LMFDB - Embedded newform 775.2.k.h.101.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(101,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			101.5
Character	$\chi$	$=$	775.101
Dual form			775.2.k.h.376.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.334686 + 1.03006i) q^{2} +(0.849570 + 2.61471i) q^{3} +(0.669031 + 0.486079i) q^{4} -2.97764 q^{6} +(-4.04839 - 2.94133i) q^{7} +(-2.47704 + 1.79968i) q^{8} +(-3.68788 + 2.67940i) q^{9} +(-1.13130 - 0.821939i) q^{11} +(-0.702567 + 2.16228i) q^{12} +(-0.196715 - 0.605427i) q^{13} +(4.38467 - 3.18565i) q^{14} +(-0.513645 - 1.58084i) q^{16} +(-1.94151 + 1.41059i) q^{17} +(-1.52566 - 4.69549i) q^{18} +(0.848048 - 2.61002i) q^{19} +(4.25132 - 13.0842i) q^{21} +(1.22527 - 0.890214i) q^{22} +(-6.02940 + 4.38062i) q^{23} +(-6.81005 - 4.94779i) q^{24} +0.689462 q^{26} +(-3.46636 - 2.51846i) q^{27} +(-1.27878 - 3.93568i) q^{28} +(0.238536 - 0.734139i) q^{29} +(-3.70997 + 4.15164i) q^{31} -4.32332 q^{32} +(1.18801 - 3.65632i) q^{33} +(-0.803191 - 2.47197i) q^{34} -3.76971 q^{36} +7.89911 q^{37} +(2.40464 + 1.74708i) q^{38} +(1.41589 - 1.02871i) q^{39} +(-2.21167 + 6.80681i) q^{41} +(12.0546 + 8.75821i) q^{42} +(-1.59181 + 4.89908i) q^{43} +(-0.357348 - 1.09980i) q^{44} +(-2.49433 - 7.67676i) q^{46} +(1.04775 + 3.22464i) q^{47} +(3.69705 - 2.68606i) q^{48} +(5.57493 + 17.1579i) q^{49} +(-5.33772 - 3.87808i) q^{51} +(0.162677 - 0.500668i) q^{52} +(-1.08466 + 0.788052i) q^{53} +(3.75430 - 2.72766i) q^{54} +15.3215 q^{56} +7.54493 q^{57} +(0.676370 + 0.491412i) q^{58} +(1.16069 + 3.57224i) q^{59} -6.15910 q^{61} +(-3.03475 - 5.21098i) q^{62} +22.8110 q^{63} +(2.47425 - 7.61494i) q^{64} +(3.36861 + 2.44744i) q^{66} +3.34130 q^{67} -1.98459 q^{68} +(-16.5764 - 12.0435i) q^{69} +(1.69553 - 1.23188i) q^{71} +(4.31298 - 13.2740i) q^{72} +(8.89448 + 6.46222i) q^{73} +(-2.64372 + 8.13653i) q^{74} +(1.83605 - 1.33397i) q^{76} +(2.16236 + 6.65506i) q^{77} +(0.585747 + 1.80274i) q^{78} +(-5.88488 + 4.27562i) q^{79} +(-0.585816 + 1.80296i) q^{81} +(-6.27119 - 4.55629i) q^{82} +(2.68206 - 8.25452i) q^{83} +(9.20423 - 6.68727i) q^{84} +(-4.51358 - 3.27931i) q^{86} +2.12221 q^{87} +4.28151 q^{88} +(8.03470 + 5.83755i) q^{89} +(-0.984379 + 3.02961i) q^{91} -6.16318 q^{92} +(-14.0072 - 6.17339i) q^{93} -3.67223 q^{94} +(-3.67297 - 11.3042i) q^{96} +(-13.9505 - 10.1356i) q^{97} -19.5394 q^{98} +6.37441 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{4} - 4 q^{6} - 8 q^{9} - 14 q^{11} + 16 q^{14} - 22 q^{16} + 2 q^{19} - 38 q^{21} + 30 q^{24} + 12 q^{26} - 20 q^{29} + 26 q^{31} + 2 q^{34} - 44 q^{36} + 18 q^{39} - 20 q^{41} - 62 q^{44} - 70 q^{46}+ \cdots + 52 q^{99}+O(q^{100}) $ 56 * q - 2 * q^4 - 4 * q^6 - 8 * q^9 - 14 * q^11 + 16 * q^14 - 22 * q^16 + 2 * q^19 - 38 * q^21 + 30 * q^24 + 12 * q^26 - 20 * q^29 + 26 * q^31 + 2 * q^34 - 44 * q^36 + 18 * q^39 - 20 * q^41 - 62 * q^44 - 70 * q^46 + 42 * q^49 + 10 * q^51 + 26 * q^54 + 208 * q^56 + 50 * q^59 + 56 * q^61 - 12 * q^64 + 60 * q^66 - 34 * q^69 - 8 * q^71 + 84 * q^74 - 20 * q^76 - 122 * q^79 + 42 * q^81 + 40 * q^84 + 78 * q^86 + 28 * q^89 - 20 * q^91 - 160 * q^94 - 70 * q^96 + 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.334686	+	1.03006i	−0.236659	+	0.728360i	0.760238	+	0.649644i	$0.225082\pi$
$2$	−0.334686	+	1.03006i	−0.236659	+	0.728360i	−0.996897	+	0.0787163i	$0.974918\pi$
$3$	0.849570	+	2.61471i	0.490500	+	1.50960i	0.823854	+	0.566801i	$0.191819\pi$
$3$	0.849570	+	2.61471i	0.490500	+	1.50960i	−0.333355	+	0.942801i	$0.608181\pi$
$4$	0.669031	+	0.486079i	0.334515	+	0.243040i
$5$		0			0
$5$		0			0
$6$	−2.97764			−1.21562
$7$	−4.04839	−	2.94133i	−1.53015	−	1.11172i	−0.956157	−	0.292855i	$-0.905395\pi$
$7$	−4.04839	−	2.94133i	−1.53015	−	1.11172i	−0.573990	−	0.818862i	$-0.694605\pi$
$8$	−2.47704	+	1.79968i	−0.875767	+	0.636282i
$9$	−3.68788	+	2.67940i	−1.22929	+	0.893134i
$10$		0			0
$11$	−1.13130	−	0.821939i	−0.341100	−	0.247824i	0.404026	−	0.914748i	$-0.367611\pi$
$11$	−1.13130	−	0.821939i	−0.341100	−	0.247824i	−0.745126	+	0.666924i	$0.767611\pi$
$12$	−0.702567	+	2.16228i	−0.202814	+	0.624196i
$13$	−0.196715	−	0.605427i	−0.0545590	−	0.167915i	0.920064	−	0.391768i	$-0.128136\pi$
