LMFDB - Embedded newform 76.6.d.a.75.13

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			75.13
Character	$\chi$	$=$	76.75
Dual form			76.6.d.a.75.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.73141 - 4.25166i) q^{2} +29.4761 q^{3} +(-4.15316 + 31.7293i) q^{4} -71.3638 q^{5} +(-109.988 - 125.322i) q^{6} +160.370i q^{7} +(150.399 - 100.737i) q^{8} +625.843 q^{9} +O(q^{10})$	\(q+(-3.73141 - 4.25166i) q^{2} +29.4761 q^{3} +(-4.15316 + 31.7293i) q^{4} -71.3638 q^{5} +(-109.988 - 125.322i) q^{6} +160.370i q^{7} +(150.399 - 100.737i) q^{8} +625.843 q^{9} +(266.288 + 303.414i) q^{10} -139.176i q^{11} +(-122.419 + 935.259i) q^{12} +946.762i q^{13} +(681.838 - 598.406i) q^{14} -2103.53 q^{15} +(-989.503 - 263.554i) q^{16} +880.453 q^{17} +(-2335.28 - 2660.87i) q^{18} +(862.513 + 1316.12i) q^{19} +(296.385 - 2264.33i) q^{20} +4727.09i q^{21} +(-591.728 + 519.322i) q^{22} +1491.83i q^{23} +(4433.19 - 2969.35i) q^{24} +1967.79 q^{25} +(4025.31 - 3532.76i) q^{26} +11284.7 q^{27} +(-5088.43 - 666.041i) q^{28} -2448.22i q^{29} +(7849.13 + 8943.49i) q^{30} -196.845 q^{31} +(2571.70 + 5190.45i) q^{32} -4102.37i q^{33} +(-3285.33 - 3743.38i) q^{34} -11444.6i q^{35} +(-2599.23 + 19857.6i) q^{36} -4503.97i q^{37} +(2377.30 - 8578.09i) q^{38} +27906.9i q^{39} +(-10733.1 + 7189.01i) q^{40} +15914.6i q^{41} +(20097.9 - 17638.7i) q^{42} -12075.4i q^{43} +(4415.96 + 578.019i) q^{44} -44662.6 q^{45} +(6342.74 - 5566.62i) q^{46} -23620.8i q^{47} +(-29166.7 - 7768.55i) q^{48} -8911.49 q^{49} +(-7342.65 - 8366.39i) q^{50} +25952.4 q^{51} +(-30040.1 - 3932.05i) q^{52} +3991.90i q^{53} +(-42108.0 - 47978.8i) q^{54} +9932.12i q^{55} +(16155.2 + 24119.5i) q^{56} +(25423.6 + 38794.1i) q^{57} +(-10409.0 + 9135.33i) q^{58} -28997.9 q^{59} +(8736.29 - 66743.6i) q^{60} +11336.7 q^{61} +(734.511 + 836.919i) q^{62} +100366. i q^{63} +(12472.0 - 30301.7i) q^{64} -67564.6i q^{65} +(-17441.9 + 15307.6i) q^{66} +27482.9 q^{67} +(-3656.66 + 27936.2i) q^{68} +43973.4i q^{69} +(-48658.5 + 42704.5i) q^{70} -6688.31 q^{71} +(94126.4 - 63045.8i) q^{72} -81370.8 q^{73} +(-19149.3 + 16806.2i) q^{74} +58003.0 q^{75} +(-45341.8 + 21900.9i) q^{76} +22319.6 q^{77} +(118651. - 104132. i) q^{78} -12559.2 q^{79} +(70614.7 + 18808.2i) q^{80} +180551. q^{81} +(67663.3 - 59383.8i) q^{82} -18195.6i q^{83} +(-149987. - 19632.3i) q^{84} -62832.5 q^{85} +(-51340.5 + 45058.3i) q^{86} -72164.2i q^{87} +(-14020.2 - 20932.0i) q^{88} -11664.2i q^{89} +(166654. + 189890. i) q^{90} -151832. q^{91} +(-47334.7 - 6195.80i) q^{92} -5802.25 q^{93} +(-100428. + 88138.9i) q^{94} +(-61552.2 - 93923.3i) q^{95} +(75803.8 + 152995. i) q^{96} +31104.8i q^{97} +(33252.4 + 37888.6i) q^{98} -87102.2i 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 $

$2$	−3.73141	−	4.25166i	−0.659626	−	0.751594i
$2$	−3.73141	−	4.25166i	−0.659626	−	0.751594i
$3$	29.4761			1.89090			0.945448	−	0.325774i	$-0.105625\pi$
$3$	29.4761			1.89090			0.945448	+	0.325774i	$0.105625\pi$
$4$	−4.15316	+	31.7293i	−0.129786	+	0.991542i
$5$	−71.3638			−1.27659			−0.638297	−	0.769790i	$-0.720361\pi$
$5$	−71.3638			−1.27659			−0.638297	+	0.769790i	$0.720361\pi$
$6$	−109.988	−	125.322i	−1.24728	−	1.42119i
$7$			160.370i			1.23702i	0.785776	+	0.618511i	$0.212264\pi$
$7$			160.370i			1.23702i	−0.785776	+	0.618511i	$0.787736\pi$
$8$	150.399	−	100.737i	0.830847	−	0.556501i
$9$	625.843			2.57549
$10$	266.288	+	303.414i	0.842076	+	0.959481i
$11$		−	139.176i		−	0.346803i	−0.984851	−	0.173401i	$-0.944524\pi$
$11$		−	139.176i		−	0.346803i	0.984851	−	0.173401i	$-0.0554757\pi$
$12$	−122.419	+	935.259i	−0.245412	+	1.87490i
$13$			946.762i			1.55375i	0.629652	+	0.776877i	$0.283198\pi$
$13$			946.762i			1.55375i	−0.629652	+	0.776877i	$0.716802\pi$
$14$	681.838	−	598.406i	0.929738	−	0.815973i
$15$	−2103.53			−2.41391
$16$	−989.503	−	263.554i	−0.966311	−	0.257377i
$17$	880.453			0.738897			0.369449	−	0.929251i	$-0.379547\pi$
$17$	880.453			0.738897			0.369449	+	0.929251i	$0.379547\pi$
$18$	−2335.28	−	2660.87i	−1.69886	−	1.93572i
$19$	862.513	+	1316.12i	0.548128	+	0.836395i
$19$	862.513	+	1316.12i	0.548128	+	0.836395i
$20$	296.385	−	2264.33i	0.165684	−	1.26580i
$21$			4727.09i			2.33908i
$22$	−591.728	+	519.322i	−0.260655	+	0.228760i
$23$			1491.83i			0.588030i	0.955801	+	0.294015i	$0.0949915\pi$
$23$			1491.83i			0.588030i	−0.955801	+	0.294015i	$0.905008\pi$
$24$	4433.19	−	2969.35i	1.57105	−	1.05228i
$25$	1967.79			0.629694
$26$	4025.31	−	3532.76i	1.16779	−	1.02490i
$27$	11284.7			2.97908
$28$	−5088.43	−	666.041i	−1.22656	−	0.160548i
$29$		−	2448.22i		−	0.540575i	−0.962780	−	0.270288i	$-0.912881\pi$
$29$		−	2448.22i		−	0.540575i	0.962780	−	0.270288i	$-0.0871188\pi$
$30$	7849.13	+	8943.49i	1.59228	+	1.81428i
$31$	−196.845			−0.0367893			−0.0183946	−	0.999831i	$-0.505856\pi$
$31$	−196.845			−0.0367893			−0.0183946	+	0.999831i	$0.505856\pi$
$32$	2571.70	+	5190.45i	0.443961	+	0.896046i
$33$		−	4102.37i		−	0.655767i
$34$	−3285.33	−	3743.38i	−0.487396	−	0.555350i
$35$		−	11444.6i		−	1.57918i
$36$	−2599.23	+	19857.6i	−0.334262	+	2.55370i
$37$		−	4503.97i		−	0.540868i	−0.962738	−	0.270434i	$-0.912833\pi$
$37$		−	4503.97i		−	0.540868i	0.962738	−	0.270434i	$-0.0871672\pi$
$38$	2377.30	−	8578.09i	0.267070	−	0.963677i
$39$			27906.9i			2.93799i
$40$	−10733.1	+	7189.01i	−1.06066	+	0.710426i
$41$			15914.6i			1.47855i	0.673405	+	0.739274i	$0.264831\pi$
$41$			15914.6i			1.47855i	−0.673405	+	0.739274i	$0.735169\pi$
$42$	20097.9	−	17638.7i	1.75804	−	1.54292i
$43$		−	12075.4i		−	0.995935i	−0.867196	−	0.497968i	$-0.834080\pi$
$43$		−	12075.4i		−	0.995935i	0.867196	−	0.497968i	$-0.165920\pi$
$44$	4415.96	+	578.019i	0.343869	+	0.0450102i
$45$	−44662.6			−3.28785
$46$	6342.74	−	5566.62i	0.441960	−	0.387880i
$47$		−	23620.8i		−	1.55973i	−0.625946	−	0.779866i	$-0.715287\pi$
$47$		−	23620.8i		−	1.55973i	0.625946	−	0.779866i	$-0.284713\pi$
$48$	−29166.7	−	7768.55i	−1.82719	−	0.486673i
$49$	−8911.49			−0.530225
$50$	−7342.65	−	8366.39i	−0.415363	−	0.473274i
$51$	25952.4			1.39718
$52$	−30040.1	−	3932.05i	−1.54061	−	0.201656i
$53$			3991.90i			0.195205i	0.995226	+	0.0976023i	$0.0311173\pi$
$53$			3991.90i			0.195205i	−0.995226	+	0.0976023i	$0.968883\pi$
$54$	−42108.0	−	47978.8i	−1.96508	−	2.23906i
$55$			9932.12i			0.442726i
$56$	16155.2	+	24119.5i	0.688404	+	1.02778i
$57$	25423.6	+	38794.1i	1.03645	+	1.58154i
$58$	−10409.0	+	9135.33i	−0.406293	+	0.356578i
$59$	−28997.9			−1.08452			−0.542260	−	0.840211i	$-0.682431\pi$
$59$	−28997.9			−1.08452			−0.542260	+	0.840211i	$0.682431\pi$
$60$	8736.29	−	66743.6i	0.313292	−	2.39349i
$61$	11336.7			0.390088			0.195044	−	0.980795i	$-0.437515\pi$
$61$	11336.7			0.390088			0.195044	+	0.980795i	$0.437515\pi$
$62$	734.511	+	836.919i	0.0242672	+	0.0276506i
$63$			100366.i			3.18593i
$64$	12472.0	−	30301.7i	0.380614	−	0.924734i
$65$		−	67564.6i		−	1.98352i
$66$	−17441.9	+	15307.6i	−0.492871	+	0.432561i
$67$	27482.9			0.747955			0.373977	−	0.927438i	$-0.377994\pi$
$67$	27482.9			0.747955			0.373977	+	0.927438i	$0.377994\pi$
$68$	−3656.66	+	27936.2i	−0.0958986	+	0.732647i
$69$			43973.4i			1.11190i
$70$	−48658.5	+	42704.5i	−1.18690	+	1.04167i
$71$	−6688.31			−0.157460			−0.0787301	−	0.996896i	$-0.525087\pi$
$71$	−6688.31			−0.157460			−0.0787301	+	0.996896i	$0.525087\pi$
$72$	94126.4	−	63045.8i	2.13983	−	1.43326i
$73$	−81370.8			−1.78715			−0.893576	−	0.448912i	$-0.851812\pi$
$73$	−81370.8			−1.78715			−0.893576	+	0.448912i	$0.851812\pi$
$74$	−19149.3	+	16806.2i	−0.406513	+	0.356771i
$75$	58003.0			1.19069
$76$	−45341.8	+	21900.9i	−0.900460	+	0.434939i
$77$	22319.6			0.429003
$78$	118651.	−	104132.i	2.20817	−	1.93797i
$79$	−12559.2			−0.226409			−0.113204	−	0.993572i	$-0.536112\pi$
$79$	−12559.2			−0.226409			−0.113204	+	0.993572i	$0.536112\pi$
$80$	70614.7	+	18808.2i	1.23359	+	0.328566i
$81$	180551.			3.05764
$82$	67663.3	−	59383.8i	1.11127	−	0.975289i
