LMFDB - Embedded newform 76.6.d.a.75.1

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			75.1
Character	$\chi$	$=$	76.75
Dual form			76.6.d.a.75.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.61709 - 0.669578i) q^{2} +15.7189 q^{3} +(31.1033 + 7.52215i) q^{4} -23.2669 q^{5} +(-88.2945 - 10.5250i) q^{6} -110.037i q^{7} +(-169.673 - 63.0787i) q^{8} +4.08426 q^{9} +O(q^{10})$	\(q+(-5.61709 - 0.669578i) q^{2} +15.7189 q^{3} +(31.1033 + 7.52215i) q^{4} -23.2669 q^{5} +(-88.2945 - 10.5250i) q^{6} -110.037i q^{7} +(-169.673 - 63.0787i) q^{8} +4.08426 q^{9} +(130.692 + 15.5790i) q^{10} -468.514i q^{11} +(488.911 + 118.240i) q^{12} +546.656i q^{13} +(-73.6787 + 618.090i) q^{14} -365.730 q^{15} +(910.834 + 467.928i) q^{16} -170.574 q^{17} +(-22.9417 - 2.73473i) q^{18} +(257.452 - 1552.36i) q^{19} +(-723.677 - 175.017i) q^{20} -1729.67i q^{21} +(-313.707 + 2631.68i) q^{22} -3433.96i q^{23} +(-2667.08 - 991.529i) q^{24} -2583.65 q^{25} +(366.028 - 3070.61i) q^{26} -3755.50 q^{27} +(827.719 - 3422.53i) q^{28} -5802.64i q^{29} +(2054.34 + 244.885i) q^{30} +2393.90 q^{31} +(-4802.92 - 3238.27i) q^{32} -7364.53i q^{33} +(958.130 + 114.213i) q^{34} +2560.23i q^{35} +(127.034 + 30.7225i) q^{36} -6131.91i q^{37} +(-2485.55 + 8547.35i) q^{38} +8592.83i q^{39} +(3947.77 + 1467.64i) q^{40} +3811.84i q^{41} +(-1158.15 + 9715.71i) q^{42} +12927.3i q^{43} +(3524.24 - 14572.3i) q^{44} -95.0280 q^{45} +(-2299.30 + 19288.9i) q^{46} -11778.9i q^{47} +(14317.3 + 7355.32i) q^{48} +4698.75 q^{49} +(14512.6 + 1729.96i) q^{50} -2681.24 q^{51} +(-4112.03 + 17002.8i) q^{52} -867.587i q^{53} +(21094.9 + 2514.60i) q^{54} +10900.9i q^{55} +(-6941.02 + 18670.4i) q^{56} +(4046.86 - 24401.4i) q^{57} +(-3885.32 + 32593.9i) q^{58} +4514.86 q^{59} +(-11375.4 - 2751.08i) q^{60} -28013.8 q^{61} +(-13446.7 - 1602.90i) q^{62} -449.422i q^{63} +(24810.2 + 21405.6i) q^{64} -12719.0i q^{65} +(-4931.13 + 41367.2i) q^{66} +39412.5 q^{67} +(-5305.42 - 1283.09i) q^{68} -53978.1i q^{69} +(1714.27 - 14381.0i) q^{70} -20861.8 q^{71} +(-692.991 - 257.630i) q^{72} +86574.9 q^{73} +(-4105.79 + 34443.5i) q^{74} -40612.2 q^{75} +(19684.7 - 46346.9i) q^{76} -51554.1 q^{77} +(5753.57 - 48266.7i) q^{78} -46538.8 q^{79} +(-21192.3 - 10887.2i) q^{80} -60024.8 q^{81} +(2552.33 - 21411.5i) q^{82} +10127.1i q^{83} +(13010.8 - 53798.5i) q^{84} +3968.73 q^{85} +(8655.84 - 72613.8i) q^{86} -91211.2i q^{87} +(-29553.3 + 79494.4i) q^{88} +102692. i q^{89} +(533.781 + 63.6286i) q^{90} +60152.6 q^{91} +(25830.8 - 106808. i) q^{92} +37629.5 q^{93} +(-7886.89 + 66163.1i) q^{94} +(-5990.10 + 36118.5i) q^{95} +(-75496.7 - 50902.0i) q^{96} +155902. i q^{97} +(-26393.3 - 3146.18i) q^{98} -1913.54i 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 $

$2$	−5.61709	−	0.669578i	−0.992970	−	0.118366i
$2$	−5.61709	−	0.669578i	−0.992970	−	0.118366i
$3$	15.7189			1.00837			0.504184	−	0.863596i	$-0.331793\pi$
$3$	15.7189			1.00837			0.504184	+	0.863596i	$0.331793\pi$
$4$	31.1033	+	7.52215i	0.971979	+	0.235067i
$5$	−23.2669			−0.416210			−0.208105	−	0.978106i	$-0.566730\pi$
$5$	−23.2669			−0.416210			−0.208105	+	0.978106i	$0.566730\pi$
$6$	−88.2945	−	10.5250i	−1.00128	−	0.119356i
$7$		−	110.037i		−	0.848781i	−0.905479	−	0.424390i	$-0.860488\pi$
$7$		−	110.037i		−	0.848781i	0.905479	−	0.424390i	$-0.139512\pi$
$8$	−169.673	−	63.0787i	−0.937322	−	0.348464i
$9$	4.08426			0.0168077
$10$	130.692	+	15.5790i	0.413284	+	0.0492650i
$11$		−	468.514i		−	1.16746i	−0.811949	−	0.583729i	$-0.801593\pi$
$11$		−	468.514i		−	1.16746i	0.811949	−	0.583729i	$-0.198407\pi$
$12$	488.911	+	118.240i	0.980113	+	0.237035i
$13$			546.656i			0.897130i	0.893750	+	0.448565i	$0.148065\pi$
$13$			546.656i			0.897130i	−0.893750	+	0.448565i	$0.851935\pi$
$14$	−73.6787	+	618.090i	−0.100467	+	0.842814i
$15$	−365.730			−0.419693
$16$	910.834	+	467.928i	0.889487	+	0.456961i
$17$	−170.574			−0.143150			−0.0715749	−	0.997435i	$-0.522803\pi$
$17$	−170.574			−0.143150			−0.0715749	+	0.997435i	$0.522803\pi$
$18$	−22.9417	−	2.73473i	−0.0166895	−	0.00198945i
$19$	257.452	−	1552.36i	0.163611	−	0.986525i
$19$	257.452	−	1552.36i	0.163611	−	0.986525i
$20$	−723.677	−	175.017i	−0.404548	−	0.0978374i
$21$		−	1729.67i		−	0.855884i
$22$	−313.707	+	2631.68i	−0.138187	+	1.15925i
$23$		−	3433.96i		−	1.35355i	−0.736188	−	0.676777i	$-0.763376\pi$
$23$		−	3433.96i		−	1.35355i	0.736188	−	0.676777i	$-0.236624\pi$
$24$	−2667.08	−	991.529i	−0.945167	−	0.351380i
$25$	−2583.65			−0.826769
$26$	366.028	−	3070.61i	0.106189	−	0.890823i
$27$	−3755.50			−0.991420
$28$	827.719	−	3422.53i	0.199521	−	0.824997i
$29$		−	5802.64i		−	1.28124i	−0.767858	−	0.640620i	$-0.778677\pi$
$29$		−	5802.64i		−	1.28124i	0.767858	−	0.640620i	$-0.221323\pi$
$30$	2054.34	+	244.885i	0.416743	+	0.0496773i
$31$	2393.90			0.447406			0.223703	−	0.974657i	$-0.428185\pi$
$31$	2393.90			0.447406			0.223703	+	0.974657i	$0.428185\pi$
$32$	−4802.92	−	3238.27i	−0.829145	−	0.559033i
$33$		−	7364.53i		−	1.17723i
$34$	958.130	+	114.213i	0.142144	+	0.0169440i
$35$			2560.23i			0.353271i
$36$	127.034	+	30.7225i	0.0163367	+	0.00395093i
$37$		−	6131.91i		−	0.736363i	−0.929754	−	0.368181i	$-0.879981\pi$
$37$		−	6131.91i		−	0.736363i	0.929754	−	0.368181i	$-0.120019\pi$
$38$	−2485.55	+	8547.35i	−0.279231	+	0.960224i
$39$			8592.83i			0.904638i
$40$	3947.77	+	1467.64i	0.390123	+	0.145034i
$41$			3811.84i			0.354140i	0.984198	+	0.177070i	$0.0566619\pi$
$41$			3811.84i			0.354140i	−0.984198	+	0.177070i	$0.943338\pi$
$42$	−1158.15	+	9715.71i	−0.101307	+	0.849867i
$43$			12927.3i			1.06620i	0.846054	+	0.533098i	$0.178972\pi$
$43$			12927.3i			1.06620i	−0.846054	+	0.533098i	$0.821028\pi$
$44$	3524.24	−	14572.3i	0.274431	−	1.13474i
$45$	−95.0280			−0.00699553
$46$	−2299.30	+	19288.9i	−0.160214	+	1.34404i
$47$		−	11778.9i		−	0.777786i	−0.921283	−	0.388893i	$-0.872858\pi$
$47$		−	11778.9i		−	0.777786i	0.921283	−	0.388893i	$-0.127142\pi$
$48$	14317.3	+	7355.32i	0.896931	+	0.460785i
$49$	4698.75			0.279571
$50$	14512.6	+	1729.96i	0.820957	+	0.0978611i
$51$	−2681.24			−0.144348
$52$	−4112.03	+	17002.8i	−0.210886	+	0.871992i
$53$		−	867.587i		−	0.0424252i	−0.999775	−	0.0212126i	$-0.993247\pi$
$53$		−	867.587i		−	0.0424252i	0.999775	−	0.0212126i	$-0.00675268\pi$
$54$	21094.9	+	2514.60i	0.984451	+	0.117350i
$55$			10900.9i			0.485908i
$56$	−6941.02	+	18670.4i	−0.295769	+	0.795581i
$57$	4046.86	−	24401.4i	0.164980	−	0.994781i
$58$	−3885.32	+	32593.9i	−0.151655	+	1.27223i
$59$	4514.86			0.168855			0.0844275	−	0.996430i	$-0.473094\pi$
$59$	4514.86			0.168855			0.0844275	+	0.996430i	$0.473094\pi$
$60$	−11375.4	−	2751.08i	−0.407933	−	0.0986562i
$61$	−28013.8			−0.963933			−0.481966	−	0.876190i	$-0.660077\pi$
$61$	−28013.8			−0.963933			−0.481966	+	0.876190i	$0.660077\pi$
$62$	−13446.7	−	1602.90i	−0.444260	−	0.0529575i
$63$		−	449.422i		−	0.0142660i
$64$	24810.2	+	21405.6i	0.757146	+	0.653246i
$65$		−	12719.0i		−	0.373395i
$66$	−4931.13	+	41367.2i	−0.139343	+	1.16895i
$67$	39412.5			1.07262			0.536311	−	0.844021i	$-0.319817\pi$
$67$	39412.5			1.07262			0.536311	+	0.844021i	$0.319817\pi$
$68$	−5305.42	−	1283.09i	−0.139139	−	0.0336499i
$69$		−	53978.1i		−	1.36488i
$70$	1714.27	−	14381.0i	0.0418152	−	0.350788i
$71$	−20861.8			−0.491140			−0.245570	−	0.969379i	$-0.578975\pi$
$71$	−20861.8			−0.491140			−0.245570	+	0.969379i	$0.578975\pi$
$72$	−692.991	−	257.630i	−0.0157542	−	0.00585687i
$73$	86574.9			1.90145			0.950724	−	0.310037i	$-0.100341\pi$
$73$	86574.9			1.90145			0.950724	+	0.310037i	$0.100341\pi$
$74$	−4105.79	+	34443.5i	−0.0871601	+	0.731186i
$75$	−40612.2			−0.833688
$76$	19684.7	−	46346.9i	0.390926	−	0.920422i
$77$	−51554.1			−0.990915
$78$	5753.57	−	48266.7i	0.107078	−	0.898279i
$79$	−46538.8			−0.838971			−0.419486	−	0.907762i	$-0.637790\pi$
$79$	−46538.8			−0.838971			−0.419486	+	0.907762i	$0.637790\pi$
$80$	−21192.3	−	10887.2i	−0.370213	−	0.190192i
$81$	−60024.8			−1.01653