$13$	−0.196715	−	0.605427i	−0.0545590	−	0.167915i	−0.974623	+	0.223853i	$0.928136\pi$
$14$	4.38467	−	3.18565i	1.17185	−	0.851401i
$15$		0			0
$16$	−0.513645	−	1.58084i	−0.128411	−	0.395209i
$17$	−1.94151	+	1.41059i	−0.470885	+	0.342118i	−0.797786	−	0.602941i	$-0.793996\pi$
$17$	−1.94151	+	1.41059i	−0.470885	+	0.342118i	0.326901	+	0.945058i	$0.393996\pi$
$18$	−1.52566	−	4.69549i	−0.359601	−	1.10674i
$19$	0.848048	−	2.61002i	0.194556	−	0.598781i	−0.805426	−	0.592697i	$-0.798063\pi$
$19$	0.848048	−	2.61002i	0.194556	−	0.598781i	0.999981	−	0.00608415i	$-0.00193666\pi$
$20$		0			0
$21$	4.25132	−	13.0842i	0.927714	−	2.85521i
$22$	1.22527	−	0.890214i	0.261229	−	0.189794i
$23$	−6.02940	+	4.38062i	−1.25722	+	0.913422i	−0.998618	−	0.0525629i	$-0.983261\pi$
$23$	−6.02940	+	4.38062i	−1.25722	+	0.913422i	−0.258600	+	0.965985i	$0.583261\pi$
$24$	−6.81005	−	4.94779i	−1.39010	−	1.00996i
$25$		0			0
$26$	0.689462			0.135215
$27$	−3.46636	−	2.51846i	−0.667102	−	0.484678i
$28$	−1.27878	−	3.93568i	−0.241666	−	0.743773i
$29$	0.238536	−	0.734139i	0.0442950	−	0.136326i	−0.926463	−	0.376385i	$-0.877167\pi$
$29$	0.238536	−	0.734139i	0.0442950	−	0.136326i	0.970758	+	0.240059i	$0.0771669\pi$
$30$		0			0
$31$	−3.70997	+	4.15164i	−0.666331	+	0.745656i
$31$	−3.70997	+	4.15164i	−0.666331	+	0.745656i
$32$	−4.32332			−0.764263
$33$	1.18801	−	3.65632i	0.206806	−	0.636484i
$34$	−0.803191	−	2.47197i	−0.137746	−	0.423939i
$35$		0			0
$36$	−3.76971			−0.628285
$37$	7.89911			1.29861			0.649303	−	0.760530i	$-0.275061\pi$
$37$	7.89911			1.29861			0.649303	+	0.760530i	$0.275061\pi$
$38$	2.40464	+	1.74708i	0.390085	+	0.283413i
$39$	1.41589	−	1.02871i	0.226724	−	0.164725i
$40$		0			0
$41$	−2.21167	+	6.80681i	−0.345404	+	1.06305i	0.615963	+	0.787775i	$0.288767\pi$
$41$	−2.21167	+	6.80681i	−0.345404	+	1.06305i	−0.961367	+	0.275270i	$0.911233\pi$
$42$	12.0546	+	8.75821i	1.86007	+	1.35142i
$43$	−1.59181	+	4.89908i	−0.242748	+	0.747103i	0.753250	+	0.657734i	$0.228485\pi$
$43$	−1.59181	+	4.89908i	−0.242748	+	0.747103i	−0.995999	+	0.0893688i	$0.971515\pi$
$44$	−0.357348	−	1.09980i	−0.0538723	−	0.165802i
$45$		0			0
$46$	−2.49433	−	7.67676i	−0.367769	−	1.13188i
$47$	1.04775	+	3.22464i	0.152830	+	0.470362i	0.997935	−	0.0642386i	$-0.0204619\pi$
$47$	1.04775	+	3.22464i	0.152830	+	0.470362i	−0.845105	+	0.534601i	$0.820462\pi$
$48$	3.69705	−	2.68606i	0.533623	−	0.387700i
$49$	5.57493	+	17.1579i	0.796419	+	2.45112i
$50$		0			0
$51$	−5.33772	−	3.87808i	−0.747431	−	0.543040i
$52$	0.162677	−	0.500668i	0.0225592	−	0.0694302i
$53$	−1.08466	+	0.788052i	−0.148989	+	0.108247i	−0.659783	−	0.751456i	$-0.729352\pi$
$53$	−1.08466	+	0.788052i	−0.148989	+	0.108247i	0.510793	+	0.859704i	$0.329352\pi$
$54$	3.75430	−	2.72766i	0.510896	−	0.371187i
$55$		0			0
$56$	15.3215			2.04742
$57$	7.54493			0.999351
$58$	0.676370	+	0.491412i	0.0888117	+	0.0645255i
$59$	1.16069	+	3.57224i	0.151109	+	0.465066i	0.997746	−	0.0671049i	$-0.0213762\pi$
$59$	1.16069	+	3.57224i	0.151109	+	0.465066i	−0.846637	+	0.532171i	$0.821376\pi$
$60$		0			0
$61$	−6.15910			−0.788593			−0.394296	−	0.918983i	$-0.629012\pi$
$61$	−6.15910			−0.788593			−0.394296	+	0.918983i	$0.629012\pi$
$62$	−3.03475	−	5.21098i	−0.385413	−	0.661795i
$63$	22.8110			2.87391
$64$	2.47425	−	7.61494i	0.309281	−	0.951868i
$65$		0			0
$66$	3.36861	+	2.44744i	0.414647	+	0.301259i
$67$	3.34130			0.408205			0.204102	−	0.978950i	$-0.434572\pi$
$67$	3.34130			0.408205			0.204102	+	0.978950i	$0.434572\pi$
$68$	−1.98459			−0.240666
$69$	−16.5764	−	12.0435i	−1.99557	−	1.44987i
$70$		0			0
$71$	1.69553	−	1.23188i	0.201223	−	0.146197i	−0.482611	−	0.875835i	$-0.660311\pi$
$71$	1.69553	−	1.23188i	0.201223	−	0.146197i	0.683834	+	0.729638i	$0.260311\pi$
$72$	4.31298	−	13.2740i	0.508290	−	1.56436i
$73$	8.89448	+	6.46222i	1.04102	+	0.756346i	0.970485	−	0.241163i	$-0.0775290\pi$
$73$	8.89448	+	6.46222i	1.04102	+	0.756346i	0.0705361	+	0.997509i	$0.477529\pi$
$74$	−2.64372	+	8.13653i	−0.307326	+	0.945853i
$75$		0			0
$76$	1.83605	−	1.33397i	0.210609	−	0.153017i
$77$	2.16236	+	6.65506i	0.246424	+	0.758414i
$78$	0.585747	+	1.80274i	0.0663228	+	0.204120i
$79$	−5.88488	+	4.27562i	−0.662101	+	0.481045i	−0.867372	−	0.497661i	$-0.834193\pi$