$83$		−	18195.6i		−	0.289915i	−0.989438	−	0.144958i	$-0.953695\pi$
$83$		−	18195.6i		−	0.289915i	0.989438	−	0.144958i	$-0.0463046\pi$
$84$	−149987.	−	19632.3i	−2.31930	−	0.303580i
$85$	−62832.5			−0.943272
$86$	−51340.5	+	45058.3i	−0.748539	+	0.656945i
$87$		−	72164.2i		−	1.02217i
$88$	−14020.2	−	20932.0i	−0.192996	−	0.288140i
$89$		−	11664.2i		−	0.156092i	−0.996950	−	0.0780460i	$-0.975132\pi$
$89$		−	11664.2i		−	0.156092i	0.996950	−	0.0780460i	$-0.0248681\pi$
$90$	166654.	+	189890.i	2.16875	+	2.47113i
$91$	−151832.			−1.92203
$92$	−47334.7	−	6195.80i	−0.583056	−	0.0763182i
$93$	−5802.25			−0.0695647
$94$	−100428.	+	88138.9i	−1.17229	+	1.02884i
$95$	−61552.2	−	93923.3i	−0.699737	−	1.06774i
$96$	75803.8	+	152995.i	0.839485	+	1.69433i
$97$			31104.8i			0.335659i	0.985816	+	0.167830i	$0.0536758\pi$
$97$			31104.8i			0.335659i	−0.985816	+	0.167830i	$0.946324\pi$
$98$	33252.4	+	37888.6i	0.349750	+	0.398514i
$99$		−	87102.2i		−	0.893185i
$100$	−8172.56	+	62436.8i	−0.0817256	+	0.624368i
$101$	−28919.3			−0.282088			−0.141044	−	0.990003i	$-0.545046\pi$
$101$	−28919.3			−0.282088			−0.141044	+	0.990003i	$0.545046\pi$
$102$	−96838.9	−	110341.i	−0.921615	−	1.05011i
$103$	59622.1			0.553750			0.276875	−	0.960906i	$-0.410701\pi$
$103$	59622.1			0.553750			0.276875	+	0.960906i	$0.410701\pi$
$104$	95374.4	+	142392.i	0.864666	+	1.29093i
$105$		−	337343.i		−	2.98606i
$106$	16972.2	−	14895.4i	0.146715	−	0.128762i
$107$	27385.8			0.231242			0.115621	−	0.993293i	$-0.463114\pi$
$107$	27385.8			0.231242			0.115621	+	0.993293i	$0.463114\pi$
$108$	−46867.3	+	358057.i	−0.386643	+	2.95388i
$109$			37981.6i			0.306202i	0.988211	+	0.153101i	$0.0489259\pi$
$109$			37981.6i			0.306202i	−0.988211	+	0.153101i	$0.951074\pi$
$110$	42228.0	−	37060.8i	0.332750	−	0.292034i
$111$		−	132760.i		−	1.02273i
$112$	42266.1	−	158686.i	0.318381	−	1.19535i
$113$		−	122780.i		−	0.904549i	−0.891879	−	0.452274i	$-0.850613\pi$
$113$		−	122780.i		−	0.904549i	0.891879	−	0.452274i	$-0.149387\pi$
$114$	70073.6	−	252849.i	0.505001	−	1.82221i
$115$		−	106463.i		−	0.750676i
$116$	77680.6	+	10167.9i	0.536003	+	0.0701592i
$117$			592525.i			4.00167i
$118$	108203.	+	123289.i	0.715377	+	0.815118i
$119$			141198.i			0.914032i
$120$	−316370.	+	211904.i	−2.00559	+	1.34334i
$121$	141681.			0.879728
$122$	−42301.9	−	48199.8i	−0.257312	−	0.293188i
$123$			469100.i			2.79578i
$124$	817.530	−	6245.78i	0.00477474	−	0.0364781i
$125$	82582.6			0.472730
$126$	426723.	−	374508.i	2.39453	−	2.10153i
$127$	334765.			1.84175			0.920876	−	0.389855i	$-0.127475\pi$
$127$	334765.			1.84175			0.920876	+	0.389855i	$0.127475\pi$
$128$	−175370.	+	60041.6i	−0.946087	+	0.323912i
$129$		−	355937.i		−	1.88321i
$130$	−287261.	+	252111.i	−1.49080	+	1.30838i
$131$		−	138971.i		−	0.707533i	−0.935334	−	0.353767i	$-0.884901\pi$
$131$		−	138971.i		−	0.707533i	0.935334	−	0.353767i	$-0.115099\pi$
$132$	130165.	+	17037.8i	0.650221	+	0.0851095i
$133$	−211066.	+	138321.i	−1.03464	+	0.678046i
$134$	−102550.	−	116848.i	−0.493371	−	0.562158i
$135$	−805322.			−3.80308
$136$	132420.	−	88694.5i	0.613910	−	0.411197i
$137$	97083.5			0.441920			0.220960	−	0.975283i	$-0.429081\pi$
$137$	97083.5			0.441920			0.220960	+	0.975283i	$0.429081\pi$
$138$	186960.	−	164083.i	0.835699	−	0.733441i
$139$		−	268260.i		−	1.17766i	−0.808258	−	0.588828i	$-0.799589\pi$
$139$		−	268260.i		−	1.17766i	0.808258	−	0.588828i	$-0.200411\pi$
$140$	363130.	+	47531.3i	1.56582	+	0.204955i
$141$		−	696250.i		−	2.94929i
$142$	24956.8	+	28436.4i	0.103865	+	0.118346i
$143$	131766.			0.538846
$144$	−619273.	−	164943.i	−2.48872	−	0.662871i
$145$			174715.i			0.690096i
$146$	303628.	+	345961.i	1.17885	+	1.34321i
$147$	−262676.			−1.00260
$148$	142908.	+	18705.7i	0.536294	+	0.0701972i
$149$	411244.			1.51752			0.758760	−	0.651370i	$-0.225806\pi$
$149$	411244.			1.51752			0.758760	+	0.651370i	$0.225806\pi$
$150$	−216433.	−	246609.i	−0.785408	−	0.894912i
$151$	−118745.			−0.423813			−0.211907	−	0.977290i	$-0.567967\pi$
$151$	−118745.			−0.423813			−0.211907	+	0.977290i	$0.567967\pi$
$152$	262304.	+	111056.i	0.920864	+	0.389883i
$153$	551025.			1.90302
$154$	−83283.6	−	94895.3i	−0.282981	−	0.322436i
$155$	14047.6			0.0469650
$156$	−885468.	−	115902.i	−2.91314	−	0.381310i
$157$	−529209.			−1.71348			−0.856738	−	0.515752i	$-0.827513\pi$
$157$	−529209.			−1.71348			−0.856738	+	0.515752i	$0.827513\pi$
$158$	46863.5	+	53397.3i	0.149345	+	0.170168i
$159$			117666.i			0.369111i
$160$	−183526.	−	370411.i	−0.566759	−	1.14389i
$161$	−239244.			−0.727406
$162$	−673709.	−	767639.i	−2.01690	−	2.29810i
$163$		−	180326.i		−	0.531607i	−0.964027	−	0.265803i	$-0.914363\pi$
$163$		−	180326.i		−	0.531607i	0.964027	−	0.265803i	$-0.0856372\pi$
$164$	−504959.	−	66095.8i	−1.46604	−	0.191895i
$165$			292761.i			0.837149i
$166$	−77361.4	+	67895.2i	−0.217898	+	0.191236i
$167$	208590.			0.578766			0.289383	−	0.957213i	$-0.406550\pi$
$167$	208590.			0.578766			0.289383	+	0.957213i	$0.406550\pi$
$168$	476194.	+	710951.i	1.30170	+	1.94342i
$169$	−525066.			−1.41415
$170$	234454.	+	267142.i	0.622207	+	0.708957i
$171$	539798.	+	823684.i	1.41169	+	2.15412i
$172$	383145.	+	50151.1i	0.987511	+	0.129259i
$173$			82101.3i			0.208562i	0.994548	+	0.104281i	$0.0332541\pi$
$173$			82101.3i			0.208562i	−0.994548	+	0.104281i	$0.966746\pi$
$174$	−306817.	+	269274.i	−0.768258	+	0.674251i
$175$			315575.i			0.778946i
$176$	−36680.4	+	137715.i	−0.0892590	+	0.335119i
$177$	−854748.			−2.05071
$178$	−49592.2	+	43524.0i	−0.117318	+	0.102962i
$179$	537272.			1.25332			0.626660	−	0.779293i	$-0.284422\pi$
$179$	537272.			1.25332			0.626660	+	0.779293i	$0.284422\pi$
$180$	185491.	−	1.41711e6i	0.426718	−	3.26004i
$181$		−	466070.i		−	1.05744i	−0.848797	−	0.528719i	$-0.822673\pi$
$181$		−	466070.i		−	1.05744i	0.848797	−	0.528719i	$-0.177327\pi$
$182$	566548.	+	645538.i	1.26782	+	1.44459i
$183$	334163.			0.737615
$184$	150283.	+	224370.i	0.327239	+	0.488563i
$185$			321421.i			0.690470i
$186$	21650.6	+	24669.2i	0.0458867	+	0.0522844i
$187$		−	122538.i		−	0.256251i
$188$	749473.	+	98101.0i	1.54654	+	0.202432i
$189$			1.80973e6i			3.68519i
$190$	−169653.	+	612165.i	−0.340940	+	1.23023i
$191$		−	271824.i		−	0.539143i	−0.962980	−	0.269572i	$-0.913118\pi$
$191$		−	271824.i		−	0.539143i	0.962980	−	0.269572i	$-0.0868821\pi$
$192$	367625.	−	893177.i	0.719701	−	1.74858i
$193$		−	311959.i		−	0.602842i	−0.953491	−	0.301421i	$-0.902539\pi$
$193$		−	311959.i		−	0.602842i	0.953491	−	0.301421i	$-0.0974610\pi$
$194$	132247.	−	116065.i	0.252279	−	0.221410i
$195$		−	1.99154e6i		−	3.75062i
$196$	37010.8	−	282756.i	0.0688159	−	0.525741i
$197$	−359897.			−0.660713			−0.330357	−	0.943856i	$-0.607169\pi$
$197$	−359897.			−0.660713			−0.330357	+	0.943856i	$0.607169\pi$
$198$	−370329.	+	325014.i	−0.671312	+	0.589168i
$199$			204639.i			0.366316i	0.983083	+	0.183158i	$0.0586321\pi$
$199$			204639.i			0.366316i	−0.983083	+	0.183158i	$0.941368\pi$
$200$	295955.	−	198231.i	0.523180	−	0.350425i
$201$	810089.			1.41430
$202$	107910.	+	122955.i	0.186072	+	0.212015i
$203$	392621.			0.668704
$204$	−107784.	+	823451.i	−0.181334	+	1.38536i
$205$		−	1.13573e6i		−	1.88751i
$206$	−222474.	−	253493.i	−0.365268	−	0.416195i
$207$			933651.i			1.51446i
$208$	249523.	−	936824.i	0.399901	−	1.50141i
$209$	183172.	−	120041.i	0.290064	−	0.190092i
$210$	−1.43427e6	+	1.25876e6i	−2.24430	+	1.96968i
$211$	657870.			1.01727			0.508633	−	0.860984i	$-0.330151\pi$
$211$	657870.			1.01727			0.508633	+	0.860984i	$0.330151\pi$
$212$	−126660.	−	16579.0i	−0.193554	−	0.0253349i
$213$	−197146.			−0.297741
$214$	−102188.	−	116435.i	−0.152533	−	0.173800i
$215$			861748.i			1.27141i
$216$	1.69722e6	−	1.13680e6i	2.47516	−	1.65786i
$217$		−	31568.1i		−	0.0455092i
$218$	161485.	−	141725.i	0.230139	−	0.201979i
$219$	−2.39850e6			−3.37932
$220$	−315140.	−	41249.7i	−0.438982	−	0.0574598i
$221$			833580.i			1.14806i
$222$	−564449.	+	495381.i	−0.768674	+	0.674617i