$82$	2552.33	−	21411.5i	0.0419181	−	0.351651i
$83$			10127.1i			0.161357i	0.996740	+	0.0806787i	$0.0257088\pi$
$83$			10127.1i			0.161357i	−0.996740	+	0.0806787i	$0.974291\pi$
$84$	13010.8	−	53798.5i	0.201190	−	0.831901i
$85$	3968.73			0.0595804
$86$	8655.84	−	72613.8i	0.126201	−	1.05870i
$87$		−	91211.2i		−	1.29196i
$88$	−29553.3	+	79494.4i	−0.406817	+	1.09428i
$89$			102692.i			1.37423i	0.726548	+	0.687116i	$0.241124\pi$
$89$			102692.i			1.37423i	−0.726548	+	0.687116i	$0.758876\pi$
$90$	533.781	+	63.6286i	0.00694635	+	0.000828031i
$91$	60152.6			0.761467
$92$	25830.8	−	106808.i	0.318176	−	1.31563i
$93$	37629.5			0.451150
$94$	−7886.89	+	66163.1i	−0.0920632	+	0.772318i
$95$	−5990.10	+	36118.5i	−0.0680965	+	0.410602i
$96$	−75496.7	−	50902.0i	−0.836084	−	0.563712i
$97$			155902.i			1.68237i	0.540749	+	0.841184i	$0.318141\pi$
$97$			155902.i			1.68237i	−0.540749	+	0.841184i	$0.681859\pi$
$98$	−26393.3	−	3146.18i	−0.277606	−	0.0330916i
$99$		−	1913.54i		−	0.0196222i
$100$	−80360.2	−	19434.6i	−0.803602	−	0.194346i
$101$	35843.4			0.349628			0.174814	−	0.984601i	$-0.444068\pi$
$101$	35843.4			0.349628			0.174814	+	0.984601i	$0.444068\pi$
$102$	15060.8	+	1795.30i	0.143333	+	0.0170858i
$103$	187717.			1.74346			0.871729	−	0.489988i	$-0.162999\pi$
$103$	187717.			1.74346			0.871729	+	0.489988i	$0.162999\pi$
$104$	34482.3	−	92753.0i	0.312617	−	0.840900i
$105$			40244.0i			0.356228i
$106$	−580.917	+	4873.31i	−0.00502169	+	0.0421269i
$107$	−89520.2			−0.755895			−0.377947	−	0.925827i	$-0.623370\pi$
$107$	−89520.2			−0.755895			−0.377947	+	0.925827i	$0.623370\pi$
$108$	−116808.	−	28249.4i	−0.963640	−	0.233051i
$109$			57655.6i			0.464810i	0.972619	+	0.232405i	$0.0746594\pi$
$109$			57655.6i			0.464810i	−0.972619	+	0.232405i	$0.925341\pi$
$110$	7298.97	−	61231.0i	0.0575148	−	0.482492i
$111$		−	96387.0i		−	0.742525i
$112$	51489.6	−	100226.i	0.387860	−	0.754979i
$113$		−	5685.06i		−	0.0418831i	−0.999781	−	0.0209416i	$-0.993334\pi$
$113$		−	5685.06i		−	0.0418831i	0.999781	−	0.0209416i	$-0.00666639\pi$
$114$	−39070.2	+	134355.i	−0.281568	+	0.968260i
$115$			79897.5i			0.563363i
$116$	43648.3	−	180481.i	0.301178	−	1.24534i
$117$			2232.69i			0.0150787i
$118$	−25360.3	−	3023.05i	−0.167668	−	0.0199866i
$119$			18769.6i			0.121503i
$120$	62054.6	+	23069.8i	0.393388	+	0.146248i
$121$	−58454.5			−0.362956
$122$	157356.	+	18757.4i	0.957156	+	0.114097i
$123$			59918.0i			0.357104i
$124$	74458.2	+	18007.3i	0.434869	+	0.105170i
$125$	132822.			0.760320
$126$	−300.923	+	2524.44i	−0.00168861	+	0.0141657i
$127$	−267475.			−1.47155			−0.735774	−	0.677227i	$-0.763182\pi$
$127$	−267475.			−1.47155			−0.735774	+	0.677227i	$0.763182\pi$
$128$	−125028.	−	136849.i	−0.674501	−	0.738274i
$129$			203203.i			1.07512i
$130$	−8516.33	+	71443.5i	−0.0441972	+	0.370770i
$131$		−	128052.i		−	0.651940i	−0.945380	−	0.325970i	$-0.894309\pi$
$131$		−	128052.i		−	0.651940i	0.945380	−	0.325970i	$-0.105691\pi$
$132$	55397.1	−	229062.i	0.276728	−	1.14424i
$133$	−170818.	−	28329.4i	−0.837343	−	0.138870i
$134$	−221383.	−	26389.7i	−1.06508	−	0.126962i
$135$	87378.6			0.412639
$136$	28941.9	+	10759.6i	0.134178	+	0.0498826i
$137$	65239.4			0.296967			0.148484	−	0.988915i	$-0.452561\pi$
$137$	65239.4			0.296967			0.148484	+	0.988915i	$0.452561\pi$
$138$	−36142.6	+	303200.i	−0.161555	+	1.35529i
$139$		−	47832.4i		−	0.209984i	−0.994473	−	0.104992i	$-0.966518\pi$
$139$		−	47832.4i		−	0.209984i	0.994473	−	0.104992i	$-0.0334816\pi$
$140$	−19258.4	+	79631.6i	−0.0830425	+	0.343372i
$141$		−	185152.i		−	0.784295i
$142$	117182.	+	13968.6i	0.487687	+	0.0581342i
$143$	256116.			1.04736
$144$	3720.09	+	1911.14i	0.0149502	+	0.00768045i
$145$			135009.i			0.533265i
$146$	−486299.	−	57968.6i	−1.88808	−	0.225066i
$147$	73859.3			0.281911
$148$	46125.2	−	190723.i	0.173095	−	0.715729i
$149$	144519.			0.533287			0.266643	−	0.963795i	$-0.414085\pi$
$149$	144519.			0.533287			0.266643	+	0.963795i	$0.414085\pi$
$150$	228122.	+	27193.0i	0.827827	+	0.0986801i
$151$	−161316.			−0.575750			−0.287875	−	0.957668i	$-0.592949\pi$
$151$	−161316.			−0.575750			−0.287875	+	0.957668i	$0.592949\pi$
$152$	−141603.	+	247154.i	−0.497124	+	0.867679i
$153$	−696.670			−0.00240602
$154$	289584.	+	34519.5i	0.983949	+	0.117290i
$155$	−55698.5			−0.186215
$156$	−64636.6	+	267266.i	−0.212651	+	0.879289i
$157$	242346.			0.784671			0.392335	−	0.919822i	$-0.371667\pi$
$157$	242346.			0.784671			0.392335	+	0.919822i	$0.371667\pi$
$158$	261412.	+	31161.3i	0.833073	+	0.0993055i
$159$		−	13637.5i		−	0.0427802i
$160$	111749.	+	75344.3i	0.345099	+	0.232675i
$161$	−377864.			−1.14887
$162$	337164.	+	40191.3i	1.00938	+	0.120322i
$163$			584956.i			1.72446i	0.506513	+	0.862232i	$0.330934\pi$
$163$			584956.i			1.72446i	−0.506513	+	0.862232i	$0.669066\pi$
$164$	−28673.3	+	118561.i	−0.0832468	+	0.344217i
$165$			171350.i			0.489974i
$166$	6780.86	−	56884.7i	0.0190992	−	0.160223i
$167$	80572.8			0.223562			0.111781	−	0.993733i	$-0.464345\pi$
$167$	80572.8			0.223562			0.111781	+	0.993733i	$0.464345\pi$
$168$	−109105.	+	293479.i	−0.298245	+	0.802239i
$169$	72460.6			0.195157
$170$	−22292.7	−	2657.37i	−0.0591616	−	0.00705228i
$171$	1051.50	−	6340.24i	0.00274992	−	0.0165812i
$172$	−97241.2	+	402082.i	−0.250628	+	1.03632i
$173$		−	459055.i		−	1.16614i	−0.812423	−	0.583069i	$-0.801852\pi$
$173$		−	459055.i		−	1.16614i	0.812423	−	0.583069i	$-0.198148\pi$
$174$	−61073.0	+	512341.i	−0.152924	+	1.28288i
$175$			284299.i			0.701746i
$176$	219231.	−	426739.i	0.533482	−	1.03844i
$177$	70968.6			0.170268
$178$	68760.0	−	576828.i	0.162662	−	1.36457i
$179$	385503.			0.899281			0.449640	−	0.893210i	$-0.351552\pi$
$179$	385503.			0.899281			0.449640	+	0.893210i	$0.351552\pi$
$180$	−2955.69	−	714.815i	−0.00679951	−	0.00164442i
$181$		−	749604.i		−	1.70073i	−0.526192	−	0.850366i	$-0.676381\pi$
$181$		−	749604.i		−	1.70073i	0.526192	−	0.850366i	$-0.323619\pi$
$182$	−337882.	−	40276.9i	−0.756114	−	0.0901316i
$183$	−440346.			−0.972000
$184$	−216610.	+	582652.i	−0.471665	+	1.26872i
$185$			142670.i			0.306482i
$186$	−211368.	−	25195.9i	−0.447978	−	0.0534007i
$187$			79916.4i			0.167121i
$188$	88602.7	−	366363.i	0.182832	−	0.755992i
$189$			413245.i			0.841499i
$190$	57831.0	−	198870.i	0.116219	−	0.399655i
$191$		−	510934.i		−	1.01340i	−0.862122	−	0.506701i	$-0.830865\pi$
$191$		−	510934.i		−	1.01340i	0.862122	−	0.506701i	$-0.169135\pi$
$192$	389989.	+	336472.i	0.763482	+	0.658713i
$193$		−	761097.i		−	1.47078i	−0.677646	−	0.735389i	$-0.737000\pi$
$193$		−	761097.i		−	1.47078i	0.677646	−	0.735389i	$-0.263000\pi$
$194$	104388.	−	875712.i	0.199135	−	1.67054i
$195$		−	199928.i		−	0.376520i
$196$	146147.	+	35344.7i	0.271737	+	0.0657180i
$197$	−595391.			−1.09304			−0.546521	−	0.837445i	$-0.684048\pi$
$197$	−595391.			−1.09304			−0.546521	+	0.837445i	$0.684048\pi$
$198$	−1281.26	+	10748.5i	−0.00232260	+	0.0194843i
$199$		−	92384.6i		−	0.165374i	−0.996576	−	0.0826869i	$-0.973650\pi$
$199$		−	92384.6i		−	0.165374i	0.996576	−	0.0826869i	$-0.0263501\pi$
$200$	438377.	+	162973.i	0.774949	+	0.288099i
$201$	619521.			1.08160
$202$	−201336.	−	24000.0i	−0.347170	−	0.0413840i
$203$	−638508.			−1.08749
$204$	−83395.5	−	20168.7i	−0.140303	−	0.0339315i
$205$		−	88689.6i		−	0.147397i
$206$	−1.05443e6	−	125691.i	−1.73120	−	0.206366i
$207$		−	14025.2i		−	0.0227501i
$208$	−255796.	+	497913.i	−0.409953	+	0.797985i
$209$	−727302.	−	120620.i	−1.15173	−	0.191009i
$210$	26946.5	−	226054.i	0.0421652	−	0.353723i
$211$	14300.8			0.0221134			0.0110567	−	0.999939i	$-0.496480\pi$
$211$	14300.8			0.0221134			0.0110567	+	0.999939i	$0.496480\pi$
$212$	6526.13	−	26984.9i	0.00997277	−	0.0412364i
$213$	−327924.			−0.495250
$214$	502843.	+	59940.7i	0.750581	+	0.0894721i
$215$		−	300778.i		−	0.443762i
$216$	637208.	+	236892.i	0.929280	+	0.345474i
$217$		−	263419.i		−	0.379749i
$218$	38604.9	−	323856.i	0.0550175	−	0.461542i
$219$	1.36086e6			1.91736