$79$	−5.88488	+	4.27562i	−0.662101	+	0.481045i	0.205271	+	0.978705i	$0.434193\pi$
$80$		0			0
$81$	−0.585816	+	1.80296i	−0.0650907	+	0.200329i
$82$	−6.27119	−	4.55629i	−0.692537	−	0.503158i
$83$	2.68206	−	8.25452i	0.294394	−	0.906052i	−0.689030	−	0.724733i	$-0.741963\pi$
$83$	2.68206	−	8.25452i	0.294394	−	0.906052i	0.983424	−	0.181319i	$-0.0580367\pi$
$84$	9.20423	−	6.68727i	1.00426	−	0.729641i
$85$		0			0
$86$	−4.51358	−	3.27931i	−0.486712	−	0.353617i
$87$	2.12221			0.227525
$88$	4.28151			0.456410
$89$	8.03470	+	5.83755i	0.851676	+	0.618779i	0.925608	−	0.378484i	$-0.123555\pi$
$89$	8.03470	+	5.83755i	0.851676	+	0.618779i	−0.0739315	+	0.997263i	$0.523555\pi$
$90$		0			0
$91$	−0.984379	+	3.02961i	−0.103191	+	0.317589i
$92$	−6.16318			−0.642556
$93$	−14.0072	−	6.17339i	−1.45248	−	0.640151i
$94$	−3.67223			−0.378762
$95$		0			0
$96$	−3.67297	−	11.3042i	−0.374871	−	1.15373i
$97$	−13.9505	−	10.1356i	−1.41646	−	1.02912i	−0.992343	−	0.123509i	$-0.960585\pi$
$97$	−13.9505	−	10.1356i	−1.41646	−	1.02912i	−0.424115	−	0.905608i	$-0.639415\pi$
$98$	−19.5394			−1.97378
$99$	6.37441			0.640653
$100$		0			0
$101$	2.82366	−	2.05151i	0.280965	−	0.204133i	−0.438373	−	0.898793i	$-0.644445\pi$
$101$	2.82366	−	2.05151i	0.280965	−	0.204133i	0.719338	+	0.694660i	$0.244445\pi$
$102$	5.78111	−	4.20022i	0.572415	−	0.415884i
$103$	2.54309	−	7.82683i	0.250578	−	0.771200i	−0.744091	−	0.668079i	$-0.767117\pi$
$103$	2.54309	−	7.82683i	0.250578	−	0.771200i	0.994669	−	0.103122i	$-0.0328831\pi$
$104$	1.57684	+	1.14564i	0.154622	+	0.112340i
$105$		0			0
$106$	−0.448718	−	1.38101i	−0.0435833	−	0.134136i
$107$	−4.80437	+	3.49058i	−0.464456	+	0.337447i	−0.795277	−	0.606247i	$-0.792674\pi$
$107$	−4.80437	+	3.49058i	−0.464456	+	0.337447i	0.330821	+	0.943694i	$0.392674\pi$
$108$	−1.09493	−	3.36985i	−0.105360	−	0.324264i
$109$	−3.44220	−	10.5940i	−0.329703	−	1.01472i	−0.969273	−	0.245988i	$-0.920887\pi$
$109$	−3.44220	−	10.5940i	−0.329703	−	1.01472i	0.639570	−	0.768733i	$-0.279113\pi$
$110$		0			0
$111$	6.71085	+	20.6539i	0.636966	+	1.96038i
$112$	−2.57032	+	7.91064i	−0.242873	+	0.747485i
$113$	10.0475	+	7.29991i	0.945186	+	0.686718i	0.949664	−	0.313272i	$-0.101425\pi$
$113$	10.0475	+	7.29991i	0.945186	+	0.686718i	−0.00447704	+	0.999990i	$0.501425\pi$
$114$	−2.52518	+	7.77171i	−0.236505	+	0.727887i
$115$		0			0
$116$	0.516437	−	0.375214i	0.0479500	−	0.0348377i
$117$	2.34765	+	1.70566i	0.217040	+	0.157689i
$118$	−4.06808			−0.374497
$119$	12.0090			1.10086
$120$		0			0
$121$	−2.79493	−	8.60190i	−0.254084	−	0.781991i
$122$	2.06137	−	6.34423i	0.186627	−	0.574380i
$123$	−19.6768			−1.77420
$124$	−4.50011	+	0.974232i	−0.404122	+	0.0874886i
$125$		0			0
$126$	−7.63451	+	23.4966i	−0.680137	+	2.09324i
$127$	−3.27595	−	10.0823i	−0.290693	−	0.894662i	−0.984634	−	0.174630i	$-0.944127\pi$
$127$	−3.27595	−	10.0823i	−0.290693	−	0.894662i	0.693941	−	0.720032i	$-0.255873\pi$
$128$	0.0204481	+	0.0148564i	0.00180737	+	0.00131313i
$129$	−14.1620			−1.24690
$130$		0			0
$131$	3.13546	+	2.27805i	0.273947	+	0.199034i	0.716273	−	0.697820i	$-0.245847\pi$
$131$	3.13546	+	2.27805i	0.273947	+	0.199034i	−0.442326	+	0.896854i	$0.645847\pi$
$132$	2.57208	−	1.86872i	0.223871	−	0.162651i
$133$	−11.1102	+	8.07201i	−0.963373	+	0.699932i
$134$	−1.11829	+	3.44173i	−0.0966052	+	0.297320i
$135$		0			0
$136$	2.27059	−	6.98817i	0.194702	−	0.599231i
$137$	6.76461	+	20.8193i	0.577940	+	1.77872i	0.625943	+	0.779869i	$0.284714\pi$
$137$	6.76461	+	20.8193i	0.577940	+	1.77872i	−0.0480027	+	0.998847i	$0.515286\pi$
$138$	17.9534	−	13.0439i	1.52829	−	1.11037i
$139$	1.65531	+	5.09453i	0.140402	+	0.432112i	0.996391	−	0.0848813i	$-0.0270511\pi$
$139$	1.65531	+	5.09453i	0.140402	+	0.432112i	−0.855989	+	0.516994i	$0.827051\pi$
$140$		0			0
$141$	−7.54136	+	5.47912i	−0.635097	+	0.461425i
$142$	0.701433	+	2.15879i	0.0588630	+	0.181162i
$143$	−0.275080	+	0.846608i	−0.0230033	+	0.0707970i
$144$	6.12996	+	4.45368i	0.510830	+	0.371140i
$145$		0			0
$146$	−9.63332	+	6.99901i	−0.797259	+	0.579242i
$147$	−40.1265	+	29.1536i	−3.30958	+	2.40455i
$148$	5.28475	+	3.83959i	0.434404	+	0.315613i
$149$	−1.57437			−0.128977			−0.0644886	−	0.997918i	$-0.520542\pi$