$223$	779985.			1.05033			0.525163	−	0.851001i	$-0.324004\pi$
$223$	779985.			1.05033			0.525163	+	0.851001i	$0.324004\pi$
$224$	−832392.	+	412423.i	−1.10843	+	0.549190i
$225$	1.23153e6			1.62177
$226$	−522019.	+	458143.i	−0.679853	+	0.596664i
$227$	−670276.			−0.863354			−0.431677	−	0.902028i	$-0.642078\pi$
$227$	−670276.			−0.863354			−0.431677	+	0.902028i	$0.642078\pi$
$228$	−1.33650e6	+	645555.i	−1.70268	+	0.822424i
$229$	−109449.			−0.137919			−0.0689593	−	0.997619i	$-0.521968\pi$
$229$	−109449.			−0.137919			−0.0689593	+	0.997619i	$0.521968\pi$
$230$	−452642.	+	397256.i	−0.564203	+	0.495166i
$231$	657896.			0.811199
$232$	−246628.	−	368212.i	−0.300831	−	0.449136i
$233$	816310.			0.985066			0.492533	−	0.870294i	$-0.336071\pi$
$233$	816310.			0.985066			0.492533	+	0.870294i	$0.336071\pi$
$234$	2.51921e6	−	2.21095e6i	3.00763	−	2.63961i
$235$			1.68567e6i			1.99115i
$236$	120433.	−	920086.i	0.140756	−	1.07535i
$237$	−370196.			−0.428116
$238$	600326.	−	526868.i	0.686981	−	0.602920i
$239$		−	1.50386e6i		−	1.70299i	−0.524360	−	0.851497i	$-0.675695\pi$
$239$		−	1.50386e6i		−	1.70299i	0.524360	−	0.851497i	$-0.324305\pi$
$240$	2.08145e6	+	554394.i	2.33259	+	0.621284i
$241$			1.61223e6i			1.78806i	0.448003	+	0.894032i	$0.352135\pi$
$241$			1.61223e6i			1.78806i	−0.448003	+	0.894032i	$0.647865\pi$
$242$	−528670.	−	602379.i	−0.580292	−	0.661198i
$243$	2.57975e6			2.80260
$244$	−47083.2	+	359706.i	−0.0506280	+	0.386789i
$245$	635958.			0.676883
$246$	1.99445e6	−	1.75041e6i	2.10129	−	1.84417i
$247$	−1.24605e6	+	816595.i	−1.29955	+	0.851656i
$248$	−29605.4	+	19829.7i	−0.0305663	+	0.0204733i
$249$		−	536336.i		−	0.548199i
$250$	−308149.	−	351113.i	−0.311825	−	0.355301i
$251$			982801.i			0.984649i	0.870412	+	0.492325i	$0.163853\pi$
$251$			982801.i			0.984649i	−0.870412	+	0.492325i	$0.836147\pi$
$252$	−3.18456e6	−	416837.i	−3.15899	−	0.413490i
$253$	207627.			0.203930
$254$	−1.24915e6	−	1.42331e6i	−1.21487	−	1.38425i
$255$	−1.85206e6			−1.78363
$256$	909655.	+	521575.i	0.867514	+	0.497412i
$257$			1.66201e6i			1.56964i	0.619723	+	0.784820i	$0.287245\pi$
$257$			1.66201e6i			1.56964i	−0.619723	+	0.784820i	$0.712755\pi$
$258$	−1.51332e6	+	1.32815e6i	−1.41541	+	1.24221i
$259$	722302.			0.669066
$260$	2.14378e6	+	280606.i	1.96674	+	0.257433i
$261$		−	1.53220e6i		−	1.39224i
$262$	−590858.	+	518559.i	−0.531777	+	0.466708i
$263$		−	1.62129e6i		−	1.44534i	−0.691193	−	0.722671i	$-0.742914\pi$
$263$		−	1.62129e6i		−	1.44534i	0.691193	−	0.722671i	$-0.257086\pi$
$264$	−413262.	−	616994.i	−0.364935	−	0.544842i
$265$		−	284877.i		−	0.249197i
$266$	1.37567e6	+	381247.i	1.19209	+	0.330371i
$267$		−	343816.i		−	0.295153i
$268$	−114141.	+	872014.i	−0.0970742	+	0.741629i
$269$		−	1.48663e6i		−	1.25262i	−0.779572	−	0.626312i	$-0.784563\pi$
$269$		−	1.48663e6i		−	1.25262i	0.779572	−	0.626312i	$-0.215437\pi$
$270$	3.00499e6	+	3.42395e6i	2.50861	+	2.85837i
$271$			635235.i			0.525426i	0.964874	+	0.262713i	$0.0846172\pi$
$271$			635235.i			0.525426i	−0.964874	+	0.262713i	$0.915383\pi$
$272$	−871211.	−	232047.i	−0.714004	−	0.190175i
$273$	−4.47543e6			−3.63436
$274$	−362258.	−	412766.i	−0.291502	−	0.332145i
$275$		−	273870.i		−	0.218380i
$276$	−1.39525e6	−	182628.i	−1.10250	−	0.144310i
$277$	1.86068e6			1.45704			0.728521	−	0.685023i	$-0.240208\pi$
$277$	1.86068e6			1.45704			0.728521	+	0.685023i	$0.240208\pi$
$278$	−1.14055e6	+	1.00099e6i	−0.885119	+	0.776813i
$279$	−123194.			−0.0947503
$280$	−1.15290e6	−	1.72126e6i	−0.878813	−	1.31205i
$281$			1.62510e6i			1.22776i	0.789397	+	0.613882i	$0.210393\pi$
$281$			1.62510e6i			1.22776i	−0.789397	+	0.613882i	$0.789607\pi$
$282$	−2.96022e6	+	2.59800e6i	−2.21667	+	1.94543i
$283$		−	1.93793e6i		−	1.43837i	−0.694817	−	0.719187i	$-0.744515\pi$
$283$		−	1.93793e6i		−	1.43837i	0.694817	−	0.719187i	$-0.255485\pi$
$284$	27777.6	−	212216.i	0.0204362	−	0.156128i
$285$	−1.81432e6	−	2.76850e6i	−1.32313	−	2.01898i
$286$	−491675.	−	560226.i	−0.355437	−	0.404993i
$287$	−2.55222e6			−1.82900
$288$	1.60948e6	+	3.24841e6i	1.14342	+	2.30775i
$289$	−644659.			−0.454031
$290$	742827.	−	651932.i	0.518672	−	0.455205i
$291$			916851.i			0.634697i
$292$	337946.	−	2.58184e6i	0.231948	−	1.77204i
$293$		−	485189.i		−	0.330173i	−0.986279	−	0.165087i	$-0.947210\pi$
$293$		−	485189.i		−	0.330173i	0.986279	−	0.165087i	$-0.0527904\pi$
$294$	980154.	+	1.11681e6i	0.661342	+	0.753548i
$295$	2.06940e6			1.38449
$296$	−453719.	−	677395.i	−0.300994	−	0.449379i
$297$		−	1.57056e6i		−	1.03315i
$298$	−1.53452e6	−	1.74847e6i	−1.00100	−	1.14056i
$299$	−1.41241e6			−0.913654
$300$	−240896.	+	1.84040e6i	−0.154535	+	1.18062i
$301$	1.93653e6			1.23199
$302$	443088.	+	504865.i	0.279558	+	0.318535i
$303$	−852429.			−0.533398
$304$	−506590.	−	1.52962e6i	−0.314393	−	0.949293i
$305$	−809031.			−0.497984
$306$	−2.05610e6	−	2.34277e6i	−1.25528	−	1.43030i
$307$	22512.8			0.0136327			0.00681637	−	0.999977i	$-0.497830\pi$
$307$	22512.8			0.0136327			0.00681637	+	0.999977i	$0.497830\pi$
$308$	−92696.9	+	708187.i	−0.0556786	+	0.425374i
$309$	1.75743e6			1.04708
$310$	−52417.5	−	59725.8i	−0.0309793	−	0.0352986i
$311$			316398.i			0.185495i	0.995690	+	0.0927476i	$0.0295650\pi$
$311$			316398.i			0.185495i	−0.995690	+	0.0927476i	$0.970435\pi$
$312$	2.81127e6	+	4.19718e6i	1.63499	+	2.44102i
$313$	−2.11326e6			−1.21925			−0.609624	−	0.792691i	$-0.708680\pi$
$313$	−2.11326e6			−1.21925			−0.609624	+	0.792691i	$0.708680\pi$
$314$	1.97470e6	+	2.25001e6i	1.13025	+	1.28784i
$315$		−	7.16253e6i		−	4.06715i
$316$	52160.3	−	398495.i	0.0293848	−	0.224494i
$317$		−	2.30604e6i		−	1.28890i	−0.764648	−	0.644448i	$-0.777087\pi$
$317$		−	2.30604e6i		−	1.28890i	0.764648	−	0.644448i	$-0.222913\pi$
$318$	500275.	−	439059.i	0.277422	−	0.243476i
$319$	−340734.			−0.187473
$320$	−890046.	+	2.16244e6i	−0.485890	+	1.18051i
$321$	807228.			0.437254
$322$	892719.	+	1.01718e6i	0.479816	+	0.546714i
$323$	759402.	+	1.15878e6i	0.405010	+	0.618010i
$324$	−749855.	+	5.72875e6i	−0.396840	+	3.03178i
$325$			1.86303e6i			0.978391i
$326$	−766686.	+	672872.i	−0.399552	+	0.350662i
$327$			1.11955e6i			0.578995i
$328$	1.60319e6	+	2.39354e6i	0.822813	+	1.22845i
$329$	3.78807e6			1.92942
$330$	1.24472e6	−	1.09241e6i	0.629196	−	0.552206i
$331$	71095.5			0.0356675			0.0178337	−	0.999841i	$-0.494323\pi$
$331$	71095.5			0.0356675			0.0178337	+	0.999841i	$0.494323\pi$
$332$	577334.	+	75569.1i	0.287463	+	0.0376270i
$333$		−	2.81878e6i		−	1.39300i
$334$	−778337.	−	886855.i	−0.381770	−	0.434997i
$335$	−1.96128e6			−0.954835
$336$	1.24584e6	−	4.67746e6i	0.602025	−	2.26028i
$337$		−	143735.i		−	0.0689427i	−0.999406	−	0.0344713i	$-0.989025\pi$
$337$		−	143735.i		−	0.0689427i	0.999406	−	0.0344713i	$-0.0109747\pi$
$338$	1.95923e6	+	2.23240e6i	0.932813	+	1.06287i
$339$		−	3.61908e6i		−	1.71041i
$340$	260953.	−	1.99363e6i	0.122424	−	0.935294i
$341$			27396.1i			0.0127586i
$342$	1.48782e6	−	5.36854e6i	0.687834	−	2.48194i
$343$			1.26620e6i			0.581122i
$344$	−1.21645e6	−	1.81614e6i	−0.554239	−	0.827470i
$345$		−	3.13811e6i		−	1.41945i
$346$	349066.	−	306354.i	0.156754	−	0.137573i
$347$		−	915553.i		−	0.408187i	−0.978951	−	0.204094i	$-0.934575\pi$
$347$		−	915553.i		−	0.408187i	0.978951	−	0.204094i	$-0.0654247\pi$
$348$	2.28972e6	+	299709.i	1.01353	+	0.132664i
$349$	−666577.			−0.292946			−0.146473	−	0.989215i	$-0.546792\pi$
$349$	−666577.			−0.292946			−0.146473	+	0.989215i	$0.546792\pi$
$350$	1.34172e6	−	1.17754e6i	0.585451	−	0.513813i
$351$			1.06840e7i			4.62876i
$352$	722386.	−	357918.i	0.310751	−	0.153967i
$353$	−1.79638e6			−0.767293			−0.383647	−	0.923480i	$-0.625332\pi$
$353$	−1.79638e6			−0.767293			−0.383647	+	0.923480i	$0.625332\pi$
$354$	3.18941e6	+	3.63409e6i	1.35270	+	1.54130i
$355$	477304.			0.201013
$356$	370098.	+	48443.3i	0.154772	+	0.0202586i
$357$			4.16198e6i			1.72834i
$358$	−2.00478e6	−	2.28430e6i	−0.826723	−	0.941987i