$220$	−81997.9	+	339053.i	−0.114221	+	0.472292i
$221$		−	93245.3i		−	0.128424i
$222$	−64538.6	+	541414.i	−0.0878896	+	0.737305i
$223$	242174.			0.326111			0.163055	−	0.986617i	$-0.447865\pi$
$223$	242174.			0.326111			0.163055	+	0.986617i	$0.447865\pi$
$224$	−356331.	+	528501.i	−0.474497	+	0.703763i
$225$	−10552.3			−0.0138961
$226$	−3806.59	+	31933.5i	−0.00495752	+	0.0415887i
$227$	−1.07618e6			−1.38618			−0.693088	−	0.720853i	$-0.743750\pi$
$227$	−1.07618e6			−1.38618			−0.693088	+	0.720853i	$0.743750\pi$
$228$	309422.	−	728523.i	0.394198	−	0.928125i
$229$	398882.			0.502639			0.251319	−	0.967904i	$-0.419136\pi$
$229$	398882.			0.502639			0.251319	+	0.967904i	$0.419136\pi$
$230$	53497.6	−	448791.i	0.0666829	−	0.559403i
$231$	−810375.			−0.999208
$232$	−366023.	+	984553.i	−0.446466	+	1.20093i
$233$	1.38405e6			1.67018			0.835090	−	0.550114i	$-0.185416\pi$
$233$	1.38405e6			1.67018			0.835090	+	0.550114i	$0.185416\pi$
$234$	1494.96	−	12541.2i	0.00178480	−	0.0149727i
$235$			274058.i			0.323722i
$236$	140427.	+	33961.4i	0.164124	+	0.0396923i
$237$	−731539.			−0.845992
$238$	12567.7	−	105430.i	0.0143818	−	0.120649i
$239$		−	1.68237e6i		−	1.90514i	−0.304319	−	0.952570i	$-0.598429\pi$
$239$		−	1.68237e6i		−	1.90514i	0.304319	−	0.952570i	$-0.401571\pi$
$240$	−333119.	−	171135.i	−0.373312	−	0.191784i
$241$		−	1.11088e6i		−	1.23203i	−0.787733	−	0.616017i	$-0.788745\pi$
$241$		−	1.11088e6i		−	1.23203i	0.787733	−	0.616017i	$-0.211255\pi$
$242$	328344.	+	39139.8i	0.360405	+	0.0429616i
$243$	−30939.1			−0.0336118
$244$	−871321.	−	210724.i	−0.936923	−	0.226589i
$245$	−109325.			−0.116360
$246$	40119.8	−	336565.i	0.0422689	−	0.354594i
$247$	848606.	+	140737.i	0.885041	+	0.146780i
$248$	−406181.	−	151004.i	−0.419363	−	0.155905i
$249$			159187.i			0.162708i
$250$	−746075.	−	88935.0i	−0.754975	−	0.0899958i
$251$		−	693709.i		−	0.695013i	−0.937678	−	0.347506i	$-0.887029\pi$
$251$		−	693709.i		−	0.695013i	0.937678	−	0.347506i	$-0.112971\pi$
$252$	3380.62	−	13978.5i	0.00335348	−	0.0138663i
$253$	−1.60886e6			−1.58022
$254$	1.50243e6	+	179096.i	1.46120	+	0.174181i
$255$	62384.1			0.0600791
$256$	610663.	+	852410.i	0.582373	+	0.812921i
$257$			669228.i			0.632035i	0.948753	+	0.316018i	$0.102346\pi$
$257$			669228.i			0.632035i	−0.948753	+	0.316018i	$0.897654\pi$
$258$	136060.	−	1.14141e6i	0.127257	−	1.06756i
$259$	−674740.			−0.625011
$260$	95674.0	−	395602.i	0.0877729	−	0.362932i
$261$		−	23699.5i		−	0.0215347i
$262$	−85740.6	+	719278.i	−0.0771673	+	0.647356i
$263$			290712.i			0.259164i	0.991569	+	0.129582i	$0.0413635\pi$
$263$			290712.i			0.259164i	−0.991569	+	0.129582i	$0.958637\pi$
$264$	−464545.	+	1.24957e6i	−0.410221	+	1.10344i
$265$			20186.0i			0.0176578i
$266$	940529.	+	273504.i	0.815020	+	0.237006i
$267$			1.61420e6i			1.38573i
$268$	1.22586e6	+	296467.i	1.04257	+	0.252138i
$269$			1.94547e6i			1.63924i	0.572904	+	0.819622i	$0.305817\pi$
$269$			1.94547e6i			1.63924i	−0.572904	+	0.819622i	$0.694183\pi$
$270$	−490813.	−	58506.8i	−0.409739	−	0.0488424i
$271$		−	814834.i		−	0.673979i	−0.941508	−	0.336989i	$-0.890591\pi$
$271$		−	814834.i		−	0.673979i	0.941508	−	0.336989i	$-0.109409\pi$
$272$	−155365.	−	79816.4i	−0.127330	−	0.0654139i
$273$	945534.			0.767839
$274$	−366455.	−	43682.8i	−0.294879	−	0.0351507i
$275$			1.21048e6i			0.965217i
$276$	406032.	−	1.67890e6i	0.320839	−	1.32664i
$277$	2.21797e6			1.73683			0.868413	−	0.495841i	$-0.165140\pi$
$277$	2.21797e6			1.73683			0.868413	+	0.495841i	$0.165140\pi$
$278$	−32027.5	+	268679.i	−0.0248549	+	0.208507i
$279$	9777.31			0.00751985
$280$	161496.	−	434403.i	0.123102	−	0.331129i
$281$		−	334610.i		−	0.252798i	−0.991979	−	0.126399i	$-0.959658\pi$
$281$		−	334610.i		−	0.252798i	0.991979	−	0.126399i	$-0.0403419\pi$
$282$	−123973.	+	1.04001e6i	−0.0928337	+	0.778782i
$283$			1.28558e6i			0.954182i	0.878854	+	0.477091i	$0.158309\pi$
$283$			1.28558e6i			0.954182i	−0.878854	+	0.477091i	$0.841691\pi$
$284$	−648871.	−	156925.i	−0.477378	−	0.115451i
$285$	−94157.8	+	567744.i	−0.0686664	+	0.414038i
$286$	−1.43863e6	−	171490.i	−1.04000	−	0.123972i
$287$	419446.			0.300588
$288$	−19616.4	−	13225.9i	−0.0139360	−	0.00939605i
$289$	−1.39076e6			−0.979508
$290$	90399.1	−	758358.i	0.0631203	−	0.529516i
$291$			2.45060e6i			1.69645i
$292$	2.69277e6	+	651229.i	1.84817	+	0.446968i
$293$			1.67633e6i			1.14075i	0.821384	+	0.570376i	$0.193202\pi$
$293$			1.67633e6i			1.14075i	−0.821384	+	0.570376i	$0.806798\pi$
$294$	−414874.	−	49454.5i	−0.279929	−	0.0333686i
$295$	−105047.			−0.0702792
$296$	−386793.	+	1.04042e6i	−0.256596	+	0.690209i
$297$			1.75950e6i			1.15744i
$298$	−811779.	−	96767.0i	−0.529538	−	0.0631229i
$299$	1.87719e6			1.21431
$300$	−1.26318e6	−	305491.i	−0.810327	−	0.195973i
$301$	1.42249e6			0.904967
$302$	906123.	+	108013.i	0.571702	+	0.0681491i
$303$	563420.			0.352554
$304$	960888.	−	1.29347e6i	0.596333	−	0.802737i
$305$	651792.			0.401199
$306$	3913.26	+	466.475i	0.00238910	+	0.000284790i
$307$	2.64043e6			1.59893			0.799463	−	0.600716i	$-0.205118\pi$
$307$	2.64043e6			1.59893			0.799463	+	0.600716i	$0.205118\pi$
$308$	−1.60350e6	−	387798.i	−0.963149	−	0.232932i
$309$	2.95071e6			1.75805
$310$	312863.	+	37294.5i	0.184906	+	0.0220415i
$311$		−	1.47596e6i		−	0.865316i	−0.901558	−	0.432658i	$-0.857576\pi$
$311$		−	1.47596e6i		−	0.865316i	0.901558	−	0.432658i	$-0.142424\pi$
$312$	542025.	−	1.45798e6i	0.315234	−	0.847937i
$313$	−2.98637e6			−1.72299			−0.861495	−	0.507765i	$-0.830472\pi$
$313$	−2.98637e6			−1.72299			−0.861495	+	0.507765i	$0.830472\pi$
$314$	−1.36128e6	−	162270.i	−0.779154	−	0.0928781i
$315$			10456.6i			0.00593767i
$316$	−1.44751e6	−	350072.i	−0.815463	−	0.197215i
$317$			3.19327e6i			1.78479i	0.451251	+	0.892397i	$0.350978\pi$
$317$			3.19327e6i			1.78479i	−0.451251	+	0.892397i	$0.649022\pi$
$318$	−9131.39	+	76603.2i	−0.00506371	+	0.0424795i
$319$	−2.71862e6			−1.49579
$320$	−577254.	−	498040.i	−0.315132	−	0.271888i
$321$	−1.40716e6			−0.762221
$322$	2.12250e6	+	253010.i	1.14079	+	0.135987i
$323$	−43914.6	+	264792.i	−0.0234209	+	0.141221i
$324$	−1.86697e6	−	451516.i	−0.988041	−	0.238952i
$325$		−	1.41237e6i		−	0.741719i
$326$	391674.	−	3.28575e6i	0.204118	−	1.71234i
$327$			906283.i			0.468700i
$328$	240446.	−	646769.i	0.123405	−	0.331944i
$329$	−1.29612e6			−0.660170
$330$	114732.	−	962485.i	0.0579962	−	0.486530i
$331$	−2.87286e6			−1.44127			−0.720634	−	0.693316i	$-0.756149\pi$
$331$	−2.87286e6			−1.44127			−0.720634	+	0.693316i	$0.756149\pi$
$332$	−76177.4	+	314986.i	−0.0379298	+	0.156836i
$333$		−	25044.4i		−	0.0123765i
$334$	−452584.	−	53949.8i	−0.221990	−	0.0264620i
$335$	−917004.			−0.446436
$336$	809361.	−	1.57544e6i	0.391106	−	0.761298i
$337$		−	3.50825e6i		−	1.68273i	−0.540464	−	0.841367i	$-0.681751\pi$
$337$		−	3.50825e6i		−	1.68273i	0.540464	−	0.841367i	$-0.318249\pi$
$338$	−407017.	−	48518.0i	−0.193785	−	0.0231000i
$339$		−	89362.9i		−	0.0422336i
$340$	123441.	+	29853.4i	0.0579109	+	0.0140054i
$341$		−	1.12158e6i		−	0.522327i
$342$	−10151.7	+	34909.6i	−0.00469323	+	0.0161391i
$343$		−	2.36644e6i		−	1.08608i
$344$	815438.	−	2.19342e6i	0.371531	−	0.999369i
$345$			1.25590e6i			0.568078i
$346$	−307373.	+	2.57855e6i	−0.138031	+	1.15794i
$347$			534186.i			0.238160i	0.992885	+	0.119080i	$0.0379945\pi$
$347$			534186.i			0.238160i	−0.992885	+	0.119080i	$0.962006\pi$
$348$	686104.	−	2.83697e6i	0.303698	−	1.25576i
$349$	738288.			0.324461			0.162230	−	0.986753i	$-0.448131\pi$
$349$	738288.			0.324461			0.162230	+	0.986753i	$0.448131\pi$
$350$	190360.	−	1.59693e6i	0.0830627	−	0.696812i
$351$		−	2.05296e6i		−	0.889433i
$352$	−1.51717e6	+	2.25024e6i	−0.652648	+	0.967992i
$353$	3.10279e6			1.32530			0.662652	−	0.748928i	$-0.269431\pi$
$353$	3.10279e6			1.32530			0.662652	+	0.748928i	$0.269431\pi$
$354$	−398637.	−	47519.0i	−0.169071	−	0.0201539i
$355$	485388.			0.204418
$356$	−772462.	+	3.19405e6i	−0.323037	+	1.33572i
