66} +21754.5 q^{67} +(-2139.68 + 4394.49i) q^{68} +38907.7i q^{69} +(6372.67 - 3985.07i) q^{70} -12897.9 q^{71} +(65315.3 - 6931.54i) q^{72} +33382.4 q^{73} +(-58366.7 + 36498.8i) q^{74} +42553.4 q^{75} +(37416.4 - 33697.7i) q^{76} -6576.16 q^{77} +(-14082.0 + 8805.99i) q^{78} -57062.3 q^{79} +(-23597.0 - 30119.2i) q^{80} -15563.5 q^{81} +(-27172.5 + 16992.0i) q^{82} -14789.3i q^{83} +(25181.5 + 12260.9i) q^{84} +5707.21 q^{85} +(-92278.8 + 57705.3i) q^{86} -1338.64i q^{87} +(3532.90 + 33290.2i) q^{88} -138076. i q^{89} +(-40663.9 - 65027.1i) q^{90} -4241.58 q^{91} +(45478.6 + 22143.5i) q^{92} -104878. q^{93} +(-127693. + 79851.0i) q^{94} +(-54503.0 - 22056.0i) q^{95} +(48539.6 - 134062. i) q^{96} +34257.8i q^{97} +(-46616.6 - 74546.4i) q^{98} +67103.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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