$359$		−	87104.2i		−	0.0356700i	−0.999841	−	0.0178350i	$-0.994323\pi$
$359$		−	87104.2i		−	0.0356700i	0.999841	−	0.0178350i	$-0.00567736\pi$
$360$	−6.71722e6	+	4.49919e6i	−2.73170	+	1.82969i
$361$	−988242.	+	2.27034e6i	−0.399112	+	0.916902i
$362$	−1.98157e6	+	1.73910e6i	−0.794764	+	0.697514i
$363$	4.17621e6			1.66347
$364$	630583.	−	4.81753e6i	0.249453	−	1.90577i
$365$	5.80693e6			2.28147
$366$	−1.24690e6	−	1.42074e6i	−0.486551	−	0.554387i
$367$			2.34683e6i			0.909530i	0.890612	+	0.454765i	$0.150277\pi$
$367$			2.34683e6i			0.909530i	−0.890612	+	0.454765i	$0.849723\pi$
$368$	393177.	−	1.47617e6i	0.151345	−	0.568220i
$369$			9.96003e6i			3.80798i
$370$	1.36657e6	−	1.19935e6i	0.518953	−	0.455452i
$371$	−640180.			−0.241472
$372$	24097.6	−	184101.i	0.00902853	−	0.0689763i
$373$			3.26142e6i			1.21377i	0.794791	+	0.606883i	$0.207580\pi$
$373$			3.26142e6i			1.21377i	−0.794791	+	0.606883i	$0.792420\pi$
$374$	−520989.	+	457239.i	−0.192597	+	0.169030i
$375$	2.43422e6			0.893883
$376$	−2.37950e6	−	3.55256e6i	−0.867992	−	1.29590i
$377$	2.31789e6			0.839922
$378$	7.69436e6	−	6.75285e6i	2.76976	−	2.43085i
$379$	2.17009e6			0.776032			0.388016	−	0.921653i	$-0.373160\pi$
$379$	2.17009e6			0.776032			0.388016	+	0.921653i	$0.373160\pi$
$380$	3.23576e6	−	1.56293e6i	1.14952	−	0.555241i
$381$	9.86759e6			3.48256
$382$	−1.15570e6	+	1.01429e6i	−0.405216	+	0.355633i
$383$	−4.92352e6			−1.71506			−0.857530	−	0.514435i	$-0.828002\pi$
$383$	−4.92352e6			−1.71506			−0.857530	+	0.514435i	$0.828002\pi$
$384$	−5.16924e6	+	1.76979e6i	−1.78895	+	0.612484i
$385$	−1.59281e6			−0.547662
$386$	−1.32634e6	+	1.16405e6i	−0.453093	+	0.397651i
$387$		−	7.55732e6i		−	2.56502i
$388$	−986936.	−	129183.i	−0.332820	−	0.0435639i
$389$	−2.24015e6			−0.750590			−0.375295	−	0.926905i	$-0.622459\pi$
$389$	−2.24015e6			−0.750590			−0.375295	+	0.926905i	$0.622459\pi$
$390$	−8.46736e6	+	7.43126e6i	−2.81894	+	2.47401i
$391$			1.31349e6i			0.434494i
$392$	−1.34028e6	+	897721.i	−0.440536	+	0.295071i
$393$		−	4.09634e6i		−	1.33787i
$394$	1.34292e6	+	1.53016e6i	0.435824	+	0.496588i
$395$	896271.			0.289033
$396$	2.76370e6	+	361749.i	0.885630	+	0.115923i
$397$	−4.56336e6			−1.45314			−0.726571	−	0.687091i	$-0.758887\pi$
$397$	−4.56336e6			−1.45314			−0.726571	+	0.687091i	$0.758887\pi$
$398$	870056.	−	763593.i	0.275321	−	0.241632i
$399$	−6.22141e6	+	4.07717e6i	−1.95639	+	1.28211i
$400$	−1.94714e6	−	518620.i	−0.608481	−	0.162069i
$401$			1.38466e6i			0.430014i	0.976612	+	0.215007i	$0.0689775\pi$
$401$			1.38466e6i			0.430014i	−0.976612	+	0.215007i	$0.931023\pi$
$402$	−3.02278e6	−	3.44422e6i	−0.932912	−	1.06298i
$403$		−	186366.i		−	0.0571615i
$404$	120106.	−	917590.i	0.0366111	−	0.279702i
$405$	−1.28848e7			−3.90337
$406$	−1.46503e6	−	1.66929e6i	−0.441095	−	0.502594i
$407$	−626844.			−0.187574
$408$	3.90322e6	−	2.61437e6i	1.16084	−	0.777530i
$409$		−	42755.9i		−	0.0126383i	−0.999980	−	0.00631913i	$-0.997989\pi$
$409$		−	42755.9i		−	0.0126383i	0.999980	−	0.00631913i	$-0.00201146\pi$
$410$	−4.82871e6	+	4.23786e6i	−1.41864	+	1.24505i
$411$	2.86165e6			0.835625
$412$	−247620.	+	1.89177e6i	−0.0718691	+	0.549067i
$413$		−	4.65040e6i		−	1.34157i
$414$	3.96956e6	−	3.48383e6i	1.13826	−	0.998979i
$415$			1.29851e6i			0.370104i
$416$	−4.91412e6	+	2.43479e6i	−1.39224	+	0.689807i
$417$		−	7.90726e6i		−	2.22683i
$418$	−1.19386e6	−	330862.i	−0.334206	−	0.0926204i
$419$			3.54141e6i			0.985464i	0.870181	+	0.492732i	$0.164002\pi$
$419$			3.54141e6i			0.985464i	−0.870181	+	0.492732i	$0.835998\pi$
$420$	1.07037e7	+	1.40104e6i	2.96080	+	0.387549i
$421$			2.44805e6i			0.673156i	0.941656	+	0.336578i	$0.109270\pi$
$421$			2.44805e6i			0.673156i	−0.941656	+	0.336578i	$0.890730\pi$
$422$	−2.45478e6	−	2.79704e6i	−0.671015	−	0.764570i
$423$		−	1.47829e7i		−	4.01707i
$424$	402134.	+	600379.i	0.108631	+	0.162185i
$425$	1.73255e6			0.465279
$426$	735632.	+	838196.i	0.196398	+	0.223780i
$427$			1.81807e6i			0.482548i
$428$	−113738.	+	868934.i	−0.0300120	+	0.229286i
$429$	3.88397e6			1.01890
$430$	3.66386e6	−	3.21553e6i	0.955580	−	0.838653i
$431$	635887.			0.164887			0.0824436	−	0.996596i	$-0.473728\pi$
$431$	635887.			0.164887			0.0824436	+	0.996596i	$0.473728\pi$
$432$	−1.11663e7	−	2.97414e6i	−2.87872	−	0.766746i
$433$			6.62132e6i			1.69717i	0.529060	+	0.848584i	$0.322545\pi$
$433$			6.62132e6i			1.69717i	−0.529060	+	0.848584i	$0.677455\pi$
$434$	−134217.	+	117793.i	−0.0342044	+	0.0300190i
$435$			5.14991e6i			1.30490i
$436$	−1.20513e6	−	157744.i	−0.303612	−	0.0397407i
$437$	−1.96342e6	+	1.28672e6i	−0.491825	+	0.322315i
$438$	8.94978e6	+	1.01976e7i	2.22909	+	2.53987i
$439$	−884092.			−0.218946			−0.109473	−	0.993990i	$-0.534916\pi$
$439$	−884092.			−0.218946			−0.109473	+	0.993990i	$0.534916\pi$
$440$	1.00054e6	+	1.49379e6i	0.246378	+	0.367838i
$441$	−5.57720e6			−1.36559
$442$	3.54409e6	−	3.11043e6i	0.862878	−	0.757294i
$443$		−	2.74688e6i		−	0.665013i	−0.943101	−	0.332507i	$-0.892106\pi$
$443$		−	2.74688e6i		−	0.665013i	0.943101	−	0.332507i	$-0.107894\pi$
$444$	4.21238e6	+	551372.i	1.01408	+	0.132736i
$445$			832403.i			0.199266i
$446$	−2.91045e6	−	3.31623e6i	−0.692823	−	0.789419i
$447$	1.21219e7			2.86947
$448$	4.85948e6	+	2.00013e6i	1.14392	+	0.470828i
$449$		−	8.05140e6i		−	1.88476i	−0.334546	−	0.942379i	$-0.608583\pi$
$449$		−	8.05140e6i		−	1.88476i	0.334546	−	0.942379i	$-0.391417\pi$
$450$	−4.59535e6	−	5.23605e6i	−1.06976	−	1.21891i
$451$	2.21493e6			0.512764
$452$	3.89573e6	+	509925.i	0.896898	+	0.117398i
$453$	−3.50016e6			−0.801387
$454$	2.50108e6	+	2.84978e6i	0.569491	+	0.648892i
$455$	1.08353e7			2.45365
$456$	7.73171e6	+	3.27351e6i	1.74126	+	0.737228i
$457$	−1.14844e6			−0.257228			−0.128614	−	0.991695i	$-0.541053\pi$
$457$	−1.14844e6			−0.257228			−0.128614	+	0.991695i	$0.541053\pi$
$458$	408399.	+	465339.i	0.0909748	+	0.103659i
$459$	9.93568e6			2.20123
$460$	3.37799e6	+	442156.i	0.744327	+	0.0974274i
$461$	−5.96110e6			−1.30639			−0.653197	−	0.757188i	$-0.726573\pi$
$461$	−5.96110e6			−1.30639			−0.653197	+	0.757188i	$0.726573\pi$
$462$	−2.45488e6	−	2.79715e6i	−0.535088	−	0.609692i
$463$			6.44235e6i			1.39666i	0.715775	+	0.698331i	$0.246074\pi$
$463$			6.44235e6i			1.39666i	−0.715775	+	0.698331i	$0.753926\pi$
$464$	−645239.	+	2.42252e6i	−0.139132	+	0.522364i
$465$	414070.			0.0888059
$466$	−3.04599e6	−	3.47067e6i	−0.649775	−	0.740369i
$467$			4.90280e6i			1.04028i	0.854080	+	0.520142i	$0.174121\pi$
$467$			4.90280e6i			1.04028i	−0.854080	+	0.520142i	$0.825879\pi$
$468$	−1.88004e7	−	2.46085e6i	−3.96783	−	0.519362i
$469$			4.40743e6i			0.925237i
$470$	7.16690e6	−	6.28993e6i	1.49653	−	1.31341i
$471$	−1.55990e7			−3.24000
$472$	−4.36127e6	+	2.92118e6i	−0.901069	+	0.603536i
$473$	−1.68061e6			−0.345393
$474$	1.38135e6	+	1.57395e6i	0.282396	+	0.321769i
$475$	1.69725e6	+	2.58985e6i	0.345153	+	0.526673i
$476$	−4.48012e6	−	586418.i	−0.906301	−	0.118629i
$477$			2.49830e6i			0.502747i
$478$	−6.39390e6	+	5.61152e6i	−1.27996	+	1.12334i
$479$			3.35404e6i			0.667928i	0.942586	+	0.333964i	$0.108386\pi$
$479$			3.35404e6i			0.667928i	−0.942586	+	0.333964i	$0.891614\pi$
$480$	−5.40965e6	−	1.09183e7i	−1.07168	−	2.16297i
$481$	4.26419e6			0.840377
$482$	6.85463e6	−	6.01587e6i	1.34390	−	1.17945i
$483$	−7.05200e6			−1.37545
$484$	−588424.	+	4.49545e6i	−0.114177	+	0.872287i
$485$		−	2.21976e6i		−	0.428501i
$486$	−9.62609e6	−	1.09682e7i	−1.84867	−	2.10642i
$487$	95452.1			0.0182374			0.00911871	−	0.999958i	$-0.497097\pi$
$487$	95452.1			0.0182374			0.00911871	+	0.999958i	$0.497097\pi$
$488$	1.70503e6	−	1.14203e6i	0.324103	−	0.217084i
$489$		−	5.31533e6i		−	1.00521i
$490$	−2.37302e6	−	2.70388e6i	−0.446490	−	0.508741i
$491$		−	6.06237e6i		−	1.13485i	−0.823425	−	0.567425i	$-0.807940\pi$
$491$		−	6.06237e6i		−	1.13485i	0.823425	−	0.567425i	$-0.192060\pi$
$492$	−1.48842e7	−	1.94825e6i	−2.77213	−	0.362854i
$493$		−	2.15555e6i		−	0.399430i
$494$	8.12141e6	+	2.25074e6i	1.49732	+	0.414961i