$357$			295037.i			0.122520i
$358$	−2.16540e6	−	258124.i	−0.892959	−	0.106444i
$359$		−	2.59116e6i		−	1.06111i	−0.847652	−	0.530553i	$-0.821984\pi$
$359$		−	2.59116e6i		−	1.06111i	0.847652	−	0.530553i	$-0.178016\pi$
$360$	16123.7	+	5994.24i	0.00655706	+	0.00243769i
$361$	−2.34354e6	−	799315.i	−0.946463	−	0.322812i
$362$	−501918.	+	4.21059e6i	−0.201308	+	1.68877i
$363$	−918841.			−0.365994
$364$	1.87095e6	+	452477.i	0.740130	+	0.178996i
$365$	−2.01433e6			−0.791403
$366$	2.47346e6	+	294846.i	0.965167	+	0.115051i
$367$		−	3.94011e6i		−	1.52701i	−0.645800	−	0.763507i	$-0.723476\pi$
$367$		−	3.94011e6i		−	1.52701i	0.645800	−	0.763507i	$-0.276524\pi$
$368$	1.60685e6	−	3.12777e6i	0.618522	−	1.20397i
$369$			15568.6i			0.00595227i
$370$	95528.9	−	801392.i	0.0362769	−	0.304327i
$371$	−95467.1			−0.0360097
$372$	1.17040e6	+	283055.i	0.438508	+	0.106051i
$373$			685230.i			0.255014i	0.991838	+	0.127507i	$0.0406975\pi$
$373$			685230.i			0.255014i	−0.991838	+	0.127507i	$0.959302\pi$
$374$	53510.3	−	448897.i	0.0197814	−	0.165946i
$375$	2.08782e6			0.766683
$376$	−742998.	+	1.99857e6i	−0.271030	+	0.729036i
$377$	3.17204e6			1.14944
$378$	276700.	−	2.32123e6i	0.0996046	−	0.835583i
$379$	454450.			0.162513			0.0812566	−	0.996693i	$-0.474107\pi$
$379$	454450.			0.162513			0.0812566	+	0.996693i	$0.474107\pi$
$380$	−458001.	+	1.07835e6i	−0.162707	+	0.383089i
$381$	−4.20442e6			−1.48386
$382$	−342110.	+	2.86996e6i	−0.119952	+	1.00628i
$383$	2.53189e6			0.881959			0.440980	−	0.897517i	$-0.354631\pi$
$383$	2.53189e6			0.881959			0.440980	+	0.897517i	$0.354631\pi$
$384$	−1.96531e6	−	2.15112e6i	−0.680146	−	0.744452i
$385$	1.19950e6			0.412429
$386$	−509614.	+	4.27515e6i	−0.174090	+	1.46044i
$387$			52798.6i			0.0179203i
$388$	−1.17272e6	+	4.84906e6i	−0.395470	+	1.63523i
$389$	−3.56943e6			−1.19598			−0.597991	−	0.801503i	$-0.704034\pi$
$389$	−3.56943e6			−1.19598			−0.597991	+	0.801503i	$0.704034\pi$
$390$	−133868.	+	1.12301e6i	−0.0445670	+	0.373873i
$391$			585745.i			0.193761i
$392$	−797253.	−	296391.i	−0.262048	−	0.0974204i
$393$		−	2.01283e6i		−	0.657395i
$394$	3.34437e6	+	398661.i	1.08536	+	0.129379i
$395$	1.08281e6			0.349188
$396$	14393.9	−	59517.3i	0.00461255	−	0.0190724i
$397$	2.90509e6			0.925088			0.462544	−	0.886596i	$-0.346937\pi$
$397$	2.90509e6			0.925088			0.462544	+	0.886596i	$0.346937\pi$
$398$	−61858.6	+	518932.i	−0.0195746	+	0.164211i
$399$	−2.68507e6	−	445307.i	−0.844351	−	0.140032i
$400$	−2.35328e6	−	1.20896e6i	−0.735400	−	0.377801i
$401$			2.30956e6i			0.717248i	0.933482	+	0.358624i	$0.116754\pi$
$401$			2.30956e6i			0.717248i	−0.933482	+	0.358624i	$0.883246\pi$
$402$	−3.47990e6	−	414818.i	−1.07399	−	0.128024i
$403$			1.30864e6i			0.401381i
$404$	1.11485e6	+	269620.i	0.339831	+	0.0821861i
$405$	1.39659e6			0.423088
$406$	3.58655e6	+	427531.i	1.07985	+	0.128722i
$407$	−2.87289e6			−0.859672
$408$	454935.	+	169129.i	0.135300	+	0.0503000i
$409$			1.34049e6i			0.396236i	0.980178	+	0.198118i	$0.0634829\pi$
$409$			1.34049e6i			0.396236i	−0.980178	+	0.198118i	$0.936517\pi$
$410$	−59384.6	+	498177.i	−0.0174467	+	0.146361i
$411$	1.02549e6			0.299452
$412$	5.83864e6	+	1.41204e6i	1.69461	+	0.409830i
$413$		−	496803.i		−	0.143321i
$414$	−9390.97	+	78780.8i	−0.00269283	+	0.0225902i
$415$		−	235625.i		−	0.0671586i
$416$	1.77022e6	−	2.62554e6i	0.501526	−	0.743851i
$417$		−	751874.i		−	0.211741i
$418$	4.00455e6	+	1.16452e6i	1.12102	+	0.325991i
$419$			3.35026e6i			0.932273i	0.884713	+	0.466137i	$0.154354\pi$
$419$			3.35026e6i			0.932273i	−0.884713	+	0.466137i	$0.845646\pi$
$420$	−302721.	+	1.25172e6i	−0.0837375	+	0.346246i
$421$		−	5.27807e6i		−	1.45134i	−0.688041	−	0.725672i	$-0.741529\pi$
$421$		−	5.27807e6i		−	1.45134i	0.688041	−	0.725672i	$-0.258471\pi$
$422$	−80329.1	−	9575.53i	−0.0219579	−	0.00261747i
$423$		−	48108.1i		−	0.0130728i
$424$	−54726.3	+	147207.i	−0.0147836	+	0.0397661i
$425$	440705.			0.118352
$426$	1.84198e6	+	219571.i	0.491769	+	0.0586207i
$427$			3.08256e6i			0.818168i
$428$	−2.78438e6	−	673384.i	−0.734714	−	0.177686i
$429$	4.02586e6			1.05613
$430$	−201394.	+	1.68950e6i	−0.0525262	+	0.440642i
$431$	967671.			0.250920			0.125460	−	0.992099i	$-0.459959\pi$
$431$	967671.			0.250920			0.125460	+	0.992099i	$0.459959\pi$
$432$	−3.42063e6	−	1.75730e6i	−0.881855	−	0.453040i
$433$		−	3.53653e6i		−	0.906478i	−0.891389	−	0.453239i	$-0.850268\pi$
$433$		−	3.53653e6i		−	0.906478i	0.891389	−	0.453239i	$-0.149732\pi$
$434$	−176379.	+	1.47964e6i	−0.0449493	+	0.377080i
$435$			2.12220e6i			0.537728i
$436$	−433694.	+	1.79328e6i	−0.109262	+	0.451785i
$437$	−5.33074e6	−	884079.i	−1.33532	−	0.221456i
$438$	−7.64408e6	−	911204.i	−1.90388	−	0.226950i
$439$	−5.35183e6			−1.32538			−0.662691	−	0.748893i	$-0.730586\pi$
$439$	−5.35183e6			−1.32538			−0.662691	+	0.748893i	$0.730586\pi$
$440$	687611.	−	1.84959e6i	0.169321	−	0.455452i
$441$	19190.9			0.00469894
$442$	−62435.0	+	523767.i	−0.0152010	+	0.127521i
$443$			4.14092e6i			1.00251i	0.865301	+	0.501253i	$0.167127\pi$
$443$			4.14092e6i			1.00251i	−0.865301	+	0.501253i	$0.832873\pi$
$444$	725038.	−	2.99796e6i	0.174543	−	0.721719i
$445$		−	2.38931e6i		−	0.571970i
$446$	−1.36031e6	−	162154.i	−0.323818	−	0.0386003i
$447$	2.27169e6			0.537750
$448$	2.35541e6	−	2.73005e6i	0.554462	−	0.642651i
$449$		−	7.58275e6i		−	1.77505i	−0.460758	−	0.887526i	$-0.652422\pi$
$449$		−	7.58275e6i		−	1.77505i	0.460758	−	0.887526i	$-0.347578\pi$
$450$	59273.3	+	7065.60i	0.0137984	+	0.00164482i
$451$	1.78590e6			0.413444
$452$	42763.9	−	176824.i	0.00984535	−	0.0407095i
$453$	−2.53571e6			−0.580568
$454$	6.04497e6	+	720583.i	1.37643	+	0.164076i
$455$	−1.39956e6			−0.316930
$456$	−2.22585e6	+	3.88500e6i	−0.501285	+	0.874941i
$457$	−5.80212e6			−1.29956			−0.649780	−	0.760122i	$-0.725139\pi$
$457$	−5.80212e6			−1.29956			−0.649780	+	0.760122i	$0.725139\pi$
$458$	−2.24056e6	−	267083.i	−0.499105	−	0.0594952i
$459$	640591.			0.141922
$460$	−601001.	+	2.48508e6i	−0.132428	+	0.547577i
$461$	4.35020e6			0.953360			0.476680	−	0.879077i	$-0.341840\pi$
$461$	4.35020e6			0.953360			0.476680	+	0.879077i	$0.341840\pi$
$462$	4.55195e6	+	542609.i	0.992184	+	0.118272i
$463$			1.76492e6i			0.382624i	0.981529	+	0.191312i	$0.0612742\pi$
$463$			1.76492e6i			0.382624i	−0.981529	+	0.191312i	$0.938726\pi$
$464$	2.71522e6	−	5.28524e6i	0.585477	−	1.13965i
$465$	−875520.			−0.187773
$466$	−7.77435e6	−	926732.i	−1.65844	−	0.197692i
$467$			3.47153e6i			0.736594i	0.929708	+	0.368297i	$0.120059\pi$
$467$			3.47153e6i			0.736594i	−0.929708	+	0.368297i	$0.879941\pi$
$468$	−16794.6	+	69444.0i	−0.00354450	+	0.0146562i
$469$		−	4.33685e6i		−	0.910421i
$470$	183503.	−	1.53941e6i	0.0383177	−	0.321447i
$471$	3.80942e6			0.791237
$472$	−766051.	−	284791.i	−0.158272	−	0.0588398i
$473$	6.05663e6			1.24474
$474$	4.10912e6	+	489822.i	0.840045	+	0.100137i
$475$	−665166.	+	4.01076e6i	−0.135268	+	0.815628i
$476$	−141187.	+	583796.i	−0.0285614	+	0.118098i
$477$		−	3543.46i		−	0.000713068i
$478$	−1.12648e6	+	9.45002e6i	−0.225503	+	1.89175i
$479$			940861.i			0.187364i	0.995602	+	0.0936821i	$0.0298637\pi$
$479$			940861.i			0.187364i	−0.995602	+	0.0936821i	$0.970136\pi$
$480$	1.75657e6	+	1.18433e6i	0.347987	+	0.234623i
$481$	3.35205e6			0.660613
$482$	−743817.	+	6.23988e6i	−0.145831	+	1.22337i
$483$	−5.93962e6			−1.15849
$484$	−1.81813e6	−	439704.i	−0.352786	−	0.0853192i
$485$		−	3.62734e6i		−	0.700219i
$486$	173788.	+	20716.1i	0.0333755	+	0.00397849i
$487$	6.26785e6			1.19756			0.598778	−	0.800915i	$-0.295653\pi$
$487$	6.26785e6			1.19756			0.598778	+	0.800915i	$0.295653\pi$
$488$	4.75319e6	+	1.76707e6i	0.903516	+	0.335896i
$489$			9.19488e6i			1.73890i
$490$	614089.	+	73201.7i	0.115542	+	0.0137731i
$491$		−	5.19723e6i		−	0.972899i	−0.873709	−	0.486450i	$-0.838292\pi$
$491$		−	5.19723e6i		−	0.972899i	0.873709	−	0.486450i	$-0.161708\pi$
$492$	−450713.	+	1.86365e6i	−0.0839435	+	0.347098i
$493$			989780.i			0.183409i