$149$	−1.57437			−0.128977			−0.0644886	+	0.997918i	$0.520542\pi$
$150$		0			0
$151$	6.94745	+	5.04761i	0.565375	+	0.410769i	0.833422	−	0.552637i	$-0.186378\pi$
$151$	6.94745	+	5.04761i	0.565375	+	0.410769i	−0.268047	+	0.963406i	$0.586378\pi$
$152$	2.59655	+	7.99136i	0.210608	+	0.648185i
$153$	3.38052	−	10.4042i	0.273299	−	0.841127i
$154$	−7.57880			−0.610717
$155$		0			0
$156$	1.44731			0.115877
$157$	2.59997	−	8.00189i	0.207500	−	0.638620i	−0.792101	−	0.610390i	$-0.791013\pi$
$157$	2.59997	−	8.00189i	0.207500	−	0.638620i	0.999601	−	0.0282303i	$-0.00898719\pi$
$158$	−2.43454	−	7.49276i	−0.193682	−	0.596092i
$159$	−2.98202	−	2.16656i	−0.236490	−	0.171820i
$160$		0			0
$161$	37.2942			2.93919
$162$	−1.66108	−	1.20685i	−0.130507	−	0.0948190i
$163$	2.38981	−	1.73630i	0.187184	−	0.135997i	−0.490247	−	0.871584i	$-0.663093\pi$
$163$	2.38981	−	1.73630i	0.187184	−	0.135997i	0.677431	+	0.735587i	$0.263093\pi$
$164$	−4.78832	+	3.47892i	−0.373905	+	0.271658i
$165$		0			0
$166$	7.60498	+	5.52534i	0.590261	+	0.428850i
$167$	3.23599	−	9.95936i	0.250409	−	0.770678i	−0.744291	−	0.667855i	$-0.767213\pi$
$167$	3.23599	−	9.95936i	0.250409	−	0.770678i	0.994700	−	0.102823i	$-0.0327875\pi$
$168$	13.0167	+	40.0612i	1.00426	+	3.09079i
$169$	10.1894	−	7.40301i	0.783798	−	0.569463i
$170$		0			0
$171$	3.86581	+	11.8977i	0.295626	+	0.909842i
$172$	−3.44631	+	2.50389i	−0.262779	+	0.190920i
$173$	1.31761	+	4.05518i	0.100176	+	0.308310i	0.988568	−	0.150776i	$-0.0481771\pi$
$173$	1.31761	+	4.05518i	0.100176	+	0.308310i	−0.888392	+	0.459086i	$0.848177\pi$
$174$	−0.710274	+	2.18600i	−0.0538458	+	0.165720i
$175$		0			0
$176$	−0.718264	+	2.21059i	−0.0541411	+	0.166629i
$177$	−8.35429	+	6.06974i	−0.627947	+	0.456230i
$178$	−8.70211	+	6.32245i	−0.652251	+	0.473888i
$179$	2.38375	+	1.73189i	0.178170	+	0.129448i	0.673296	−	0.739373i	$-0.264878\pi$
$179$	2.38375	+	1.73189i	0.178170	+	0.129448i	−0.495126	+	0.868821i	$0.664878\pi$
$180$		0			0
$181$	0.445493			0.0331132			0.0165566	−	0.999863i	$-0.494730\pi$
$181$	0.445493			0.0331132			0.0165566	+	0.999863i	$0.494730\pi$
$182$	−2.79121	−	2.02793i	−0.206898	−	0.150320i
$183$	−5.23259	−	16.1043i	−0.386804	−	1.19046i
$184$	7.05139	−	21.7019i	0.519835	−	1.59989i
$185$		0			0
$186$	11.0470	−	12.3621i	0.810003	−	0.906432i
$187$	3.35585			0.245404
$188$	−0.866455	+	2.66667i	−0.0631927	+	0.194487i
$189$	6.62557	+	20.3914i	0.481939	+	1.48326i
$190$		0			0
$191$	−23.6564			−1.71172			−0.855858	−	0.517211i	$-0.826970\pi$
$191$	−23.6564			−1.71172			−0.855858	+	0.517211i	$0.826970\pi$
$192$	22.0129			1.58864
$193$	−15.6959	−	11.4037i	−1.12982	−	0.820860i	−0.144148	−	0.989556i	$-0.546044\pi$
$193$	−15.6959	−	11.4037i	−1.12982	−	0.820860i	−0.985668	+	0.168696i	$0.946044\pi$
$194$	15.1093	−	10.9776i	1.08479	−	0.788143i
$195$		0			0
$196$	−4.61029	+	14.1890i	−0.329306	+	1.01350i
$197$	8.87674	+	6.44933i	0.632442	+	0.459496i	0.857245	−	0.514908i	$-0.172174\pi$
$197$	8.87674	+	6.44933i	0.632442	+	0.459496i	−0.224803	+	0.974404i	$0.572174\pi$
$198$	−2.13343	+	6.56601i	−0.151616	+	0.466626i
$199$	3.19700	+	9.83935i	0.226629	+	0.697493i	0.998122	+	0.0612552i	$0.0195103\pi$
$199$	3.19700	+	9.83935i	0.226629	+	0.697493i	−0.771493	+	0.636238i	$0.780490\pi$
$200$		0			0
$201$	2.83867	+	8.73652i	0.200224	+	0.616227i
$202$	1.16813	+	3.59514i	0.0821895	+	0.252953i
$203$	−3.12503	+	2.27047i	−0.219334	+	0.159355i
$204$	−1.68605	−	5.18911i	−0.118047	−	0.363311i
$205$		0			0
$206$	7.21095	+	5.23906i	0.502410	+	0.365022i
$207$	10.4983	−	32.3104i	0.729681	−	2.24573i
$208$	−0.856039	+	0.621949i	−0.0593557	+	0.0431244i
$209$	−3.10468	+	2.25568i	−0.214755	+	0.156029i
$210$		0			0
$211$	−14.8291			−1.02088			−0.510440	−	0.859913i	$-0.670518\pi$
$211$	−14.8291			−1.02088			−0.510440	+	0.859913i	$0.670518\pi$
$212$	−1.10873			−0.0761476
$213$	4.66148	+	3.38676i	0.319399	+	0.232057i
$214$	−1.98754	−	6.11702i	−0.135866	−	0.418151i
$215$		0			0
$216$	13.1187			0.892617
$217$	27.2307	−	5.89520i	1.84854	−	0.400192i
$218$	12.0645			0.817110
$219$	−9.34034	+	28.7466i	−0.631161	+	1.94252i
$220$		0			0
$221$	1.23593	+	0.897957i	0.0831378	+	0.0604031i
$222$	−23.5207			−1.57861