$495$			6.21595e6i			1.14024i
$496$	194779.	+	51879.4i	0.0355499	+	0.00946871i
$497$		−	1.07260e6i		−	0.194782i
$498$	−2.28032e6	+	2.00129e6i	−0.412023	+	0.361607i
$499$			550506.i			0.0989717i	0.998775	+	0.0494858i	$0.0157583\pi$
$499$			550506.i			0.0989717i	−0.998775	+	0.0494858i	$0.984242\pi$
$500$	−342978.	+	2.62029e6i	−0.0613539	+	0.468732i
$501$	6.14844e6			1.09439
$502$	4.17853e6	−	3.66724e6i	0.740056	−	0.649501i
$503$		−	6.21652e6i		−	1.09554i	−0.836630	−	0.547769i	$-0.815477\pi$
$503$		−	6.21652e6i		−	1.09554i	0.836630	−	0.547769i	$-0.184523\pi$
$504$	1.01106e7	+	1.50950e7i	1.77297	+	2.64702i
$505$	2.06379e6			0.360112
$506$	−774740.	−	882757.i	−0.134518	−	0.153273i
$507$	−1.54769e7			−2.67402
$508$	−1.39033e6	+	1.06219e7i	−0.239034	+	1.82617i
$509$		−	3.85254e6i		−	0.659102i	−0.944138	−	0.329551i	$-0.893103\pi$
$509$		−	3.85254e6i		−	0.659102i	0.944138	−	0.329551i	$-0.106897\pi$
$510$	6.91079e6	+	7.87432e6i	1.17653	+	1.34056i
$511$		−	1.30494e7i		−	2.21075i
$512$	−1.17674e6	−	5.81375e6i	−0.198383	−	0.980125i
$513$	9.73323e6	+	1.48521e7i	1.63292	+	2.49169i
$514$	7.06628e6	−	6.20163e6i	1.17973	−	1.03538i
$515$	−4.25486e6			−0.706915
$516$	1.12936e7	+	1.47826e6i	1.86728	+	0.244415i
$517$	−3.28745e6			−0.540919
$518$	−2.69520e6	−	3.07098e6i	−0.441334	−	0.502866i
$519$			2.42003e6i			0.394369i
$520$	−6.80628e6	−	1.01617e7i	−1.10383	−	1.64800i
$521$		−	1.76576e6i		−	0.284995i	−0.989795	−	0.142498i	$-0.954487\pi$
$521$		−	1.76576e6i		−	0.284995i	0.989795	−	0.142498i	$-0.0455134\pi$
$522$	−6.51441e6	+	5.71728e6i	−1.04640	+	0.918361i
$523$	5.46493e6			0.873636			0.436818	−	0.899550i	$-0.356105\pi$
$523$	5.46493e6			0.873636			0.436818	+	0.899550i	$0.356105\pi$
$524$	4.40947e6	+	577170.i	0.701549	+	0.0918280i
$525$			9.30193e6i			1.47291i
$526$	−6.89315e6	+	6.04968e6i	−1.08631	+	0.953385i
$527$	−173313.			−0.0271835
$528$	−1.08120e6	+	4.05930e6i	−0.168779	+	0.633675i
$529$	4.21079e6			0.654221
$530$	−1.21120e6	+	1.06299e6i	−0.187295	+	0.164377i
$531$	−1.81482e7			−2.79316
$532$	−3.51225e6	−	7.27145e6i	−0.538029	−	1.11389i
$533$	−1.50673e7			−2.29730
$534$	−1.46179e6	+	1.28292e6i	−0.221836	+	0.194691i
$535$	−1.95436e6			−0.295202
$536$	4.13341e6	−	2.76855e6i	0.621436	−	0.416237i
$537$	1.58367e7			2.36990
$538$	−6.32062e6	+	5.54721e6i	−0.941465	+	0.826264i
$539$			1.24026e6i			0.183883i
$540$	3.34463e6	−	2.55523e7i	0.493587	−	3.77091i
$541$	1.11044e7			1.63118			0.815588	−	0.578633i	$-0.196414\pi$
$541$	1.11044e7			1.63118			0.815588	+	0.578633i	$0.196414\pi$
$542$	2.70080e6	−	2.37032e6i	0.394907	−	0.346585i
$543$		−	1.37380e7i		−	1.99950i
$544$	2.26426e6	+	4.56995e6i	0.328042	+	0.662086i
$545$		−	2.71051e6i		−	0.390895i
$546$	1.66996e7	+	1.90280e7i	2.39732	+	2.73156i
$547$	7.93792e6			1.13433			0.567164	−	0.823605i	$-0.308041\pi$
$547$	7.93792e6			1.13433			0.567164	+	0.823605i	$0.308041\pi$
$548$	−403203.	+	3.08040e6i	−0.0573552	+	0.438183i
$549$	7.09500e6			1.00467
$550$	−1.16440e6	+	1.02192e6i	−0.164133	+	0.144049i
$551$	3.22216e6	−	2.11163e6i	0.452134	−	0.296304i
$552$	4.42976e6	+	6.61357e6i	0.618775	+	0.923821i
$553$		−	2.01411e6i		−	0.280073i
$554$	−6.94296e6	−	7.91097e6i	−0.961104	−	1.09510i
$555$			9.47424e6i			1.30561i
$556$	8.51171e6	+	1.11413e6i	1.16770	+	0.152844i
$557$	−2.38399e6			−0.325586			−0.162793	−	0.986660i	$-0.552050\pi$
$557$	−2.38399e6			−0.325586			−0.162793	+	0.986660i	$0.552050\pi$
$558$	459689.	+	523780.i	0.0624998	+	0.0712137i
$559$	1.14325e7			1.54744
$560$	−3.01627e6	+	1.13245e7i	−0.406444	+	1.52598i
$561$		−	3.61194e6i		−	0.484544i
$562$	6.90938e6	−	6.06393e6i	0.922780	−	0.809866i
$563$	−2.57932e6			−0.342952			−0.171476	−	0.985188i	$-0.554854\pi$
$563$	−2.57932e6			−0.342952			−0.171476	+	0.985188i	$0.554854\pi$
$564$	2.20916e7	+	2.89164e6i	2.92435	+	0.382777i
$565$			8.76206e6i			1.15474i
$566$	−8.23941e6	+	7.23121e6i	−1.08107	+	0.948789i
$567$			2.89549e7i			3.78237i
$568$	−1.00592e6	+	673763.i	−0.130825	+	0.0876267i
$569$			1.16131e7i			1.50373i	0.659319	+	0.751863i	$0.270845\pi$
$569$			1.16131e7i			1.50373i	−0.659319	+	0.751863i	$0.729155\pi$
$570$	−5.00072e6	+	1.80443e7i	−0.644681	+	2.32623i
$571$		−	2.53748e6i		−	0.325696i	−0.986651	−	0.162848i	$-0.947932\pi$
$571$		−	2.53748e6i		−	0.325696i	0.986651	−	0.162848i	$-0.0520680\pi$
$572$	−547247.	+	4.18086e6i	−0.0699348	+	0.534289i
$573$		−	8.01232e6i		−	1.01946i
$574$	9.52337e6	+	1.08512e7i	1.20646	+	1.37466i
$575$			2.93561e6i			0.370279i
$576$	7.80549e6	−	1.89641e7i	0.980266	−	2.38164i
$577$	−7.21334e6			−0.901980			−0.450990	−	0.892529i	$-0.648929\pi$
$577$	−7.21334e6			−0.901980			−0.450990	+	0.892529i	$0.648929\pi$
$578$	2.40549e6	+	2.74087e6i	0.299491	+	0.341247i
$579$		−	9.19534e6i		−	1.13991i
$580$	−5.54358e6	−	725618.i	−0.684259	−	0.0895649i
$581$	2.91802e6			0.358632
$582$	3.89813e6	−	3.42115e6i	0.477034	−	0.418663i
$583$	555576.			0.0676974
$584$	−1.22381e7	+	8.19708e6i	−1.48485	+	0.994551i
$585$		−	4.22848e7i		−	5.10852i
$586$	−2.06286e6	+	1.81044e6i	−0.248156	+	0.217791i
$587$		−	9.05469e6i		−	1.08462i	−0.840178	−	0.542311i	$-0.817550\pi$
$587$		−	9.05469e6i		−	1.08462i	0.840178	−	0.542311i	$-0.182450\pi$
$588$	1.09094e6	−	8.33455e6i	0.130124	−	0.994120i
$589$	−169782.	−	259072.i	−0.0201652	−	0.0307704i
$590$	−7.72180e6	−	8.79839e6i	−0.913247	−	1.04058i
$591$	−1.06084e7			−1.24934
$592$	−1.18704e6	+	4.45669e6i	−0.139207	+	0.522647i
$593$	2.39031e6			0.279137			0.139569	−	0.990212i	$-0.455428\pi$
$593$	2.39031e6			0.279137			0.139569	+	0.990212i	$0.455428\pi$
$594$	−6.67749e6	+	5.86041e6i	−0.776511	+	0.681494i
$595$		−	1.00764e7i		−	1.16685i
$596$	−1.70796e6	+	1.30485e7i	−0.196953	+	1.50468i
$597$			6.03198e6i			0.692666i
$598$	5.27027e6	+	6.00507e6i	0.602670	+	0.686697i
$599$	−8.79435e6			−1.00147			−0.500734	−	0.865601i	$-0.666936\pi$
$599$	−8.79435e6			−1.00147			−0.500734	+	0.865601i	$0.666936\pi$
$600$	8.72362e6	−	5.84307e6i	0.989278	−	0.662618i
$601$		−	1.71848e7i		−	1.94070i	−0.241707	−	0.970349i	$-0.577707\pi$
$601$		−	1.71848e7i		−	1.94070i	0.241707	−	0.970349i	$-0.422293\pi$
$602$	−7.22600e6	−	8.23347e6i	−0.812656	−	0.925959i
$603$	1.72000e7			1.92635
$604$	493169.	−	3.76772e6i	0.0550051	−	0.420229i
$605$	−1.01109e7			−1.12306
$606$	3.18076e6	+	3.62423e6i	0.351844	+	0.400899i
$607$	−1.13083e7			−1.24573			−0.622865	−	0.782329i	$-0.714032\pi$
$607$	−1.13083e7			−1.24573			−0.622865	+	0.782329i	$0.714032\pi$
$608$	−4.61313e6	+	7.86150e6i	−0.506101	+	0.862474i
$609$	1.15730e7			1.26445
$610$	3.01883e6	+	3.43972e6i	0.328484	+	0.374282i
$611$	2.23633e7			2.42344
$612$	−2.28850e6	+	1.74837e7i	−0.246986	+	1.88692i
$613$	−1.08511e7			−1.16634			−0.583169	−	0.812351i	$-0.698187\pi$
$613$	−1.08511e7			−1.16634			−0.583169	+	0.812351i	$0.698187\pi$
$614$	−84004.4	−	95716.6i	−0.00899251	−	0.0102463i
$615$		−	3.34768e7i		−	3.56908i
$616$	3.35686e6	−	2.24842e6i	0.356436	−	0.238740i
$617$	−7.66136e6			−0.810202			−0.405101	−	0.914272i	$-0.632764\pi$
$617$	−7.66136e6			−0.810202			−0.405101	+	0.914272i	$0.632764\pi$
$618$	−6.55769e6	−	7.47198e6i	−0.690684	−	0.786982i
$619$		−	7.55698e6i		−	0.792723i	−0.918095	−	0.396362i	$-0.870273\pi$
$619$		−	7.55698e6i		−	0.792723i	0.918095	−	0.396362i	$-0.129727\pi$
$620$	−58342.1	+	445723.i	−0.00609541	+	0.0465678i
$621$			1.68349e7i			1.75179i
$622$	1.34521e6	−	1.18061e6i	0.139417	−	0.122357i
$623$	1.87059e6			0.193089
$624$	7.35497e6	−	2.76139e7i	0.756170	−	2.83901i
$625$	−1.20428e7			−1.23318
$626$	7.88544e6	+	8.98485e6i	0.804248	+	0.916379i
$627$	5.39921e6	−	3.53835e6i	0.548480	−	0.359444i
$628$	2.19789e6	−	1.67915e7i	0.222386	−	1.69898i
$629$		−	3.96554e6i		−	0.399646i
$630$	−3.04526e7	+	2.67263e7i	−3.05684	+	2.68280i
$631$			1.23444e7i			1.23424i	0.786871	+	0.617118i	$0.211700\pi$
$631$			1.23444e7i			1.23424i	−0.786871	+	0.617118i	$0.788300\pi$
$632$	−1.88889e6	+	1.26518e6i	−0.188111	+	0.125997i