$494$	−4.67246e6	−	1.35874e6i	−0.861446	−	0.250507i
$495$			44522.0i			0.00816698i
$496$	2.18044e6	+	1.12017e6i	0.397961	+	0.204447i
$497$			2.29558e6i			0.416870i
$498$	106588.	−	894165.i	0.0192590	−	0.161564i
$499$		−	7.46275e6i		−	1.34168i	−0.741604	−	0.670838i	$-0.765934\pi$
$499$		−	7.46275e6i		−	1.34168i	0.741604	−	0.670838i	$-0.234066\pi$
$500$	4.13122e6	+	999111.i	0.739015	+	0.178726i
$501$	1.26652e6			0.225433
$502$	−464492.	+	3.89662e6i	−0.0822657	+	0.690127i
$503$			4.89349e6i			0.862380i	0.902261	+	0.431190i	$0.141906\pi$
$503$			4.89349e6i			0.862380i	−0.902261	+	0.431190i	$0.858094\pi$
$504$	−28349.0	+	76255.0i	−0.00497120	+	0.0133719i
$505$	−833964.			−0.145519
$506$	9.03710e6	+	1.07726e6i	1.56911	+	0.187044i
$507$	1.13900e6			0.196791
$508$	−8.31938e6	−	2.01199e6i	−1.43031	−	0.345913i
$509$			7.40546e6i			1.26695i	0.773765	+	0.633473i	$0.218371\pi$
$509$			7.40546e6i			1.26695i	−0.773765	+	0.633473i	$0.781629\pi$
$510$	−350417.	−	41771.0i	−0.0596567	−	0.00711130i
$511$		−	9.52648e6i		−	1.61391i
$512$	−2.85939e6	−	5.19695e6i	−0.482057	−	0.876140i
$513$	−966859.	+	5.82988e6i	−0.162207	+	0.978061i
$514$	448100.	−	3.75911e6i	0.0748114	−	0.627592i
$515$	−4.36760e6			−0.725645
$516$	−1.52853e6	+	6.32030e6i	−0.252725	+	1.04499i
$517$	−5.51858e6			−0.908032
$518$	3.79008e6	+	451791.i	0.620617	+	0.0739798i
$519$		−	7.21585e6i		−	1.17590i
$520$	−802295.	+	2.15807e6i	−0.130115	+	0.349991i
$521$			4.94484e6i			0.798101i	0.916929	+	0.399051i	$0.130660\pi$
$521$			4.94484e6i			0.798101i	−0.916929	+	0.399051i	$0.869340\pi$
$522$	−15868.7	+	133122.i	−0.00254897	+	0.0213833i
$523$	409687.			0.0654935			0.0327468	−	0.999464i	$-0.489575\pi$
$523$	409687.			0.0654935			0.0327468	+	0.999464i	$0.489575\pi$
$524$	963225.	−	3.98284e6i	0.153250	−	0.633672i
$525$			4.46887e6i			0.707618i
$526$	194654.	−	1.63296e6i	0.0306761	−	0.257342i
$527$	−408337.			−0.0640461
$528$	3.44607e6	−	6.70787e6i	0.537947	−	1.04713i
$529$	−5.35574e6			−0.832110
$530$	13516.1	−	113387.i	0.00209008	−	0.0175337i
$531$	18439.9			0.00283806
$532$	−5.09990e6	−	2.16605e6i	−0.781237	−	0.331811i
$533$	−2.08377e6			−0.317710
$534$	1.08083e6	−	9.06711e6i	0.164023	−	1.37599i
$535$	2.08285e6			0.314611
$536$	−6.68725e6	−	2.48609e6i	−1.00539	−	0.373770i
$537$	6.05969e6			0.906807
$538$	1.30264e6	−	1.09279e7i	0.194030	−	1.62772i
$539$		−	2.20143e6i		−	0.326387i
$540$	2.71777e6	+	657275.i	0.401077	+	0.0969980i
$541$	1.30328e6			0.191445			0.0957225	−	0.995408i	$-0.469484\pi$
$541$	1.30328e6			0.191445			0.0957225	+	0.995408i	$0.469484\pi$
$542$	−545595.	+	4.57700e6i	−0.0797760	+	0.669241i
$543$		−	1.17830e7i		−	1.71496i
$544$	819254.	+	552365.i	0.118692	+	0.0800256i
$545$		−	1.34146e6i		−	0.193459i
$546$	−5.31115e6	−	633108.i	−0.762442	−	0.0908859i
$547$	6.44982e6			0.921678			0.460839	−	0.887484i	$-0.347548\pi$
$547$	6.44982e6			0.921678			0.460839	+	0.887484i	$0.347548\pi$
$548$	2.02916e6	+	490741.i	0.288646	+	0.0698073i
$549$	−114416.			−0.0162015
$550$	810509.	−	6.79936e6i	0.114249	−	0.958432i
$551$	−9.00777e6	−	1.49390e6i	−1.26398	−	0.209625i
$552$	−3.40487e6	+	9.15866e6i	−0.475612	+	1.27933i
$553$			5.12101e6i			0.712103i
$554$	−1.24585e7	−	1.48510e6i	−1.72462	−	0.205581i
$555$			2.24262e6i			0.309047i
$556$	359803.	−	1.48775e6i	0.0493603	−	0.204100i
$557$	2.54824e6			0.348019			0.174009	−	0.984744i	$-0.444328\pi$
$557$	2.54824e6			0.348019			0.174009	+	0.984744i	$0.444328\pi$
$558$	−54920.0	−	6546.67i	−0.00746698	−	0.000890092i
$559$	−7.06679e6			−0.956516
$560$	−1.19800e6	+	2.33194e6i	−0.161431	+	0.314230i
$561$			1.25620e6i			0.168520i
$562$	−224048.	+	1.87953e6i	−0.0299226	+	0.251021i
$563$	9.38723e6			1.24815			0.624074	−	0.781365i	$-0.285476\pi$
$563$	9.38723e6			1.24815			0.624074	+	0.781365i	$0.285476\pi$
$564$	1.39274e6	−	5.75883e6i	0.184362	−	0.762318i
$565$			132273.i			0.0174322i
$566$	860793.	−	7.22119e6i	0.112943	−	0.947475i
$567$			6.60498e6i			0.862807i
$568$	3.53969e6	+	1.31593e6i	0.460356	+	0.171145i
$569$			9.34737e6i			1.21034i	0.796095	+	0.605172i	$0.206896\pi$
$569$			9.34737e6i			1.21034i	−0.796095	+	0.605172i	$0.793104\pi$
$570$	909041.	−	3.12602e6i	0.117192	−	0.403000i
$571$			3.07222e6i			0.394332i	0.980370	+	0.197166i	$0.0631738\pi$
$571$			3.07222e6i			0.394332i	−0.980370	+	0.197166i	$0.936826\pi$
$572$	7.96606e6	+	1.92654e6i	1.01801	+	0.246200i
$573$		−	8.03133e6i		−	1.02188i
$574$	−2.35606e6	−	280851.i	−0.298474	−	0.0355793i
$575$			8.87216e6i			1.11908i
$576$	101331.	+	87426.0i	0.0127259	+	0.0109795i
$577$	1.02917e7			1.28690			0.643451	−	0.765487i	$-0.277502\pi$
$577$	1.02917e7			1.28690			0.643451	+	0.765487i	$0.277502\pi$
$578$	7.81203e6	+	931223.i	0.972622	+	0.115940i
$579$		−	1.19636e7i		−	1.48309i
$580$	−1.01556e6	+	4.19923e6i	−0.125353	+	0.518323i
$581$	1.11436e6			0.136957
$582$	1.64087e6	−	1.37652e7i	0.200801	−	1.68452i
$583$	−406477.			−0.0495296
$584$	−1.46895e7	−	5.46103e6i	−1.78227	−	0.662586i
$585$		−	51947.6i		−	0.00627590i
$586$	1.12244e6	−	9.41611e6i	0.135026	−	1.13273i
$587$			1.36571e7i			1.63593i	0.575268	+	0.817965i	$0.304898\pi$
$587$			1.36571e7i			1.63593i	−0.575268	+	0.817965i	$0.695102\pi$
$588$	2.29727e6	+	555581.i	0.274011	+	0.0662680i
$589$	616313.	−	3.71619e6i	0.0732004	−	0.441377i
$590$	590055.	+	70336.8i	0.0697851	+	0.00831865i
$591$	−9.35891e6			−1.10219
$592$	2.86929e6	−	5.58516e6i	0.336489	−	0.654985i
$593$	−1.11442e7			−1.30140			−0.650702	−	0.759333i	$-0.725525\pi$
$593$	−1.11442e7			−1.30140			−0.650702	+	0.759333i	$0.725525\pi$
$594$	1.17812e6	−	9.88328e6i	0.137001	−	1.14930i
$595$		−	436709.i		−	0.0505707i
$596$	4.49504e6	+	1.08710e6i	0.518344	+	0.125358i
$597$		−	1.45218e6i		−	0.166758i
$598$	−1.05444e7	−	1.25693e6i	−1.20578	−	0.143733i
$599$	1.03986e7			1.18415			0.592077	−	0.805882i	$-0.298308\pi$
$599$	1.03986e7			1.18415			0.592077	+	0.805882i	$0.298308\pi$
$600$	6.89082e6	+	2.56177e6i	0.781434	+	0.290510i
$601$		−	2.38553e6i		−	0.269400i	−0.990886	−	0.134700i	$-0.956993\pi$
$601$		−	2.38553e6i		−	0.269400i	0.990886	−	0.134700i	$-0.0430071\pi$
$602$	−7.99024e6	−	952467.i	−0.898605	−	0.107117i
$603$	160971.			0.0180283
$604$	−5.01745e6	−	1.21344e6i	−0.559617	−	0.135340i
$605$	1.36005e6			0.151066
$606$	−3.16478e6	−	377253.i	−0.350076	−	0.0417303i
$607$	−3.25440e6			−0.358508			−0.179254	−	0.983803i	$-0.557368\pi$
$607$	−3.25440e6			−0.358508			−0.179254	+	0.983803i	$0.557368\pi$
$608$	−6.26347e6	+	6.62216e6i	−0.687157	+	0.726509i
$609$	−1.00366e7			−1.09659
$610$	−3.66117e6	−	436426.i	−0.398378	−	0.0474882i
$611$	6.43900e6			0.697775
$612$	−21668.8	−	5240.46i	−0.00233860	−	0.000565576i
$613$	−3.29689e6			−0.354366			−0.177183	−	0.984178i	$-0.556699\pi$
$613$	−3.29689e6			−0.354366			−0.177183	+	0.984178i	$0.556699\pi$
$614$	−1.48315e7	−	1.76797e6i	−1.58769	−	0.189258i
$615$		−	1.39410e6i		−	0.148630i
$616$	8.74736e6	+	3.25197e6i	0.928807	+	0.345298i
$617$	5.29269e6			0.559711			0.279855	−	0.960042i	$-0.409713\pi$
$617$	5.29269e6			0.559711			0.279855	+	0.960042i	$0.409713\pi$
$618$	−1.65744e7	−	1.97573e6i	−1.74569	−	0.208093i
$619$			3.75374e6i			0.393765i	0.980427	+	0.196882i	$0.0630817\pi$
$619$			3.75374e6i			0.393765i	−0.980427	+	0.196882i	$0.936918\pi$
$620$	−1.73241e6	−	418973.i	−0.180997	−	0.0437730i
$621$			1.28962e7i			1.34194i
$622$	−988272.	+	8.29061e6i	−0.102424	+	0.859233i
$623$	1.12999e7			1.16642
$624$	−4.02083e6	+	7.82665e6i	−0.413384	+	0.804664i
$625$	4.98356e6			0.510316
$626$	1.67747e7	+	1.99961e6i	1.71088	+	0.203943i
$627$	−1.14324e7	−	1.89601e6i	−1.16136	−	0.192607i
$628$	7.53778e6	+	1.82297e6i	0.762683	+	0.184450i
$629$			1.04595e6i			0.105410i
$630$	7001.54	−	58735.9i	0.000702817	−	0.00589593i
$631$		−	6.18008e6i		−	0.617903i	−0.951078	−	0.308952i	$-0.900022\pi$
$631$		−	6.18008e6i		−	0.617903i	0.951078	−	0.308952i	$-0.0999781\pi$
$632$	7.89639e6	+	2.93560e6i	0.786386	+	0.292351i
$633$	224794.			0.0222985