$223$	−13.4811			−0.902758			−0.451379	−	0.892332i	$-0.649068\pi$
$223$	−13.4811			−0.902758			−0.451379	+	0.892332i	$0.649068\pi$
$224$	17.5025	+	12.7163i	1.16943	+	0.849644i
$225$		0			0
$226$	−10.8821	+	7.90629i	−0.723865	+	0.525919i
$227$	6.80665	−	20.9487i	0.451773	−	1.39042i	−0.423109	−	0.906079i	$-0.639061\pi$
$227$	6.80665	−	20.9487i	0.451773	−	1.39042i	0.874882	−	0.484336i	$-0.160939\pi$
$228$	5.04779	+	3.66743i	0.334298	+	0.242882i
$229$	−1.32263	+	4.07064i	−0.0874019	+	0.268995i	−0.985199	−	0.171414i	$-0.945167\pi$
$229$	−1.32263	+	4.07064i	−0.0874019	+	0.268995i	0.897797	+	0.440409i	$0.145167\pi$
$230$		0			0
$231$	−15.5640	+	11.3079i	−1.02403	+	0.744004i
$232$	0.730348	+	2.24778i	0.0479497	+	0.147574i
$233$	5.11113	+	15.7304i	0.334841	+	1.03053i	0.966800	+	0.255533i	$0.0822510\pi$
$233$	5.11113	+	15.7304i	0.334841	+	1.03053i	−0.631959	+	0.775002i	$0.717749\pi$
$234$	−2.54266	+	1.84735i	−0.166219	+	0.120765i
$235$		0			0
$236$	−0.959855	+	2.95413i	−0.0624812	+	0.192297i
$237$	−16.1791	−	11.7548i	−1.05095	−	0.763558i
$238$	−4.01923	+	12.3699i	−0.260528	+	0.801824i
$239$	−12.1116	+	8.79963i	−0.783437	+	0.569201i	−0.906009	−	0.423259i	$-0.860886\pi$
$239$	−12.1116	+	8.79963i	−0.783437	+	0.569201i	0.122571	+	0.992460i	$0.460886\pi$
$240$		0			0
$241$	10.4677	+	7.60519i	0.674281	+	0.489894i	0.871455	−	0.490475i	$-0.163177\pi$
$241$	10.4677	+	7.60519i	0.674281	+	0.489894i	−0.197175	+	0.980368i	$0.563177\pi$
$242$	9.79587			0.629703
$243$	−18.0659			−1.15893
$244$	−4.12063	−	2.99381i	−0.263796	−	0.191659i
$245$		0			0
$246$	6.58555	−	20.2682i	0.419879	−	1.29225i
$247$	−1.74700			−0.111159
$248$	1.71816	−	16.9605i	0.109103	−	1.07700i
$249$	23.8618			1.51218
$250$		0			0
$251$	−4.44076	−	13.6673i	−0.280298	−	0.862670i	−0.987769	−	0.155927i	$-0.950164\pi$
$251$	−4.44076	−	13.6673i	−0.280298	−	0.862670i	0.707470	−	0.706743i	$-0.249836\pi$
$252$	15.2612	+	11.0879i	0.961368	+	0.698475i
$253$	10.4217			0.655205
$254$	11.4818			0.720432
$255$		0			0
$256$	12.9332	−	9.39650i	0.808323	−	0.587281i
$257$	−16.0441	+	11.6567i	−1.00081	+	0.727128i	−0.962261	−	0.272129i	$-0.912272\pi$
$257$	−16.0441	+	11.6567i	−1.00081	+	0.727128i	−0.0385449	+	0.999257i	$0.512272\pi$
$258$	4.73983	−	14.5877i	0.295089	−	0.908190i
$259$	−31.9787	−	23.2339i	−1.98706	−	1.44368i
$260$		0			0
$261$	1.08736	+	3.34655i	0.0673059	+	0.207146i
$262$	−3.39592	+	2.46728i	−0.209800	+	0.152429i
$263$	−0.0252272	−	0.0776412i	−0.00155557	−	0.00478756i	0.950276	−	0.311410i	$-0.100801\pi$
$263$	−0.0252272	−	0.0776412i	−0.00155557	−	0.00478756i	−0.951831	+	0.306622i	$0.900801\pi$
$264$	3.63744	+	11.1949i	0.223869	+	0.688998i
$265$		0			0
$266$	−4.59621	−	14.1457i	−0.281812	−	0.867328i
$267$	−8.43745	+	25.9678i	−0.516364	+	1.58920i
$268$	2.23543	+	1.62414i	0.136551	+	0.0992099i
$269$	−3.59930	+	11.0775i	−0.219453	+	0.675408i	0.779354	+	0.626584i	$0.215547\pi$
$269$	−3.59930	+	11.0775i	−0.219453	+	0.675408i	−0.998807	+	0.0488240i	$0.984453\pi$
$270$		0			0
$271$	−5.81128	+	4.22214i	−0.353010	+	0.256477i	−0.750131	−	0.661290i	$-0.770009\pi$
$271$	−5.81128	+	4.22214i	−0.353010	+	0.256477i	0.397121	+	0.917766i	$0.370009\pi$
$272$	3.22715	+	2.34466i	0.195675	+	0.142166i
$273$	−8.75784			−0.530049
$274$	−23.7091			−1.43232
$275$		0			0
$276$	−5.23606	−	16.1149i	−0.315174	−	0.970005i
$277$	4.82569	−	14.8519i	0.289947	−	0.892366i	−0.694925	−	0.719083i	$-0.744562\pi$
$277$	4.82569	−	14.8519i	0.289947	−	0.892366i	0.984872	−	0.173284i	$-0.0554378\pi$
$278$	−5.80167			−0.347961
$279$	2.55803	−	25.2513i	0.153145	−	1.51175i
$280$		0			0
$281$	−3.75049	+	11.5428i	−0.223735	+	0.688586i	0.774682	+	0.632351i	$0.217910\pi$
$281$	−3.75049	+	11.5428i	−0.223735	+	0.688586i	−0.998418	+	0.0562356i	$0.982090\pi$
$282$	−3.11982	−	9.60182i	−0.185783	−	0.571780i
$283$	4.57342	+	3.32278i	0.271861	+	0.197519i	0.715360	−	0.698756i	$-0.246263\pi$
$283$	4.57342	+	3.32278i	0.271861	+	0.197519i	−0.443498	+	0.896275i	$0.646263\pi$
$284$	1.73315			0.102844
$285$		0			0
$286$	−0.779990	−	0.566696i	−0.0461218	−	0.0335094i
$287$	28.9747	−	21.0514i	1.71032	−	1.24262i
$288$	15.9439	−	11.5839i	0.939504	−	0.682590i
$289$	−3.47360	+	10.6906i	−0.204329	+	0.628861i
$290$		0			0