$633$	1.93915e7			1.92354
$634$	−9.80448e6	+	8.60477e6i	−0.968727	+	0.850190i
$635$	−2.38901e7			−2.35117
$636$	−3.73346e6	−	488685.i	−0.365989	−	0.0479056i
$637$		−	8.43707e6i		−	0.823840i
$638$	1.27142e6	+	1.44868e6i	0.123662	+	0.140903i
$639$	−4.18584e6			−0.405537
$640$	1.25151e7	−	4.28479e6i	1.20777	−	0.413504i
$641$			1.28061e7i			1.23104i	0.788120	+	0.615522i	$0.211055\pi$
$641$			1.28061e7i			1.23104i	−0.788120	+	0.615522i	$0.788945\pi$
$642$	−3.01210e6	−	3.43206e6i	−0.288424	−	0.328637i
$643$			1.13002e7i			1.07785i	0.842354	+	0.538925i	$0.181169\pi$
$643$			1.13002e7i			1.07785i	−0.842354	+	0.538925i	$0.818831\pi$
$644$	993620.	−	7.59107e6i	0.0944073	−	0.721254i
$645$			2.54010e7i			2.40410i
$646$	2.09310e6	−	7.55261e6i	0.197337	−	0.712058i
$647$			3.65875e6i			0.343615i	0.985131	+	0.171807i	$0.0549607\pi$
$647$			3.65875e6i			0.343615i	−0.985131	+	0.171807i	$0.945039\pi$
$648$	2.71547e7	−	1.81882e7i	2.54043	−	1.70158i
$649$			4.03581e6i			0.376114i
$650$	7.92098e6	−	6.95174e6i	0.735352	−	0.645372i
$651$		−	930505.i		−	0.0860531i
$652$	5.72164e6	+	748924.i	0.527110	+	0.0689952i
$653$	−5.13543e6			−0.471296			−0.235648	−	0.971838i	$-0.575721\pi$
$653$	−5.13543e6			−0.471296			−0.235648	+	0.971838i	$0.575721\pi$
$654$	4.75995e6	−	4.17751e6i	0.435169	−	0.381920i
$655$			9.91752e6i			0.903233i
$656$	4.19435e6	−	1.57475e7i	0.380544	−	1.42874i
$657$	−5.09254e7			−4.60278
$658$	−1.41348e7	−	1.61056e7i	−1.27270	−	1.45014i
$659$	−1.11813e7			−1.00295			−0.501474	−	0.865173i	$-0.667209\pi$
$659$	−1.11813e7			−1.00295			−0.501474	+	0.865173i	$0.667209\pi$
$660$	−9.28910e6	−	1.21588e6i	−0.830069	−	0.108650i
$661$		−	7.67629e6i		−	0.683357i	−0.939817	−	0.341679i	$-0.889005\pi$
$661$		−	7.67629e6i		−	0.683357i	0.939817	−	0.341679i	$-0.110995\pi$
$662$	−265286.	−	302274.i	−0.0235272	−	0.0268074i
$663$			2.45707e7i			2.17087i
$664$	−1.83298e6	−	2.73661e6i	−0.161338	−	0.240875i
$665$	1.50625e7	−	9.87112e6i	1.32082	−	0.865590i
$666$	−1.19845e7	+	1.05180e7i	−1.04697	+	0.918858i
$667$	3.65233e6			0.317875
$668$	−866309.	+	6.61844e6i	−0.0751159	+	0.573871i
$669$	2.29910e7			1.98606
$670$	7.31835e6	+	8.33870e6i	0.629834	+	0.717648i
$671$		−	1.57780e6i		−	0.135283i
$672$	−2.45357e7	+	1.21566e7i	−2.09592	+	1.03846i
$673$		−	5.33165e6i		−	0.453758i	−0.973923	−	0.226879i	$-0.927148\pi$
$673$		−	5.33165e6i		−	0.453758i	0.973923	−	0.226879i	$-0.0728521\pi$
$674$	−611112.	+	536335.i	−0.0518169	+	0.0454764i
$675$	2.22060e7			1.87591
$676$	2.18068e6	−	1.66600e7i	0.183538	−	1.40219i
$677$		−	1.23712e7i		−	1.03739i	−0.854960	−	0.518695i	$-0.826418\pi$
$677$		−	1.23712e7i		−	1.03739i	0.854960	−	0.518695i	$-0.173582\pi$
$678$	−1.53871e7	+	1.35043e7i	−1.28553	+	1.12823i
$679$	−4.98828e6			−0.415218
$680$	−9.44997e6	+	6.32958e6i	−0.783715	+	0.524932i
$681$	−1.97572e7			−1.63251
$682$	116479.	−	102226.i	0.00958929	−	0.00841592i
$683$	−1.13115e7			−0.927827			−0.463914	−	0.885880i	$-0.653555\pi$
$683$	−1.13115e7			−0.927827			−0.463914	+	0.885880i	$0.653555\pi$
$684$	−2.83768e7	+	1.37065e7i	−2.31912	+	1.12018i
$685$	−6.92825e6			−0.564153
$686$	5.38345e6	−	4.72472e6i	0.436768	−	0.383323i
$687$	−3.22613e6			−0.260790
$688$	−3.18252e6	+	1.19487e7i	−0.256331	+	0.962383i
$689$	−3.77938e6			−0.303300
$690$	−1.33422e7	+	1.17096e7i	−1.06685	+	0.936306i
$691$		−	1.04535e7i		−	0.832852i	−0.909170	−	0.416426i	$-0.863282\pi$
$691$		−	1.04535e7i		−	0.832852i	0.909170	−	0.416426i	$-0.136718\pi$
$692$	−2.60502e6	−	340980.i	−0.206798	−	0.0270684i
$693$	1.39686e7			1.10489
$694$	−3.89262e6	+	3.41630e6i	−0.306791	+	0.269251i
$695$			1.91440e7i			1.50339i
$696$	−7.26964e6	−	1.08535e7i	−0.568839	−	0.849268i
$697$			1.40120e7i			1.09249i
$698$	2.48727e6	+	2.83406e6i	0.193235	+	0.220176i
$699$	2.40617e7			1.86266
$700$	−1.00130e7	−	1.31063e6i	−0.772358	−	0.101096i
$701$	2.19766e7			1.68914			0.844571	−	0.535443i	$-0.179855\pi$
$701$	2.19766e7			1.68914			0.844571	+	0.535443i	$0.179855\pi$
$702$	4.54245e7	−	3.98662e7i	3.47895	−	3.05325i
$703$	5.92777e6	−	3.88474e6i	0.452379	−	0.296465i
$704$	−4.21726e6	−	1.73580e6i	−0.320700	−	0.131998i
$705$			4.96871e7i			3.76505i
$706$	6.70303e6	+	7.63759e6i	0.506127	+	0.576693i
$707$		−	4.63778e6i		−	0.348949i
$708$	3.54990e6	−	2.71206e7i	0.266154	−	2.03337i
$709$	9.24351e6			0.690591			0.345296	−	0.938494i	$-0.387779\pi$
$709$	9.24351e6			0.690591			0.345296	+	0.938494i	$0.387779\pi$
$710$	−1.78102e6	−	2.02933e6i	−0.132593	−	0.151080i
$711$	−7.86008e6			−0.583113
$712$	−1.17502e6	−	1.75429e6i	−0.0868653	−	0.129689i
$713$		−	293660.i		−	0.0216332i
$714$	1.76953e7	−	1.55300e7i	1.29901	−	1.14006i
$715$	−9.40336e6			−0.687888
$716$	−2.23138e6	+	1.70473e7i	−0.162664	+	1.24272i
$717$		−	4.43280e7i		−	3.22018i
$718$	−370337.	+	325021.i	−0.0268093	+	0.0235289i
$719$		−	1.52985e7i		−	1.10364i	−0.833965	−	0.551818i	$-0.813934\pi$
$719$		−	1.52985e7i		−	1.10364i	0.833965	−	0.551818i	$-0.186066\pi$
$720$	4.41937e7	+	1.17710e7i	3.17709	+	0.846217i
$721$			9.56158e6i			0.685002i
$722$	1.33402e7	−	4.26991e6i	0.952403	−	0.304842i
$723$			4.75222e7i			3.38104i
$724$	1.47881e7	+	1.93566e6i	1.04849	+	0.137241i
$725$		−	4.81760e6i		−	0.340397i
$726$	−1.55832e7	−	1.77558e7i	−1.09727	−	1.25026i
$727$			1.87082e7i			1.31279i	0.754416	+	0.656397i	$0.227920\pi$
$727$			1.87082e7i			1.31279i	−0.754416	+	0.656397i	$0.772080\pi$
$728$	−2.28355e7	+	1.52952e7i	−1.59691	+	1.06961i
$729$	3.21672e7			2.24178
$730$	−2.16680e7	−	2.46891e7i	−1.50492	−	1.71474i
$731$		−	1.06318e7i		−	0.735893i
$732$	−1.38783e6	+	1.06028e7i	−0.0957323	+	0.731377i
$733$	2.40850e7			1.65572			0.827861	−	0.560933i	$-0.189558\pi$
$733$	2.40850e7			1.65572			0.827861	+	0.560933i	$0.189558\pi$
$734$	9.97792e6	−	8.75699e6i	0.683597	−	0.599950i
$735$	1.87456e7			1.27991
$736$	−7.74327e6	+	3.83653e6i	−0.526902	+	0.261063i
$737$		−	3.82495e6i		−	0.259393i
$738$	4.23466e7	−	3.71649e7i	2.86205	−	2.51184i
$739$		−	1.82988e7i		−	1.23257i	−0.787523	−	0.616285i	$-0.788637\pi$
$739$		−	1.82988e7i		−	1.23257i	0.787523	−	0.616285i	$-0.211363\pi$
$740$	−1.01985e7	−	1.33491e6i	−0.684630	−	0.0896134i
$741$	−3.67288e7	+	2.40701e7i	−2.45732	+	1.61039i
$742$	2.38878e6	+	2.72183e6i	0.159282	+	0.181489i
$743$	2.43858e7			1.62056			0.810280	−	0.586044i	$-0.199315\pi$
$743$	2.43858e7			1.62056			0.810280	+	0.586044i	$0.199315\pi$
$744$	−872654.	+	584503.i	−0.0577976	+	0.0387128i
$745$	−2.93480e7			−1.93726
$746$	1.38664e7	−	1.21697e7i	0.912259	−	0.800632i
$747$		−	1.13876e7i		−	0.746672i
$748$	3.88804e6	+	508919.i	0.254084	+	0.0332579i
$749$			4.39186e6i			0.286051i
$750$	−9.08306e6	−	1.03494e7i	−0.589629	−	0.671837i
$751$	−5.98976e6			−0.387534			−0.193767	−	0.981048i	$-0.562071\pi$
$751$	−5.98976e6			−0.387534			−0.193767	+	0.981048i	$0.562071\pi$
$752$	−6.22536e6	+	2.33729e7i	−0.401439	+	1.50719i
$753$			2.89692e7i			1.86187i
$754$	−8.64899e6	−	9.85486e6i	−0.554034	−	0.631280i
$755$	8.47413e6			0.541038
$756$	−5.74216e7	−	7.51610e6i	−3.65402	−	0.478287i
$757$	5.30536e6			0.336493			0.168246	−	0.985745i	$-0.446190\pi$
$757$	5.30536e6			0.336493			0.168246	+	0.985745i	$0.446190\pi$
$758$	−8.09750e6	−	9.22648e6i	−0.511891	−	0.583261i
$759$	6.12003e6			0.385611
$760$	−1.87190e7	−	7.92540e6i	−1.17557	−	0.497722i
$761$	−2.72385e7			−1.70499			−0.852493	−	0.522738i	$-0.824910\pi$
$761$	−2.72385e7			−1.70499			−0.852493	+	0.522738i	$0.824910\pi$
$762$	−3.68200e7	−	4.19536e7i	−2.29719	−	2.61747i
$763$	−6.09111e6			−0.378778
$764$	8.62479e6	+	1.12893e6i	0.534583	+	0.0699733i
$765$	−3.93233e7			−2.42938
$766$	1.83717e7	+	2.09331e7i	1.13130	+	1.28903i
$767$		−	2.74542e7i		−	1.68508i
$768$	2.68131e7	+	1.53740e7i	1.64038	+	0.940555i
$769$	769942.			0.0469507			0.0234754	−	0.999724i	$-0.492527\pi$
$769$	769942.			0.0469507			0.0234754	+	0.999724i	$0.492527\pi$
$770$	5.94344e6	+	6.77209e6i	0.361253	+	0.411620i
$771$			4.89896e7i			2.96803i