$634$	2.13815e6	−	1.79369e7i	0.211259	−	1.77225i
$635$	6.22331e6			0.612473
$636$	102584.	−	424173.i	0.0100562	−	0.0415815i
$637$			2.56860e6i			0.250812i
$638$	1.52707e7	+	1.82033e6i	1.48528	+	0.177051i
$639$	−85205.0			−0.00825492
$640$	2.90901e6	+	3.18405e6i	0.280734	+	0.307277i
$641$			6.73016e6i			0.646965i	0.946234	+	0.323482i	$0.104854\pi$
$641$			6.73016e6i			0.646965i	−0.946234	+	0.323482i	$0.895146\pi$
$642$	7.90414e6	+	942203.i	0.756863	+	0.0902209i
$643$			1.62098e7i			1.54614i	0.634318	+	0.773072i	$0.281281\pi$
$643$			1.62098e7i			1.54614i	−0.634318	+	0.773072i	$0.718719\pi$
$644$	−1.17528e7	−	2.84235e6i	−1.11668	−	0.270062i
$645$		−	4.72790e6i		−	0.447475i
$646$	423971.	−	1.45796e6i	0.0399719	−	0.137456i
$647$			7.50997e6i			0.705306i	0.935754	+	0.352653i	$0.114720\pi$
$647$			7.50997e6i			0.705306i	−0.935754	+	0.352653i	$0.885280\pi$
$648$	1.01846e7	+	3.78629e6i	0.952812	+	0.354222i
$649$		−	2.11527e6i		−	0.197131i
$650$	−945691.	+	7.93340e6i	−0.0877942	+	0.736505i
$651$		−	4.14065e6i		−	0.382927i
$652$	−4.40013e6	+	1.81941e7i	−0.405365	+	1.67614i
$653$	1.55222e7			1.42452			0.712261	−	0.701915i	$-0.247671\pi$
$653$	1.55222e7			1.42452			0.712261	+	0.701915i	$0.247671\pi$
$654$	606827.	−	5.09067e6i	0.0554780	−	0.465405i
$655$			2.97936e6i			0.271344i
$656$	−1.78367e6	+	3.47196e6i	−0.161828	+	0.315003i
$657$	353595.			0.0319589
$658$	7.28042e6	+	867854.i	0.655529	+	0.0781415i
$659$	−1.10118e7			−0.987749			−0.493875	−	0.869533i	$-0.664420\pi$
$659$	−1.10118e7			−0.987749			−0.493875	+	0.869533i	$0.664420\pi$
$660$	−1.28892e6	+	5.32954e6i	−0.115177	+	0.476245i
$661$		−	2.65926e6i		−	0.236732i	−0.992970	−	0.118366i	$-0.962234\pi$
$661$		−	2.65926e6i		−	0.236732i	0.992970	−	0.118366i	$-0.0377656\pi$
$662$	1.61371e7	+	1.92360e6i	1.43114	+	0.170597i
$663$		−	1.46572e6i		−	0.129499i
$664$	638803.	−	1.71830e6i	0.0562272	−	0.151244i
$665$	3.97439e6	+	659135.i	0.348511	+	0.0577990i
$666$	−16769.1	+	140676.i	−0.00146496	+	0.0122895i
$667$	−1.99260e7			−1.73423
$668$	2.50608e6	+	606081.i	0.217297	+	0.0525520i
$669$	3.80671e6			0.328840
$670$	5.15089e6	+	614006.i	0.443298	+	0.0528428i
$671$			1.31248e7i			1.12535i
$672$	−5.60113e6	+	8.30747e6i	−0.478468	+	0.709652i
$673$		−	1.17572e7i		−	1.00062i	−0.865848	−	0.500308i	$-0.833220\pi$
$673$		−	1.17572e7i		−	1.00062i	0.865848	−	0.500308i	$-0.166780\pi$
$674$	−2.34905e6	+	1.97061e7i	−0.199178	+	1.67091i
$675$	9.70290e6			0.819676
$676$	2.25377e6	+	545060.i	0.189689	+	0.0458751i
$677$		−	4.92504e6i		−	0.412988i	−0.978448	−	0.206494i	$-0.933795\pi$
$677$		−	4.92504e6i		−	0.412988i	0.978448	−	0.206494i	$-0.0662054\pi$
$678$	−59835.4	+	501959.i	−0.00499901	+	0.0419367i
$679$	1.71550e7			1.42796
$680$	−673387.	−	250342.i	−0.0558461	−	0.0207616i
$681$	−1.69163e7			−1.39778
$682$	−750982.	+	6.29998e6i	−0.0618256	+	0.518655i
$683$	−1.17171e7			−0.961103			−0.480552	−	0.876966i	$-0.659563\pi$
$683$	−1.17171e7			−0.961103			−0.480552	+	0.876966i	$0.659563\pi$
$684$	80397.5	−	189293.i	0.00657056	−	0.0154702i
$685$	−1.51792e6			−0.123601
$686$	−1.58451e6	+	1.32925e7i	−0.128554	+	1.07844i
$687$	6.27000e6			0.506845
$688$	−6.04905e6	+	1.17746e7i	−0.487210	+	0.948367i
$689$	474272.			0.0380609
$690$	840924.	−	7.05451e6i	0.0672410	−	0.564084i
$691$		−	8.37197e6i		−	0.667010i	−0.942748	−	0.333505i	$-0.891769\pi$
$691$		−	8.37197e6i		−	0.667010i	0.942748	−	0.333505i	$-0.108231\pi$
$692$	3.45308e6	−	1.42781e7i	0.274121	−	1.13346i
$693$	−210561.			−0.0166550
$694$	357679.	−	3.00057e6i	0.0281900	−	0.236486i
$695$			1.11291e6i			0.0873974i
$696$	−5.75348e6	+	1.54761e7i	−0.450202	+	1.21098i
$697$		−	650202.i		−	0.0506951i
$698$	−4.14703e6	−	494341.i	−0.322180	−	0.0384051i
$699$	2.17558e7			1.68416
$700$	−2.13854e6	+	8.84264e6i	−0.164957	+	0.682082i
$701$	−1.28303e7			−0.986150			−0.493075	−	0.869987i	$-0.664127\pi$
$701$	−1.28303e7			−0.986150			−0.493075	+	0.869987i	$0.664127\pi$
$702$	−1.37462e6	+	1.15317e7i	−0.105278	+	0.883181i
$703$	−9.51893e6	−	1.57867e6i	−0.726440	−	0.120477i
$704$	1.00288e7	−	1.16239e7i	0.762636	−	0.883935i
$705$			4.30789e6i			0.326432i
$706$	−1.74286e7	−	2.07756e6i	−1.31599	−	0.156871i
$707$		−	3.94412e6i		−	0.296758i
$708$	2.20736e6	+	533837.i	0.165497	+	0.0400245i
$709$	1.14516e6			0.0855560			0.0427780	−	0.999085i	$-0.486379\pi$
$709$	1.14516e6			0.0855560			0.0427780	+	0.999085i	$0.486379\pi$
$710$	−2.72647e6	−	325005.i	−0.202980	−	0.0241960i
$711$	−190077.			−0.0141012
$712$	6.47765e6	−	1.74240e7i	0.478870	−	1.28810i
$713$		−	8.22055e6i		−	0.605588i
$714$	197550.	−	1.65725e6i	0.0145021	−	0.121658i
$715$	−5.95901e6			−0.435922
$716$	1.19904e7	+	2.89981e6i	0.874082	+	0.211391i
$717$		−	2.64450e7i		−	1.92108i
$718$	−1.73498e6	+	1.45548e7i	−0.125598	+	1.05365i
$719$		−	2.45870e7i		−	1.77372i	−0.462043	−	0.886858i	$-0.652883\pi$
$719$		−	2.45870e7i		−	1.77372i	0.462043	−	0.886858i	$-0.347117\pi$
$720$	−86554.8	−	44466.3i	−0.00622243	−	0.00319668i
$721$		−	2.06560e7i		−	1.47981i
$722$	1.26286e7	+	6.05900e6i	0.901600	+	0.432572i
$723$		−	1.74618e7i		−	1.24234i
$724$	5.63864e6	−	2.33152e7i	0.399786	−	1.65308i
$725$			1.49920e7i			1.05929i
$726$	5.16121e6	+	615236.i	0.363421	+	0.0433211i
$727$			1.29300e7i			0.907324i	0.891174	+	0.453662i	$0.149883\pi$
$727$			1.29300e7i			0.907324i	−0.891174	+	0.453662i	$0.850117\pi$
$728$	−1.02063e7	−	3.79435e6i	−0.713740	−	0.265344i
$729$	1.40997e7			0.982632
$730$	1.13146e7	+	1.34875e6i	0.785839	+	0.0936750i
$731$		−	2.20507e6i		−	0.152626i
$732$	−1.36962e7	−	3.31235e6i	−0.944763	−	0.228485i
$733$	−1.70558e7			−1.17250			−0.586248	−	0.810131i	$-0.699396\pi$
$733$	−1.70558e7			−1.17250			−0.586248	+	0.810131i	$0.699396\pi$
$734$	−2.63821e6	+	2.21319e7i	−0.180746	+	1.51628i
$735$	−1.71847e6			−0.117334
$736$	−1.11201e7	+	1.64930e7i	−0.756682	+	1.12229i
$737$		−	1.84653e7i		−	1.25224i
$738$	10424.4	−	87450.0i	0.000704545	−	0.00591043i
$739$		−	5.41138e6i		−	0.364500i	−0.983252	−	0.182250i	$-0.941662\pi$
$739$		−	5.41138e6i		−	0.364500i	0.983252	−	0.182250i	$-0.0583379\pi$
$740$	−1.07319e6	+	4.43752e6i	−0.0720438	+	0.297894i
$741$	1.33392e7	+	2.21224e6i	0.892448	+	0.148009i
$742$	536247.	+	63922.7i	0.0357565	+	0.00426231i
$743$	−2.35088e7			−1.56228			−0.781138	−	0.624359i	$-0.785360\pi$
$743$	−2.35088e7			−1.56228			−0.781138	+	0.624359i	$0.785360\pi$
$744$	−6.38472e6	−	2.37362e6i	−0.422873	−	0.157209i
$745$	−3.36251e6			−0.221959
$746$	458815.	−	3.84900e6i	0.0301849	−	0.253221i
$747$			41361.7i			0.00271204i
$748$	−601143.	+	2.48567e6i	−0.0392848	+	0.162438i
$749$			9.85057e6i			0.641589i
$750$	−1.17275e7	−	1.39796e6i	−0.761293	−	0.0907490i
$751$	2.27399e7			1.47126			0.735630	−	0.677383i	$-0.236886\pi$
$751$	2.27399e7			1.47126			0.735630	+	0.677383i	$0.236886\pi$
$752$	5.51168e6	−	1.07286e7i	0.355418	−	0.691830i
$753$		−	1.09043e7i		−	0.700829i
$754$	−1.78176e7	−	2.12393e6i	−1.14136	−	0.136054i
$755$	3.75331e6			0.239633
$756$	−3.10849e6	+	1.28533e7i	−0.197809	+	0.817919i
$757$	−1.60184e7			−1.01597			−0.507985	−	0.861366i	$-0.669609\pi$
$757$	−1.60184e7			−1.01597			−0.507985	+	0.861366i	$0.669609\pi$
$758$	−2.55269e6	−	304290.i	−0.161371	−	0.0192360i
$759$	−2.52895e7			−1.59344
$760$	3.29467e6	−	5.75051e6i	0.206908	−	0.361137i
$761$	3.11406e6			0.194924			0.0974621	−	0.995239i	$-0.468928\pi$
$761$	3.11406e6			0.194924			0.0974621	+	0.995239i	$0.468928\pi$
$762$	2.36166e7	+	2.81519e6i	1.47343	+	0.175639i
$763$	6.34428e6			0.394522
$764$	3.84333e6	−	1.58918e7i	0.238218	−	0.985005i
$765$	16209.3			0.00100141
$766$	−1.42219e7	−	1.69530e6i	−0.875759	−	0.104394i
$767$			2.46807e6i			0.151485i
$768$	9.59895e6	+	1.33990e7i	0.587247	+	0.819725i
$769$	8.19329e6			0.499623			0.249812	−	0.968294i	$-0.419631\pi$
$769$	8.19329e6			0.499623			0.249812	+	0.968294i	$0.419631\pi$
$770$	−6.73771e6	−	803160.i	−0.409530	−	0.0488175i
$771$			1.05195e7i			0.637325i
$772$	5.72509e6	−	2.36727e7i	0.345732	−	1.42956i