$291$	14.6498	−	45.0874i	0.858786	−	2.64307i
$292$	2.80953	+	8.64685i	0.164415	+	0.506019i
$293$	13.4133	−	9.74536i	0.783616	−	0.569330i	−0.122446	−	0.992475i	$-0.539074\pi$
$293$	13.4133	−	9.74536i	0.783616	−	0.569330i	0.906062	+	0.423145i	$0.139074\pi$
$294$	−16.6001	−	51.0900i	−0.968139	−	2.97963i
$295$		0			0
$296$	−19.5664	+	14.2158i	−1.13728	+	0.826279i
$297$	1.85148	+	5.69828i	0.107434	+	0.330648i
$298$	0.526919	−	1.62169i	0.0305236	−	0.0939419i
$299$	3.83822	+	2.78863i	0.221970	+	0.161271i
$300$		0			0
$301$	20.8541	−	15.1514i	1.20201	−	0.873310i
$302$	−7.52454	+	5.46690i	−0.432989	+	0.314585i
$303$	7.76299	+	5.64015i	0.445972	+	0.324018i
$304$	−4.56162			−0.261627
$305$		0			0
$306$	9.58547	+	6.96425i	0.547965	+	0.398120i
$307$	0.329733	+	1.01481i	0.0188189	+	0.0579185i	0.960025	−	0.279914i	$-0.0903061\pi$
$307$	0.329733	+	1.01481i	0.0188189	+	0.0579185i	−0.941206	+	0.337833i	$0.890306\pi$
$308$	−1.78820	+	5.50351i	−0.101892	+	0.313592i
$309$	22.6254			1.28711
$310$		0			0
$311$	−20.0217			−1.13532			−0.567662	−	0.823262i	$-0.692152\pi$
$311$	−20.0217			−1.13532			−0.567662	+	0.823262i	$0.692152\pi$
$312$	−1.65589	+	5.09630i	−0.0937461	+	0.288521i
$313$	5.95865	+	18.3388i	0.336803	+	1.03657i	0.965827	+	0.259187i	$0.0834545\pi$
$313$	5.95865	+	18.3388i	0.336803	+	1.03657i	−0.629025	+	0.777385i	$0.716546\pi$
$314$	7.37223	+	5.35624i	0.416039	+	0.302270i
$315$		0			0
$316$	−6.01546			−0.338396
$317$	18.9260	+	13.7506i	1.06299	+	0.772309i	0.974640	−	0.223781i	$-0.0718399\pi$
$317$	18.9260	+	13.7506i	1.06299	+	0.772309i	0.0883523	+	0.996089i	$0.471840\pi$
$318$	3.22973	−	2.34653i	0.181114	−	0.131587i
$319$	−0.873273	+	0.634470i	−0.0488939	+	0.0355235i
$320$		0			0
$321$	−13.2085	−	9.59654i	−0.737226	−	0.535626i
$322$	−12.4818	+	38.4151i	−0.695586	+	2.14079i
$323$	2.03518	+	6.26363i	0.113240	+	0.348518i
$324$	−1.26831	+	0.921481i	−0.0704616	+	0.0511934i
$325$		0			0
$326$	0.988649	+	3.04275i	0.0547562	+	0.168522i
$327$	24.7758	−	18.0007i	1.37011	−	0.995441i
$328$	−6.77167	−	20.8410i	−0.373903	−	1.15075i
$329$	5.24303	−	16.1364i	0.289057	−	0.889627i
$330$		0			0
$331$	−6.55241	+	20.1663i	−0.360153	+	1.10844i	0.592808	+	0.805344i	$0.298019\pi$
$331$	−6.55241	+	20.1663i	−0.360153	+	1.10844i	−0.952961	+	0.303094i	$0.901981\pi$
$332$	5.80673	−	4.21884i	0.318686	−	0.231539i
$333$	−29.1310	+	21.1649i	−1.59637	+	1.15983i
$334$	9.17567	+	6.66651i	0.502070	+	0.364775i
$335$		0			0
$336$	−22.8677			−1.24753
$337$	−10.3468	−	7.51736i	−0.563624	−	0.409497i	0.269160	−	0.963096i	$-0.413254\pi$
$337$	−10.3468	−	7.51736i	−0.563624	−	0.409497i	−0.832783	+	0.553599i	$0.813254\pi$
$338$	4.21529	+	12.9733i	0.229281	+	0.705656i
$339$	−10.5511	+	32.4730i	−0.573058	+	1.76369i
$340$		0			0
$341$	7.60949	−	1.64738i	0.412077	−	0.0892108i
$342$	−13.5492			−0.732655
$343$	17.0730	−	52.5453i	0.921855	−	2.83718i
$344$	−4.87379	−	15.0000i	−0.262777	−	0.808744i
$345$		0			0
$346$	−4.61806			−0.248268
$347$	−34.2904			−1.84080			−0.920402	−	0.390974i	$-0.872138\pi$
$347$	−34.2904			−1.84080			−0.920402	+	0.390974i	$0.872138\pi$
$348$	1.41982	+	1.03156i	0.0761106	+	0.0552976i
$349$	−0.843868	+	0.613106i	−0.0451712	+	0.0328188i	−0.610142	−	0.792292i	$-0.708888\pi$
$349$	−0.843868	+	0.613106i	−0.0451712	+	0.0328188i	0.564971	+	0.825111i	$0.308888\pi$
$350$		0			0
$351$	−0.842858	+	2.59405i	−0.0449884	+	0.138460i
$352$	4.89098	+	3.55351i	0.260690	+	0.189403i
$353$	0.909726	−	2.79985i	0.0484198	−	0.149021i	−0.923923	−	0.382578i	$-0.875036\pi$
$353$	0.909726	−	2.79985i	0.0484198	−	0.149021i	0.972343	+	0.233557i	$0.0750364\pi$
$354$	−3.45612	−	10.6369i	−0.183691	−	0.565342i
$355$		0			0
$356$	2.53795	+	7.81100i	0.134511	+	0.413982i
$357$	10.2025	+	31.4000i	0.539972	+	1.66186i
$358$	−2.58176	+	1.87576i	−0.136450	+	0.0991368i
$359$	1.18848	+	3.65778i	0.0627258	+	0.193050i	0.977508	−	0.210896i	$-0.0676382\pi$
$359$	1.18848	+	3.65778i	0.0627258	+	0.193050i	−0.914783	+	0.403946i	$0.867638\pi$
$360$		0			0
$361$	9.27828	+	6.74107i	0.488331	+	0.354793i
$362$	−0.149100	+	0.458883i	−0.00783653	+	0.0241183i
$363$	20.1170	−	14.6158i	1.05587	−	0.767133i
$364$	−2.13121	+	1.54841i	−0.111706	+	0.0811590i
$365$		0			0