$772$	9.89825e6	+	1.29561e6i	0.597744	+	0.0782406i
$773$			6.87781e6i			0.414001i	0.978341	+	0.207001i	$0.0663702\pi$
$773$			6.87781e6i			0.414001i	−0.978341	+	0.207001i	$0.933630\pi$
$774$	−3.21311e7	+	2.81994e7i	−1.92785	+	1.69195i
$775$	−387352.			−0.0231660
$776$	3.13342e6	+	4.67815e6i	0.186795	+	0.278882i
$777$	2.12907e7			1.26513
$778$	8.35892e6	+	9.52435e6i	0.495109	+	0.564139i
$779$	−2.09455e7	+	1.37265e7i	−1.23665	+	0.810433i
$780$	6.31903e7	+	8.27119e6i	3.71890	+	0.486779i
$781$			930852.i			0.0546076i
$782$	5.58449e6	−	4.90115e6i	0.326563	−	0.286603i
$783$		−	2.76276e7i		−	1.61042i
$784$	8.81795e6	+	2.34866e6i	0.512362	+	0.136468i
$785$	3.77664e7			2.18741
$786$	−1.74162e7	+	1.52851e7i	−1.00554	+	0.882495i
$787$	1.53865e7			0.885527			0.442764	−	0.896638i	$-0.353998\pi$
$787$	1.53865e7			0.885527			0.442764	+	0.896638i	$0.353998\pi$
$788$	1.49471e6	−	1.14193e7i	0.0857515	−	0.655125i
$789$		−	4.77893e7i		−	2.73299i
$790$	−3.34436e6	−	3.81064e6i	−0.190653	−	0.217235i
$791$	1.96902e7			1.11895
$792$	−8.77445e6	−	1.31001e7i	−0.497058	−	0.742100i
$793$			1.07332e7i			0.606101i
$794$	1.70277e7	+	1.94018e7i	0.958531	+	1.09217i
$795$		−	8.39708e6i		−	0.471206i
$796$	−6.49307e6	−	849899.i	−0.363218	−	0.0475428i
$797$			3.13699e6i			0.174931i	0.996168	+	0.0874657i	$0.0278768\pi$
$797$			3.13699e6i			0.174931i	−0.996168	+	0.0874657i	$0.972123\pi$
$798$	4.05494e7	+	1.12377e7i	2.25412	+	0.624698i
$799$		−	2.07970e7i		−	1.15248i
$800$	5.06058e6	+	1.02137e7i	0.279560	+	0.564235i
$801$		−	7.29997e6i		−	0.402013i
$802$	5.88710e6	−	5.16674e6i	0.323196	−	0.283649i
$803$			1.13249e7i			0.619789i
$804$	−3.36443e6	+	2.57036e7i	−0.183557	+	1.40234i
$805$	1.70734e7			0.928603
$806$	−792363.	+	695407.i	−0.0429622	+	0.0377052i
$807$		−	4.38200e7i		−	2.36858i
$808$	−4.34944e6	+	2.91325e6i	−0.234372	+	0.156982i
$809$	−3.28391e7			−1.76409			−0.882044	−	0.471166i	$-0.843833\pi$
$809$	−3.28391e7			−1.76409			−0.882044	+	0.471166i	$0.843833\pi$
$810$	4.80784e7	+	5.47817e7i	2.57477	+	2.93375i
$811$	3.10053e7			1.65533			0.827663	−	0.561226i	$-0.189670\pi$
$811$	3.10053e7			1.65533			0.827663	+	0.561226i	$0.189670\pi$
$812$	−1.63062e6	+	1.24576e7i	−0.0867886	+	0.663048i
$813$			1.87243e7i			0.993525i
$814$	2.33901e6	+	2.66513e6i	0.123729	+	0.140980i
$815$			1.28688e7i			0.678646i
$816$	−2.56799e7	−	6.83985e6i	−1.35011	−	0.359601i
$817$	1.58927e7	−	1.04152e7i	0.832995	−	0.545899i
$818$	−181783.	+	159540.i	−0.00949884	+	0.00833653i
$819$	−9.50231e7			−4.95016
$820$	3.60358e7	+	4.71685e6i	1.87154	+	0.244972i
$821$	1.03865e7			0.537790			0.268895	−	0.963170i	$-0.413342\pi$
$821$	1.03865e7			0.537790			0.268895	+	0.963170i	$0.413342\pi$
$822$	−1.06780e7	−	1.21667e7i	−0.551200	−	0.628051i
$823$		−	1.23234e7i		−	0.634206i	−0.948391	−	0.317103i	$-0.897290\pi$
$823$		−	1.23234e7i		−	0.634206i	0.948391	−	0.317103i	$-0.102710\pi$
$824$	8.96712e6	−	6.00617e6i	0.460082	−	0.308162i
$825$		−	8.07262e6i		−	0.412933i
$826$	−1.97719e7	+	1.73525e7i	−1.00832	+	0.884938i
$827$	3.36646e6			0.171163			0.0855815	−	0.996331i	$-0.472725\pi$
$827$	3.36646e6			0.171163			0.0855815	+	0.996331i	$0.472725\pi$
$828$	−2.96241e7	−	3.87760e6i	−1.50165	−	0.196556i
$829$		−	1.27772e7i		−	0.645727i	−0.946446	−	0.322863i	$-0.895355\pi$
$829$		−	1.27772e7i		−	0.645727i	0.946446	−	0.322863i	$-0.104645\pi$
$830$	5.52080e6	−	4.84526e6i	0.278168	−	0.244130i
$831$	5.48457e7			2.75512
$832$	2.86885e7	+	1.18080e7i	1.43681	+	0.591381i
$833$	−7.84615e6			−0.391782
$834$	−3.36190e7	+	2.95052e7i	−1.67367	+	1.46887i
$835$	−1.48858e7			−0.738850
$836$	3.04808e6	+	6.31048e6i	0.150838	+	0.312282i
$837$	−2.22135e6			−0.109598
$838$	1.50568e7	−	1.32144e7i	0.740668	−	0.650038i
$839$	7.74948e6			0.380074			0.190037	−	0.981777i	$-0.439139\pi$
$839$	7.74948e6			0.380074			0.190037	+	0.981777i	$0.439139\pi$
$840$	−3.39830e7	−	5.07362e7i	−1.66174	−	2.48096i
$841$	1.45173e7			0.707778
$842$	1.04083e7	−	9.13469e6i	0.505940	−	0.444031i
$843$			4.79018e7i			2.32157i
$844$	−2.73224e6	+	2.08738e7i	−0.132027	+	1.00866i
$845$	3.74707e7			1.80530
$846$	−6.28519e7	+	5.51611e7i	−3.01920	+	2.64976i
$847$			2.27214e7i			1.08824i
$848$	1.05208e6	−	3.94999e6i	0.0502411	−	0.188628i
$849$		−	5.71227e7i		−	2.71981i
$850$	−6.46486e6	−	7.36621e6i	−0.306910	−	0.349701i
$851$	6.71916e6			0.318047
$852$	818777.	−	6.25530e6i	0.0386426	−	0.295223i
$853$	−1.92772e7			−0.907132			−0.453566	−	0.891223i	$-0.649848\pi$
$853$	−1.92772e7			−0.907132			−0.453566	+	0.891223i	$0.649848\pi$
$854$	7.72979e6	−	6.78395e6i	0.362680	−	0.318301i
$855$	−3.85220e7	−	5.87813e7i	−1.80216	−	2.74994i
$856$	4.11881e6	−	2.75877e6i	0.192126	−	0.128686i
$857$			4.08300e7i			1.89901i	0.313751	+	0.949505i	$0.398414\pi$
$857$			4.08300e7i			1.89901i	−0.313751	+	0.949505i	$0.601586\pi$
$858$	−1.44927e7	−	1.65133e7i	−0.672094	−	0.765800i
$859$		−	1.02334e7i		−	0.473190i	−0.971608	−	0.236595i	$-0.923969\pi$
$859$		−	1.02334e7i		−	0.473190i	0.971608	−	0.236595i	$-0.0760314\pi$
$860$	−2.73427e7	−	3.57898e6i	−1.26065	−	0.165011i
$861$	−7.52296e7			−3.45844
$862$	−2.37276e6	−	2.70357e6i	−0.108764	−	0.123928i
$863$	1.05026e7			0.480033			0.240017	−	0.970769i	$-0.422847\pi$
$863$	1.05026e7			0.480033			0.240017	+	0.970769i	$0.422847\pi$
$864$	2.90209e7	+	5.85729e7i	1.32260	+	2.66939i
$865$		−	5.85906e6i		−	0.266249i
$866$	2.81516e7	−	2.47069e7i	1.27558	−	1.11950i
$867$	−1.90021e7			−0.858526
$868$	1.00163e6	+	131107.i	0.0451243	+	0.00590646i
$869$			1.74794e6i			0.0785192i
$870$	2.18957e7	−	1.92164e7i	0.980754	−	0.860746i
$871$			2.60198e7i			1.16214i
$872$	3.82617e6	+	5.71241e6i	0.170401	+	0.254407i
$873$			1.94667e7i			0.864486i
$874$	1.27970e7	+	3.54652e6i	0.566671	+	0.157045i
$875$			1.32438e7i			0.584778i
$876$	9.96134e6	−	7.61028e7i	0.438589	−	3.35074i
$877$		−	3.28786e7i		−	1.44349i	−0.692159	−	0.721745i	$-0.743340\pi$
$877$		−	3.28786e7i		−	1.44349i	0.692159	−	0.721745i	$-0.256660\pi$
$878$	3.29891e6	+	3.75886e6i	0.144422	+	0.164558i
$879$		−	1.43015e7i		−	0.624323i
$880$	2.61765e6	−	9.82786e6i	0.113948	−	0.427811i
$881$	1.66312e7			0.721912			0.360956	−	0.932583i	$-0.382450\pi$
$881$	1.66312e7			0.721912			0.360956	+	0.932583i	$0.382450\pi$
$882$	2.08108e7	+	2.37123e7i	0.900777	+	1.02637i
$883$			2.75935e7i			1.19098i	0.803363	+	0.595490i	$0.203042\pi$
$883$			2.75935e7i			1.19098i	−0.803363	+	0.595490i	$0.796958\pi$
$884$	−2.64489e7	−	3.46199e6i	−1.13835	−	0.149003i
$885$	6.09981e7			2.61793
$886$	−1.16788e7	+	1.02497e7i	−0.499820	+	0.438660i
$887$	−1.96131e7			−0.837024			−0.418512	−	0.908211i	$-0.637448\pi$
$887$	−1.96131e7			−0.837024			−0.418512	+	0.908211i	$0.637448\pi$
$888$	−1.33739e7	−	1.99670e7i	−0.569147	−	0.849728i
$889$			5.36863e7i			2.27829i
$890$	3.53909e6	−	3.10604e6i	0.149767	−	0.131441i
$891$		−	2.51283e7i		−	1.06040i
$892$	−3.23940e6	+	2.47484e7i	−0.136318	+	1.04144i
$893$	3.10878e7	−	2.03733e7i	1.30455	−	0.854932i
$894$	−4.52318e7	−	5.15382e7i	−1.89278	−	2.15668i
$895$	−3.83418e7			−1.59998
$896$	−9.62886e6	−	2.81241e7i	−0.400686	−	1.17033i
$897$	−4.16323e7			−1.72762
$898$	−3.42318e7	+	3.00431e7i	−1.41657	+	1.24324i
$899$			481922.i			0.0198874i
$900$	−5.11474e6	+	3.90757e7i	−0.210483	+	1.60805i
$901$			3.51468e6i			0.144236i
$902$	−8.26479e6	−	9.41710e6i	−0.338233	−	0.385390i
$903$	5.70815e7			2.32957
$904$	−1.23685e7	−	1.84661e7i	−0.503382	−	0.751542i
$905$			3.32605e7i			1.34992i
$906$	1.30605e7	+	1.48815e7i	0.528616	+	0.602317i
$907$	−2.31574e7			−0.934699			−0.467349	−	0.884073i	$-0.654791\pi$
$907$	−2.31574e7			−0.934699			−0.467349	+	0.884073i	$0.654791\pi$
$908$	2.78376e6	−	2.12674e7i	0.112051	−	0.856052i
$909$	−1.80989e7			−0.726513
$910$	−4.04310e7	−	4.60681e7i	−1.61849	−	1.84415i
$911$	−2.94135e7			−1.17423			−0.587113	−	0.809505i	$-0.699735\pi$
$911$	−2.94135e7			−1.17423			−0.587113	+	0.809505i	$0.699735\pi$
$912$	−1.49323e7	−	4.50874e7i	−0.594484	−	1.79501i
$913$	−2.53239e6			−0.100543