$773$		−	1.98892e7i		−	1.19721i	−0.801045	−	0.598604i	$-0.795722\pi$
$773$		−	1.98892e7i		−	1.19721i	0.801045	−	0.598604i	$-0.204278\pi$
$774$	35352.7	−	296574.i	0.00212115	−	0.0177943i
$775$	−6.18500e6			−0.369901
$776$	9.83406e6	−	2.64523e7i	0.586244	−	1.57692i
$777$	−1.06062e7			−0.630241
$778$	2.00498e7	+	2.39001e6i	1.18757	+	0.141563i
$779$	5.91735e6	+	981366.i	0.349368	+	0.0579412i
$780$	1.50389e6	−	6.21843e6i	0.0885075	−	0.365969i
$781$			9.77403e6i			0.573385i
$782$	392202.	−	3.29018e6i	0.0229347	−	0.192399i
$783$			2.17918e7i			1.27025i
$784$	4.27978e6	+	2.19868e6i	0.248675	+	0.127753i
$785$	−5.63864e6			−0.326588
$786$	−1.34775e6	+	1.13063e7i	−0.0778131	+	0.652774i
$787$	−2.07940e7			−1.19674			−0.598371	−	0.801219i	$-0.704185\pi$
$787$	−2.07940e7			−1.19674			−0.598371	+	0.801219i	$0.704185\pi$
$788$	−1.85187e7	−	4.47863e6i	−1.06241	−	0.256939i
$789$			4.56968e6i			0.261332i
$790$	−6.08224e6	−	725026.i	−0.346734	−	0.0413320i
$791$	−625570.			−0.0355496
$792$	−120703.	+	324676.i	−0.00683764	+	0.0183924i
$793$		−	1.53139e7i		−	0.864773i
$794$	−1.63181e7	−	1.94518e6i	−0.918585	−	0.109499i
$795$			317303.i			0.0178056i
$796$	694931.	−	2.87347e6i	0.0388740	−	0.160740i
$797$			1.56737e7i			0.874030i	0.899454	+	0.437015i	$0.143964\pi$
$797$			1.56737e7i			0.874030i	−0.899454	+	0.437015i	$0.856036\pi$
$798$	1.47841e7	+	4.29919e6i	0.821840	+	0.238990i
$799$			2.00918e6i			0.111340i
$800$	1.24091e7	+	8.36656e6i	0.685512	+	0.462191i
$801$			419420.i			0.0230976i
$802$	1.54643e6	−	1.29730e7i	0.0848976	−	0.712205i
$803$		−	4.05615e7i		−	2.21986i
$804$	1.92692e7	+	4.66013e6i	1.05129	+	0.254248i
$805$	8.79172e6			0.478172
$806$	876235.	−	7.35073e6i	0.0475098	−	0.398559i
$807$			3.05807e7i			1.65296i
$808$	−6.08168e6	−	2.26096e6i	−0.327714	−	0.121833i
$809$	−1.93954e7			−1.04190			−0.520951	−	0.853587i	$-0.674423\pi$
$809$	−1.93954e7			−1.04190			−0.520951	+	0.853587i	$0.674423\pi$
$810$	−7.84476e6	−	935125.i	−0.420114	−	0.0500792i
$811$	−368174.			−0.0196563			−0.00982814	−	0.999952i	$-0.503128\pi$
$811$	−368174.			−0.0196563			−0.00982814	+	0.999952i	$0.503128\pi$
$812$	−1.98597e7	−	4.80295e6i	−1.05702	−	0.255634i
$813$		−	1.28083e7i		−	0.679619i
$814$	1.61373e7	+	1.92362e6i	0.853629	+	0.101756i
$815$		−	1.36101e7i		−	0.717740i
$816$	−2.44217e6	−	1.25463e6i	−0.128396	−	0.0659613i
$817$	2.00678e7	+	3.32816e6i	1.05183	+	0.174441i
$818$	897560.	−	7.52963e6i	0.0469008	−	0.393451i
$819$	245679.			0.0127985
$820$	667137.	−	2.75854e6i	0.0346482	−	0.143267i
$821$	1.79586e7			0.929854			0.464927	−	0.885349i	$-0.346081\pi$
$821$	1.79586e7			0.929854			0.464927	+	0.885349i	$0.346081\pi$
$822$	−5.76028e6	−	686647.i	−0.297347	−	0.0354449i
$823$		−	4.54807e6i		−	0.234060i	−0.993128	−	0.117030i	$-0.962663\pi$
$823$		−	4.54807e6i		−	0.234060i	0.993128	−	0.117030i	$-0.0373374\pi$
$824$	−3.18507e7	−	1.18410e7i	−1.63418	−	0.607532i
$825$			1.90274e7i			0.973295i
$826$	−332649.	+	2.79059e6i	−0.0169643	+	0.142313i
$827$	2.93386e7			1.49168			0.745840	−	0.666125i	$-0.232048\pi$
$827$	2.93386e7			1.49168			0.745840	+	0.666125i	$0.232048\pi$
$828$	105500.	−	436231.i	0.00534780	−	0.0221126i
$829$			2.98056e7i			1.50630i	0.657850	+	0.753149i	$0.271466\pi$
$829$			2.98056e7i			1.50630i	−0.657850	+	0.753149i	$0.728534\pi$
$830$	−157769.	+	1.32353e6i	−0.00794928	+	0.0666865i
$831$	3.48641e7			1.75136
$832$	−1.17015e7	+	1.35626e7i	−0.586046	+	0.679258i
$833$	−801486.			−0.0400206
$834$	−503438.	+	4.22334e6i	−0.0250629	+	0.210252i
$835$	−1.87468e6			−0.0930486
$836$	−2.17142e7	−	9.22255e6i	−1.07455	−	0.456389i
$837$	−8.99028e6			−0.443567
$838$	2.24326e6	−	1.88187e7i	0.110349	−	0.925719i
$839$	2.68069e7			1.31474			0.657372	−	0.753566i	$-0.271668\pi$
$839$	2.68069e7			1.31474			0.657372	+	0.753566i	$0.271668\pi$
$840$	2.53854e6	−	6.82834e6i	0.124132	−	0.333900i
$841$	−1.31594e7			−0.641575
$842$	−3.53408e6	+	2.96474e7i	−0.171789	+	1.44114i
$843$		−	5.25971e6i		−	0.254913i
$844$	444804.	+	107573.i	0.0214938	+	0.00519814i
$845$	−1.68593e6			−0.0812265
$846$	−32212.1	+	270228.i	−0.00154737	+	0.0129809i
$847$			6.43218e6i			0.308070i
$848$	405969.	−	790229.i	0.0193866	−	0.0377366i
$849$			2.02078e7i			0.962168i
$850$	−2.47548e6	−	295086.i	−0.117520	−	0.0140088i
$851$	−2.10568e7			−0.996707
$852$	−1.01995e7	−	2.46670e6i	−0.481373	−	0.116417i
$853$	2.73588e7			1.28743			0.643715	−	0.765265i	$-0.277392\pi$
$853$	2.73588e7			1.28743			0.643715	+	0.765265i	$0.277392\pi$
$854$	2.06402e6	−	1.73150e7i	0.0968430	−	0.812416i
$855$	−24465.1	+	147518.i	−0.00114454	+	0.00690126i
$856$	1.51892e7	+	5.64681e6i	0.708517	+	0.263402i
$857$		−	3.30494e7i		−	1.53713i	−0.639769	−	0.768567i	$-0.720970\pi$
$857$		−	3.30494e7i		−	1.53713i	0.639769	−	0.768567i	$-0.279030\pi$
$858$	−2.26136e7	−	2.69563e6i	−1.04870	−	0.125009i
$859$		−	7.98108e6i		−	0.369045i	−0.982828	−	0.184522i	$-0.940926\pi$
$859$		−	7.98108e6i		−	0.369045i	0.982828	−	0.184522i	$-0.0590738\pi$
$860$	2.26250e6	−	9.35519e6i	0.104314	−	0.431327i
$861$	6.59323e6			0.303103
$862$	−5.43549e6	−	647931.i	−0.249156	−	0.0297003i
$863$	−2.91608e7			−1.33282			−0.666412	−	0.745584i	$-0.732171\pi$
$863$	−2.91608e7			−1.33282			−0.666412	+	0.745584i	$0.732171\pi$
$864$	1.80374e7	+	1.21613e7i	0.822032	+	0.554237i
$865$			1.06808e7i			0.485358i
$866$	−2.36798e6	+	1.98650e7i	−0.107296	+	0.900105i
$867$	−2.18613e7			−0.987705
$868$	1.98147e6	−	8.19319e6i	0.0892666	−	0.369108i
$869$			2.18041e7i			0.979463i
$870$	1.42098e6	−	1.19206e7i	0.0636486	−	0.533948i
$871$			2.15450e7i			0.962281i
$872$	3.63684e6	−	9.78262e6i	0.161969	−	0.435676i
$873$			636743.i			0.0282767i
$874$	2.93513e7	+	8.53530e6i	1.29972	+	0.377955i
$875$		−	1.46154e7i		−	0.645345i
$876$	4.23274e7	+	1.02366e7i	1.86364	+	0.450709i
$877$			2.77279e7i			1.21736i	0.793417	+	0.608679i	$0.208300\pi$
$877$			2.77279e7i			1.21736i	−0.793417	+	0.608679i	$0.791700\pi$
$878$	3.00617e7	+	3.58347e6i	1.31606	+	0.156880i
$879$			2.63501e7i			1.15030i
$880$	−5.10081e6	+	9.92887e6i	−0.222041	+	0.432208i
$881$	−3.07665e7			−1.33548			−0.667742	−	0.744393i	$-0.732739\pi$
$881$	−3.07665e7			−1.33548			−0.667742	+	0.744393i	$0.732739\pi$
$882$	−107797.	−	12849.8i	−0.00466591	−	0.000556194i
$883$		−	3.46776e7i		−	1.49674i	−0.663280	−	0.748372i	$-0.730836\pi$
$883$		−	3.46776e7i		−	1.49674i	0.663280	−	0.748372i	$-0.269164\pi$
$884$	701406.	−	2.90024e6i	0.0301883	−	0.124826i
$885$	−1.65122e6			−0.0708673
$886$	2.77267e6	−	2.32599e7i	0.118662	−	0.995459i
$887$	−4.49131e6			−0.191674			−0.0958372	−	0.995397i	$-0.530553\pi$
$887$	−4.49131e6			−0.191674			−0.0958372	+	0.995397i	$0.530553\pi$
$888$	−6.07997e6	+	1.63543e7i	−0.258743	+	0.695985i
$889$			2.94323e7i			1.24902i
$890$	−1.59983e6	+	1.34210e7i	−0.0677016	+	0.567949i
$891$			2.81225e7i			1.18675i
$892$	7.53241e6	+	1.82167e6i	0.316973	+	0.0766579i
$893$	−1.82851e7	−	3.03250e6i	−0.767305	−	0.127254i
$894$	−1.27603e7	−	1.52107e6i	−0.533969	−	0.0636511i
$895$	−8.96945e6			−0.374290
$896$	−1.50585e7	+	1.37578e7i	−0.626633	+	0.572504i
$897$	2.95075e7			1.22448
$898$	−5.07724e6	+	4.25930e7i	−0.210105	+	1.76257i
$899$		−	1.38909e7i		−	0.573234i
$900$	−328212.	−	79376.2i	−0.0135067	−	0.00326651i
$901$			147988.i			0.00607316i
$902$	−1.00316e7	−	1.19580e6i	−0.410537	−	0.0489376i
$903$	2.23600e7			0.912540
$904$	−358606.	+	964603.i	−0.0145947	+	0.0392580i
$905$			1.74409e7i			0.707862i
$906$	1.42433e7	+	1.69785e6i	0.576487	+	0.0687194i
$907$	3.92570e7			1.58453			0.792263	−	0.610180i	$-0.208903\pi$
$907$	3.92570e7			1.58453			0.792263	+	0.610180i	$0.208903\pi$
$908$	−3.34726e7	−	8.09516e6i	−1.34733	−	0.325845i
$909$	146394.			0.00587643
$910$	7.86146e6	+	937116.i	0.314702	+	0.0375137i
$911$	−1.56304e7			−0.623985			−0.311992	−	0.950085i	$-0.600996\pi$
$911$	−1.56304e7			−0.623985			−0.311992	+	0.950085i	$0.600996\pi$
$912$	1.51041e7	−	2.03320e7i	0.601324	−	0.809455i
$913$	4.74468e6			0.188378