$366$	18.3396			0.958626
$367$	−5.51281			−0.287766			−0.143883	−	0.989595i	$-0.545959\pi$
$367$	−5.51281			−0.287766			−0.143883	+	0.989595i	$0.545959\pi$
$368$	10.0220	+	7.28142i	0.522433	+	0.379570i
$369$	−10.0818	−	31.0287i	−0.524839	−	1.61529i
$370$		0			0
$371$	6.70904			0.348316
$372$	−6.37050	−	10.9388i	−0.330295	−	0.567151i
$373$	−0.532637			−0.0275789			−0.0137895	−	0.999905i	$-0.504389\pi$
$373$	−0.532637			−0.0275789			−0.0137895	+	0.999905i	$0.504389\pi$
$374$	−1.12315	+	3.45671i	−0.0580769	+	0.178742i
$375$		0			0
$376$	−8.39864	−	6.10197i	−0.433127	−	0.314685i
$377$	−0.491391			−0.0253079
$378$	−23.2218			−1.19440
$379$	5.95047	+	4.32327i	0.305655	+	0.222071i	0.730030	−	0.683415i	$-0.239506\pi$
$379$	5.95047	+	4.32327i	0.305655	+	0.222071i	−0.424375	+	0.905487i	$0.639506\pi$
$380$		0			0
$381$	23.5792	−	17.1313i	1.20800	−	0.877663i
$382$	7.91746	−	24.3674i	0.405092	−	1.24675i
$383$	3.29142	+	2.39136i	0.168184	+	0.122193i	0.668693	−	0.743538i	$-0.266854\pi$
$383$	3.29142	+	2.39136i	0.168184	+	0.122193i	−0.500510	+	0.865731i	$0.666854\pi$
$384$	−0.0214731	+	0.0660873i	−0.00109579	+	0.00337250i
$385$		0			0
$386$	16.9997	−	12.3510i	0.865263	−	0.628650i
$387$	−7.25622	−	22.3323i	−0.368854	−	1.13522i
$388$	−4.40659	−	13.5621i	−0.223711	−	0.688511i
$389$	27.8933	−	20.2656i	1.41424	−	1.02751i	0.421556	−	0.906802i	$-0.361484\pi$
$389$	27.8933	−	20.2656i	1.41424	−	1.02751i	0.992688	−	0.120707i	$-0.0385160\pi$
$390$		0			0
$391$	5.52688	−	17.0100i	0.279507	−	0.860233i
$392$	−44.6880	−	32.4677i	−2.25708	−	1.63987i
$393$	−3.29264	+	10.1337i	−0.166092	+	0.511177i
$394$	−9.61410	+	6.98505i	−0.484351	+	0.351902i
$395$		0			0
$396$	4.26468	+	3.09847i	0.214308	+	0.155704i
$397$	1.88725			0.0947182			0.0473591	−	0.998878i	$-0.484919\pi$
$397$	1.88725			0.0947182			0.0473591	+	0.998878i	$0.484919\pi$
$398$	−11.2051			−0.561660
$399$	−30.5448	−	22.1921i	−1.52915	−	1.11100i
$400$		0			0
$401$	6.21445	−	19.1261i	0.310335	−	0.955113i	−0.667297	−	0.744791i	$-0.732549\pi$
$401$	6.21445	−	19.1261i	0.310335	−	0.955113i	0.977632	−	0.210321i	$-0.0674510\pi$
$402$	−9.94918			−0.496220
$403$	3.24332	+	1.42943i	0.161561	+	0.0712049i
$404$	2.88631			0.143599
$405$		0			0
$406$	−1.29281	−	3.97885i	−0.0641609	−	0.197467i
$407$	−8.93628	−	6.49258i	−0.442955	−	0.321825i
$408$	20.2011			1.00010
$409$	−11.8662			−0.586745			−0.293373	−	0.955998i	$-0.594778\pi$
$409$	−11.8662			−0.586745			−0.293373	+	0.955998i	$0.594778\pi$
$410$		0			0
$411$	−48.6895	+	35.3750i	−2.40168	+	1.74492i
$412$	5.50587	−	4.00025i	0.271255	−	0.197078i
$413$	5.80820	−	17.8758i	0.285803	−	0.879611i
$414$	29.7679	+	21.6277i	1.46301	+	1.06294i
$415$		0			0
$416$	0.850463	+	2.61746i	0.0416974	+	0.128331i
$417$	−11.9144	+	8.65632i	−0.583451	+	0.423902i
$418$	−1.28439	−	3.95294i	−0.0628215	−	0.193345i
$419$	4.55963	+	14.0331i	0.222752	+	0.685561i	0.998512	+	0.0545326i	$0.0173669\pi$
$419$	4.55963	+	14.0331i	0.222752	+	0.685561i	−0.775760	+	0.631028i	$0.782633\pi$
$420$		0			0
$421$	−3.13553	−	9.65018i	−0.152817	−	0.470321i	0.845117	−	0.534582i	$-0.179531\pi$
$421$	−3.13553	−	9.65018i	−0.152817	−	0.470321i	−0.997933	+	0.0642610i	$0.979531\pi$
$422$	4.96311	−	15.2749i	0.241600	−	0.743569i
$423$	−12.5041	−	9.08476i	−0.607970	−	0.441716i
$424$	1.26851	−	3.90407i	0.0616043	−	0.189599i
$425$		0			0
$426$	−5.04869	+	3.66809i	−0.244610	+	0.177719i
$427$	24.9345	+	18.1159i	1.20666	+	0.876692i
$428$	−4.91097			−0.237381
$429$	−2.44733			−0.118158
$430$		0			0
$431$	7.62147	+	23.4565i	0.367113	+	1.12986i	0.948647	+	0.316336i	$0.102453\pi$
$431$	7.62147	+	23.4565i	0.367113	+	1.12986i	−0.581534	+	0.813522i	$0.697547\pi$
$432$	−2.20079	+	6.77335i	−0.105886	+	0.325883i
$433$	15.8754			0.762922			0.381461	−	0.924385i	$-0.375421\pi$
$433$	15.8754			0.762922			0.381461	+	0.924385i	$0.375421\pi$
$434$	−3.04135	+	30.0223i	−0.145989	+	1.44111i
$435$		0			0
$436$	2.84659	−	8.76090i	0.136327	−	0.419571i
$437$	6.32029	+	19.4519i	0.302341	+	0.930509i
$438$	−26.4846	−	19.2422i	−1.26548	−	0.919426i
$439$	−1.64657			−0.0785864			−0.0392932	−	0.999228i	$-0.512511\pi$
$439$	−1.64657			−0.0785864			−0.0392932	+	0.999228i	$0.512511\pi$
$440$		0			0