$914$	4.28530e6	+	4.88277e6i	0.169674	+	0.193331i
$915$	−2.38471e7			−0.941636
$916$	454559.	−	3.47274e6i	0.0178999	−	0.136752i
$917$	2.22868e7			0.875235
$918$	−3.70741e7	−	4.22431e7i	−1.45199	−	1.65443i
$919$			1.88396e7i			0.735840i	0.929857	+	0.367920i	$0.119930\pi$
$919$			1.88396e7i			0.735840i	−0.929857	+	0.367920i	$0.880070\pi$
$920$	−1.07248e7	−	1.60119e7i	−0.417752	−	0.623697i
$921$	663590.			0.0257781
$922$	2.22433e7	+	2.53446e7i	0.861732	+	0.981877i
$923$		−	6.33224e6i		−	0.244655i
$924$	−2.73235e6	+	2.08746e7i	−0.105282	+	0.804338i
$925$		−	8.86290e6i		−	0.340582i
$926$	2.73906e7	−	2.40390e7i	1.04972	−	0.921276i
$927$	3.73141e7			1.42618
$928$	1.27074e7	−	6.29610e6i	0.484380	−	0.239995i
$929$	−7.98203e6			−0.303441			−0.151720	−	0.988423i	$-0.548481\pi$
$929$	−7.98203e6			−0.303441			−0.151720	+	0.988423i	$0.548481\pi$
$930$	−1.54507e6	−	1.76049e6i	−0.0585787	−	0.0667460i
$931$	−7.68628e6	−	1.17286e7i	−0.290631	−	0.443478i
$932$	−3.39026e6	+	2.59010e7i	−0.127848	+	0.976734i
$933$			9.32619e6i			0.350752i
$934$	2.08450e7	−	1.82944e7i	0.781871	−	0.686199i
$935$			8.74477e6i			0.327129i
$936$	5.96894e7	+	8.91153e7i	2.22693	+	3.32478i
$937$	4.28282e6			0.159361			0.0796803	−	0.996820i	$-0.474610\pi$
$937$	4.28282e6			0.159361			0.0796803	+	0.996820i	$0.474610\pi$
$938$	1.87389e7	−	1.64459e7i	0.695402	−	0.610311i
$939$	−6.22907e7			−2.30547
$940$	−5.34852e7	−	7.00086e6i	−1.97431	−	0.258423i
$941$			3.79556e6i			0.139734i	0.997556	+	0.0698670i	$0.0222575\pi$
$941$			3.79556e6i			0.139734i	−0.997556	+	0.0698670i	$0.977743\pi$
$942$	5.82064e7	+	6.63217e7i	2.13719	+	2.43517i
$943$	−2.37418e7			−0.869430
$944$	2.86935e7	+	7.64252e6i	1.04798	+	0.279130i
$945$		−	1.29149e8i		−	4.70449i
$946$	6.27103e6	+	7.14536e6i	0.227830	+	0.259595i
$947$			3.59356e7i			1.30212i	0.759028	+	0.651058i	$0.225675\pi$
$947$			3.59356e7i			1.30212i	−0.759028	+	0.651058i	$0.774325\pi$
$948$	1.53748e6	−	1.17461e7i	0.0555635	−	0.424495i
$949$		−	7.70388e7i		−	2.77680i
$950$	4.67803e6	−	1.68799e7i	0.168172	−	0.606822i
$951$		−	6.79731e7i		−	2.43717i
$952$	1.42239e7	+	2.12361e7i	0.508660	+	0.759421i
$953$		−	3.01485e7i		−	1.07531i	−0.843165	−	0.537655i	$-0.819310\pi$
$953$		−	3.01485e7i		−	1.07531i	0.843165	−	0.537655i	$-0.180690\pi$
$954$	1.06219e7	−	9.32219e6i	0.377861	−	0.331625i
$955$			1.93984e7i			0.688267i
$956$	4.77165e7	+	6.24577e6i	1.68859	+	0.221025i
$957$	−1.00435e7			−0.354492
$958$	1.42602e7	−	1.25153e7i	0.502011	−	0.440583i
$959$			1.55693e7i			0.546665i
$960$	−2.62351e7	+	6.37405e7i	−0.918767	+	2.23222i
$961$	−2.85904e7			−0.998647
$962$	−1.59114e7	−	1.81299e7i	−0.554335	−	0.631622i
$963$	1.71392e7			0.595560
$964$	−5.11548e7	−	6.69583e6i	−1.77294	−	0.232066i
$965$			2.22626e7i			0.769586i
$966$	2.63139e7	+	2.99827e7i	0.907283	+	1.03378i
$967$		−	4.55793e7i		−	1.56748i	−0.621090	−	0.783739i	$-0.713310\pi$
$967$		−	4.55793e7i		−	1.56748i	0.621090	−	0.783739i	$-0.286690\pi$
$968$	2.13087e7	−	1.42726e7i	0.730919	−	0.489569i
$969$	2.23842e7	+	3.41564e7i	0.765831	+	1.16859i
$970$	−9.43766e6	+	8.28284e6i	−0.322059	+	0.282650i
$971$	4.49562e7			1.53018			0.765088	−	0.643926i	$-0.222696\pi$
$971$	4.49562e7			1.53018			0.765088	+	0.643926i	$0.222696\pi$
$972$	−1.07141e7	+	8.18537e7i	−0.363739	+	2.77890i
$973$	4.30208e7			1.45679
$974$	−356171.	−	405830.i	−0.0120299	−	0.0137071i
$975$			5.49151e7i			1.85003i
$976$	−1.12177e7	−	2.98784e6i	−0.376946	−	0.100400i
$977$			4.29574e7i			1.43980i	0.694079	+	0.719898i	$0.255812\pi$
$977$			4.29574e7i			1.43980i	−0.694079	+	0.719898i	$0.744188\pi$
$978$	−2.25989e7	+	1.98337e7i	−0.755512	+	0.663065i
$979$	−1.62338e6			−0.0541331
$980$	−2.64124e6	+	2.01785e7i	−0.0878500	+	0.671158i
$981$			2.37705e7i			0.788618i
$982$	−2.57751e7	+	2.26212e7i	−0.852946	+	0.748577i
$983$	1.76275e7			0.581845			0.290922	−	0.956747i	$-0.406038\pi$
$983$	1.76275e7			0.581845			0.290922	+	0.956747i	$0.406038\pi$
$984$	4.72559e7	+	7.05524e7i	1.55585	+	2.32287i
$985$	2.56837e7			0.843463
$986$	−9.16464e6	+	8.04323e6i	−0.300209	+	0.263474i
$987$	1.11658e8			3.64834
$988$	−2.07350e7	−	4.29279e7i	−0.675789	−	1.39909i
$989$	1.80145e7			0.585640
$990$	2.64281e7	−	2.31943e7i	0.856994	−	0.752129i
$991$	3.92067e6			0.126816			0.0634082	−	0.997988i	$-0.479803\pi$
$991$	3.92067e6			0.126816			0.0634082	+	0.997988i	$0.479803\pi$
$992$	−506227.	−	1.02172e6i	−0.0163330	−	0.0329649i
$993$	2.09562e6			0.0674434
$994$	−4.56034e6	+	4.00233e6i	−0.146397	+	0.128483i
$995$		−	1.46038e7i		−	0.467638i
$996$	1.70176e7	+	2.22749e6i	0.543562	+	0.0711487i
$997$	−2.42573e7			−0.772868			−0.386434	−	0.922317i	$-0.626293\pi$
$997$	−2.42573e7			−0.772868			−0.386434	+	0.922317i	$0.626293\pi$
$998$	2.34056e6	−	2.05416e6i	0.0743865	−	0.0652843i
$999$		−	5.08262e7i		−	1.61129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.d.a.75.13	✓	48
4.3	odd	2	inner	76.6.d.a.75.35	yes	48
19.18	odd	2	inner	76.6.d.a.75.36	yes	48
76.75	even	2	inner	76.6.d.a.75.14	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.d.a.75.13	✓	48	1.1	even	1	trivial
76.6.d.a.75.14	yes	48	76.75	even	2	inner
76.6.d.a.75.35	yes	48	4.3	odd	2	inner
76.6.d.a.75.36	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)

\(f(q)\)	\(=\)	\(q+(-3.73141 - 4.25166i) q^{2} +29.4761 q^{3} +(-4.15316 + 31.7293i) q^{4} -71.3638 q^{5} +(-109.988 - 125.322i) q^{6} +160.370i q^{7} +(150.399 - 100.737i) q^{8} +625.843 q^{9} +O(q^{10})\)	\(q+(-3.73141 - 4.25166i) q^{2} +29.4761 q^{3} +(-4.15316 + 31.7293i) q^{4} -71.3638 q^{5} +(-109.988 - 125.322i) q^{6} +160.370i q^{7} +(150.399 - 100.737i) q^{8} +625.843 q^{9} +(266.288 + 303.414i) q^{10} -139.176i q^{11} +(-122.419 + 935.259i) q^{12} +946.762i q^{13} +(681.838 - 598.406i) q^{14} -2103.53 q^{15} +(-989.503 - 263.554i) q^{16} +880.453 q^{17} +(-2335.28 - 2660.87i) q^{18} +(862.513 + 1316.12i) q^{19} +(296.385 - 2264.33i) q^{20} +4727.09i q^{21} +(-591.728 + 519.322i) q^{22} +1491.83i q^{23} +(4433.19 - 2969.35i) q^{24} +1967.79 q^{25} +(4025.31 - 3532.76i) q^{26} +11284.7 q^{27} +(-5088.43 - 666.041i) q^{28} -2448.22i q^{29} +(7849.13 + 8943.49i) q^{30} -196.845 q^{31} +(2571.70 + 5190.45i) q^{32} -4102.37i q^{33} +(-3285.33 - 3743.38i) q^{34} -11444.6i q^{35} +(-2599.23 + 19857.6i) q^{36} -4503.97i q^{37} +(2377.30 - 8578.09i) q^{38} +27906.9i q^{39} +(-10733.1 + 7189.01i) q^{40} +15914.6i q^{41} +(20097.9 - 17638.7i) q^{42} -12075.4i q^{43} +(4415.96 + 578.019i) q^{44} -44662.6 q^{45} +(6342.74 - 5566.62i) q^{46} -23620.8i q^{47} +(-29166.7 - 7768.55i) q^{48} -8911.49 q^{49} +(-7342.65 - 8366.39i) q^{50} +25952.4 q^{51} +(-30040.1 - 3932.05i) q^{52} +3991.90i q^{53} +(-42108.0 - 47978.8i) q^{54} +9932.12i q^{55} +(16155.2 + 24119.5i) q^{56} +(25423.6 + 38794.1i) q^{57} +(-10409.0 + 9135.33i) q^{58} -28997.9 q^{59} +(8736.29 - 66743.6i) q^{60} +11336.7 q^{61} +(734.511 + 836.919i) q^{62} +100366. i q^{63} +(12472.0 - 30301.7i) q^{64} -67564.6i q^{65} +(-17441.9 + 15307.6i) q^{66} +27482.9 q^{67} +(-3656.66 + 27936.2i) q^{68} +43973.4i q^{69} +(-48658.5 + 42704.5i) q^{70} -6688.31 q^{71} +(94126.4 - 63045.8i) q^{72} -81370.8 q^{73} +(-19149.3 + 16806.2i) q^{74} +58003.0 q^{75} +(-45341.8 + 21900.9i) q^{76} +22319.6 q^{77} +(118651. - 104132. i) q^{78} -12559.2 q^{79} +(70614.7 + 18808.2i) q^{80} +180551. q^{81} +(67663.3 - 59383.8i) q^{82} -18195.6i q^{83} +(-149987. - 19632.3i) q^{84} -62832.5 q^{85} +(-51340.5 + 45058.3i) q^{86} -72164.2i q^{87} +(-14020.2 - 20932.0i) q^{88} -11664.2i q^{89} +(166654. + 189890. i) q^{90} -151832. q^{91} +(-47334.7 - 6195.80i) q^{92} -5802.25 q^{93} +(-100428. + 88138.9i) q^{94} +(-61552.2 - 93923.3i) q^{95} +(75803.8 + 152995. i) q^{96} +31104.8i q^{97} +(33252.4 + 37888.6i) q^{98} -87102.2i 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

Fields

Representations

Groups

Database

Properties

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