$914$	3.25910e7	+	3.88497e6i	1.29042	+	0.153823i
$915$	1.02455e7			0.404556
$916$	1.24066e7	+	3.00045e6i	0.488554	+	0.118154i
$917$	−1.40905e7			−0.553354
$918$	−3.59825e6	−	428925.i	−0.140924	−	0.0167987i
$919$			2.86249e7i			1.11803i	0.829156	+	0.559017i	$0.188821\pi$
$919$			2.86249e7i			1.11803i	−0.829156	+	0.559017i	$0.811179\pi$
$920$	5.03983e6	−	1.35565e7i	0.196312	−	0.528053i
$921$	4.15046e7			1.61231
$922$	−2.44354e7	−	2.91280e6i	−0.946658	−	0.112845i
$923$		−	1.14042e7i		−	0.440617i
$924$	−2.52054e7	−	6.09576e6i	−0.971209	−	0.234881i
$925$			1.58427e7i			0.608802i
$926$	1.18175e6	−	9.91370e6i	0.0452896	−	0.379934i
$927$	766688.			0.0293035
$928$	−1.87905e7	+	2.78696e7i	−0.716256	+	1.06233i
$929$	1.41752e7			0.538879			0.269439	−	0.963017i	$-0.413162\pi$
$929$	1.41752e7			0.538879			0.269439	+	0.963017i	$0.413162\pi$
$930$	4.91787e6	+	586229.i	0.186453	+	0.0222259i
$931$	1.20970e6	−	7.29415e6i	0.0457408	−	0.275804i
$932$	4.30487e7	+	1.04111e7i	1.62338	+	0.392605i
$933$		−	2.32005e7i		−	0.872557i
$934$	2.32446e6	−	1.94999e7i	0.0871875	−	0.731416i
$935$		−	1.85940e6i		−	0.0695576i
$936$	140835.	−	378828.i	0.00525437	−	0.0141336i
$937$	2.26890e7			0.844240			0.422120	−	0.906540i	$-0.361286\pi$
$937$	2.26890e7			0.844240			0.422120	+	0.906540i	$0.361286\pi$
$938$	−2.90386e6	+	2.43605e7i	−0.107763	+	0.904021i
$939$	−4.69425e7			−1.73741
$940$	−2.06151e6	+	8.52412e6i	−0.0760966	+	0.314651i
$941$		−	4.51643e7i		−	1.66273i	−0.555728	−	0.831364i	$-0.687560\pi$
$941$		−	4.51643e7i		−	1.66273i	0.555728	−	0.831364i	$-0.312440\pi$
$942$	−2.13979e7	−	2.55070e6i	−0.785675	−	0.0936554i
$943$	1.30897e7			0.479348
$944$	4.11229e6	+	2.11263e6i	0.150194	+	0.0771601i
$945$		−	9.61492e6i		−	0.350240i
$946$	−3.40206e7	−	4.05538e6i	−1.23599	−	0.147334i
$947$		−	1.33758e6i		−	0.0484670i	−0.999706	−	0.0242335i	$-0.992285\pi$
$947$		−	1.33758e6i		−	0.0484670i	0.999706	−	0.0242335i	$-0.00771452\pi$
$948$	−2.27533e7	−	5.50275e6i	−0.822287	−	0.198865i
$949$			4.73266e7i			1.70585i
$950$	6.42181e6	−	2.20834e7i	0.230860	−	0.793883i
$951$			5.01948e7i			1.79973i
$952$	1.18396e6	−	3.18469e6i	0.0423394	−	0.113887i
$953$		−	3.99419e7i		−	1.42461i	−0.701869	−	0.712306i	$-0.747651\pi$
$953$		−	3.99419e7i		−	1.42461i	0.701869	−	0.712306i	$-0.252349\pi$
$954$	−2372.62	+	19903.9i	−8.44029e−5	+	0.000708056i
$955$			1.18878e7i			0.421788i
$956$	1.26550e7	−	5.23273e7i	0.447836	−	1.85176i
$957$	−4.27337e7			−1.50831
$958$	629980.	−	5.28490e6i	0.0221775	−	0.186047i
$959$		−	7.17878e6i		−	0.252060i
$960$	−9.07381e6	−	7.82865e6i	−0.317769	−	0.274163i
$961$	−2.28984e7			−0.799828
$962$	−1.88287e7	−	2.24446e6i	−0.655969	−	0.0781940i
$963$	−365624.			−0.0127048
$964$	8.35617e6	−	3.45519e7i	0.289611	−	1.19751i
$965$			1.77083e7i			0.612153i
$966$	3.33634e7	+	3.97704e6i	1.15034	+	0.137125i
$967$		−	8.43013e6i		−	0.289913i	−0.989438	−	0.144957i	$-0.953696\pi$
$967$		−	8.43013e6i		−	0.289913i	0.989438	−	0.144957i	$-0.0463042\pi$
$968$	9.91817e6	+	3.68723e6i	0.340207	+	0.126477i
$969$	−690290.	+	4.16225e6i	−0.0236169	+	0.142403i
$970$	−2.42879e6	+	2.03751e7i	−0.0828819	+	0.695296i
$971$	−3.48978e7			−1.18782			−0.593910	−	0.804532i	$-0.702416\pi$
$971$	−3.48978e7			−1.18782			−0.593910	+	0.804532i	$0.702416\pi$
$972$	−962309.	−	232729.i	−0.0326700	−	0.00790104i
$973$	−5.26336e6			−0.178230
$974$	−3.52070e7	−	4.19681e6i	−1.18914	−	0.141750i
$975$		−	2.22009e7i		−	0.747927i
$976$	−2.55159e7	−	1.31084e7i	−0.857405	−	0.440480i
$977$			1.52349e7i			0.510626i	0.966858	+	0.255313i	$0.0821785\pi$
$977$			1.52349e7i			0.510626i	−0.966858	+	0.255313i	$0.917821\pi$
$978$	6.15669e6	−	5.16484e7i	0.205826	−	1.72667i
$979$	4.81125e7			1.60436
$980$	−3.40038e6	−	822361.i	−0.113100	−	0.0273525i
$981$			235481.i			0.00781237i
$982$	−3.47995e6	+	2.91933e7i	−0.115158	+	0.966060i
$983$	4.05649e7			1.33896			0.669479	−	0.742831i	$-0.266517\pi$
$983$	4.05649e7			1.33896			0.669479	+	0.742831i	$0.266517\pi$
$984$	3.77955e6	−	1.01665e7i	0.124438	−	0.334722i
$985$	1.38529e7			0.454935
$986$	662735.	−	5.55968e6i	0.0217094	−	0.182120i
$987$	−2.03736e7			−0.665695
$988$	2.53358e7	+	1.07607e7i	0.825738	+	0.350712i
$989$	4.43919e7			1.44315
$990$	29810.9	−	250084.i	0.000966690	−	0.00810956i
$991$	8.28010e6			0.267825			0.133913	−	0.990993i	$-0.457246\pi$
$991$	8.28010e6			0.267825			0.133913	+	0.990993i	$0.457246\pi$
$992$	−1.14977e7	−	7.75208e6i	−0.370964	−	0.250115i
$993$	−4.51582e7			−1.45333
$994$	1.53707e6	−	1.28945e7i	0.0493432	−	0.413940i
$995$			2.14950e6i			0.0688303i
$996$	−1.19743e6	+	4.95123e6i	−0.0382473	+	0.158149i
$997$	9.71205e6			0.309438			0.154719	−	0.987959i	$-0.450553\pi$
$997$	9.71205e6			0.309438			0.154719	+	0.987959i	$0.450553\pi$
$998$	−4.99689e6	+	4.19189e7i	−0.158809	+	1.33224i
$999$			2.30284e7i			0.730045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.d.a.75.1	✓	48
4.3	odd	2	inner	76.6.d.a.75.47	yes	48
19.18	odd	2	inner	76.6.d.a.75.48	yes	48
76.75	even	2	inner	76.6.d.a.75.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.d.a.75.1	✓	48	1.1	even	1	trivial
76.6.d.a.75.2	yes	48	76.75	even	2	inner
76.6.d.a.75.47	yes	48	4.3	odd	2	inner
76.6.d.a.75.48	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)

\(f(q)\)	\(=\)	\(q+(-5.61709 - 0.669578i) q^{2} +15.7189 q^{3} +(31.1033 + 7.52215i) q^{4} -23.2669 q^{5} +(-88.2945 - 10.5250i) q^{6} -110.037i q^{7} +(-169.673 - 63.0787i) q^{8} +4.08426 q^{9} +O(q^{10})\)	\(q+(-5.61709 - 0.669578i) q^{2} +15.7189 q^{3} +(31.1033 + 7.52215i) q^{4} -23.2669 q^{5} +(-88.2945 - 10.5250i) q^{6} -110.037i q^{7} +(-169.673 - 63.0787i) q^{8} +4.08426 q^{9} +(130.692 + 15.5790i) q^{10} -468.514i q^{11} +(488.911 + 118.240i) q^{12} +546.656i q^{13} +(-73.6787 + 618.090i) q^{14} -365.730 q^{15} +(910.834 + 467.928i) q^{16} -170.574 q^{17} +(-22.9417 - 2.73473i) q^{18} +(257.452 - 1552.36i) q^{19} +(-723.677 - 175.017i) q^{20} -1729.67i q^{21} +(-313.707 + 2631.68i) q^{22} -3433.96i q^{23} +(-2667.08 - 991.529i) q^{24} -2583.65 q^{25} +(366.028 - 3070.61i) q^{26} -3755.50 q^{27} +(827.719 - 3422.53i) q^{28} -5802.64i q^{29} +(2054.34 + 244.885i) q^{30} +2393.90 q^{31} +(-4802.92 - 3238.27i) q^{32} -7364.53i q^{33} +(958.130 + 114.213i) q^{34} +2560.23i q^{35} +(127.034 + 30.7225i) q^{36} -6131.91i q^{37} +(-2485.55 + 8547.35i) q^{38} +8592.83i q^{39} +(3947.77 + 1467.64i) q^{40} +3811.84i q^{41} +(-1158.15 + 9715.71i) q^{42} +12927.3i q^{43} +(3524.24 - 14572.3i) q^{44} -95.0280 q^{45} +(-2299.30 + 19288.9i) q^{46} -11778.9i q^{47} +(14317.3 + 7355.32i) q^{48} +4698.75 q^{49} +(14512.6 + 1729.96i) q^{50} -2681.24 q^{51} +(-4112.03 + 17002.8i) q^{52} -867.587i q^{53} +(21094.9 + 2514.60i) q^{54} +10900.9i q^{55} +(-6941.02 + 18670.4i) q^{56} +(4046.86 - 24401.4i) q^{57} +(-3885.32 + 32593.9i) q^{58} +4514.86 q^{59} +(-11375.4 - 2751.08i) q^{60} -28013.8 q^{61} +(-13446.7 - 1602.90i) q^{62} -449.422i q^{63} +(24810.2 + 21405.6i) q^{64} -12719.0i q^{65} +(-4931.13 + 41367.2i) q^{66} +39412.5 q^{67} +(-5305.42 - 1283.09i) q^{68} -53978.1i q^{69} +(1714.27 - 14381.0i) q^{70} -20861.8 q^{71} +(-692.991 - 257.630i) q^{72} +86574.9 q^{73} +(-4105.79 + 34443.5i) q^{74} -40612.2 q^{75} +(19684.7 - 46346.9i) q^{76} -51554.1 q^{77} +(5753.57 - 48266.7i) q^{78} -46538.8 q^{79} +(-21192.3 - 10887.2i) q^{80} -60024.8 q^{81} +(2552.33 - 21411.5i) q^{82} +10127.1i q^{83} +(13010.8 - 53798.5i) q^{84} +3968.73 q^{85} +(8655.84 - 72613.8i) q^{86} -91211.2i q^{87} +(-29553.3 + 79494.4i) q^{88} +102692. i q^{89} +(533.781 + 63.6286i) q^{90} +60152.6 q^{91} +(25830.8 - 106808. i) q^{92} +37629.5 q^{93} +(-7886.89 + 66163.1i) q^{94} +(-5990.10 + 36118.5i) q^{95} +(-75496.7 - 50902.0i) q^{96} +155902. i q^{97} +(-26393.3 - 3146.18i) q^{98} -1913.54i 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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Database

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