$441$	−66.5325	−	48.3387i	−3.16822	−	2.30184i
$442$	−1.33860	+	0.972547i	−0.0636705	+	0.0462593i
$443$	−14.5828	+	10.5950i	−0.692848	+	0.503383i	−0.877595	−	0.479403i	$-0.840853\pi$
$443$	−14.5828	+	10.5950i	−0.692848	+	0.503383i	0.184747	+	0.982786i	$0.440853\pi$
$444$	−5.54965	+	17.0801i	−0.263375	+	0.810585i
$445$		0			0
$446$	4.51192	−	13.8863i	0.213646	−	0.657533i
$447$	−1.33754	−	4.11651i	−0.0632633	−	0.194704i
$448$	−32.4147	+	23.5507i	−1.53145	+	1.11267i
$449$	1.49885	+	4.61297i	0.0707349	+	0.217700i	0.980174	−	0.198137i	$-0.0634889\pi$
$449$	1.49885	+	4.61297i	0.0707349	+	0.217700i	−0.909440	+	0.415836i	$0.863489\pi$
$450$		0			0
$451$	8.09684	−	5.88270i	0.381265	−	0.277006i
$452$	3.17373	+	9.76773i	0.149280	+	0.459436i
$453$	−7.29570	+	22.4539i	−0.342782	+	1.05497i
$454$	19.3003	+	14.0225i	0.905807	+	0.658108i
$455$		0			0
$456$	−18.6891	+	13.5784i	−0.875198	+	0.635869i
$457$	−3.32344	+	2.41462i	−0.155464	+	0.112951i	−0.662798	−	0.748798i	$-0.730631\pi$
$457$	−3.32344	+	2.41462i	−0.155464	+	0.112951i	0.507334	+	0.861750i	$0.330631\pi$
$458$	−3.75032	−	2.72477i	−0.175241	−	0.127320i
$459$	10.2825			0.479945
$460$		0			0
$461$	−18.8029	−	13.6611i	−0.875738	−	0.636261i	0.0563827	−	0.998409i	$-0.482043\pi$
$461$	−18.8029	−	13.6611i	−0.875738	−	0.636261i	−0.932120	+	0.362149i	$0.882043\pi$
$462$	−6.43872	−	19.8164i	−0.299557	−	0.921940i
$463$	9.51077	−	29.2711i	0.442003	−	1.36035i	−0.443734	−	0.896158i	$-0.646347\pi$
$463$	9.51077	−	29.2711i	0.442003	−	1.36035i	0.885737	−	0.464187i	$-0.153653\pi$
$464$	−1.28308			−0.0595653
$465$		0			0
$466$	−17.9139			−0.829844
$467$	−5.16147	+	15.8854i	−0.238844	+	0.735088i	0.757744	+	0.652552i	$0.226302\pi$
$467$	−5.16147	+	15.8854i	−0.238844	+	0.735088i	−0.996588	+	0.0825353i	$0.973698\pi$
$468$	0.741559	+	2.28228i	0.0342786	+	0.105499i
$469$	−13.5269	−	9.82785i	−0.624613	−	0.453808i
$470$		0			0
$471$	23.1315			1.06584
$472$	−9.30397	−	6.75973i	−0.428250	−	0.311142i
$473$	5.82756	−	4.23397i	0.267952	−	0.194678i
$474$	17.5231	−	12.7312i	0.804861	−	0.584766i
$475$		0			0
$476$	8.03437	+	5.83731i	0.368255	+	0.267553i
$477$	1.88859	−	5.81248i	0.0864726	−	0.266135i
$478$	−5.01052	−	15.4208i	−0.229176	−	0.705331i
$479$	3.66602	−	2.66352i	0.167505	−	0.121699i	−0.500875	−	0.865520i	$-0.666988\pi$
$479$	3.66602	−	2.66352i	0.167505	−	0.121699i	0.668379	+	0.743820i	$0.266988\pi$
$480$		0			0
$481$	−1.55387	−	4.78233i	−0.0708506	−	0.218056i
$482$	−11.3372	+	8.23693i	−0.516393	+	0.375182i
$483$	31.6840	+	97.5134i	1.44167	+	4.43702i
$484$	2.31131	−	7.11349i	0.105060	−	0.323341i
$485$		0			0
$486$	6.04640	−	18.6089i	0.274270	−	0.844116i
$487$	12.1341	−	8.81591i	0.549847	−	0.399487i	−0.277882	−	0.960615i	$-0.589633\pi$
$487$	12.1341	−	8.81591i	0.549847	−	0.399487i	0.827729	+	0.561128i	$0.189633\pi$
$488$	15.2564	−	11.0844i	0.690623	−	0.501767i
$489$	6.57021	+	4.77354i	0.297115	+	0.215867i
$490$		0			0
$491$	40.2267			1.81541			0.907703	−	0.419613i	$-0.137834\pi$
$491$	40.2267			1.81541			0.907703	+	0.419613i	$0.137834\pi$
$492$	−13.1644	−	9.56448i	−0.593496	−	0.431200i
$493$	0.572447	+	1.76181i	0.0257817	+	0.0793480i
$494$	0.584697	−	1.79951i	0.0263068	−	0.0809639i
$495$		0			0
$496$	8.46867	+	3.73239i	0.380255	+	0.167589i
$497$	−10.4875			−0.470430
$498$	−7.98620	+	24.5790i	−0.357870	+	1.10141i
$499$	−12.6135	−	38.8202i	−0.564656	−	1.73783i	−0.668972	−	0.743288i	$-0.733265\pi$
$499$	−12.6135	−	38.8202i	−0.564656	−	1.73783i	0.104316	−	0.994544i	$-0.466735\pi$
$500$		0			0
$501$	28.7900			1.28624
$502$	15.5643			0.694670
$503$	−5.91042	−	4.29417i	−0.263533	−	0.191468i	0.448170	−	0.893948i	$-0.352076\pi$
$503$	−5.91042	−	4.29417i	−0.263533	−	0.191468i	−0.711703	+	0.702480i	$0.752076\pi$
$504$	−56.5038	+	41.0524i	−2.51688	+	1.82862i
$505$		0			0
$506$	−3.48799	+	10.7349i	−0.155060	+	0.477225i
$507$	28.0133	+	20.3529i	1.24412	+	0.903903i
$508$	2.70910	−	8.33776i	0.120197	−	0.369928i
$509$	6.40708	+	19.7190i	0.283989	+	0.874028i	0.986700	+	0.162553i	$0.0519727\pi$
$509$	6.40708	+	19.7190i	0.283989	+	0.874028i	−0.702711	+	0.711475i	$0.748027\pi$
$510$		0			0
$511$	−17.0008	−	52.3232i	−0.752072	−	2.31464i
$512$	5.36600	+	16.5149i	0.237146	+	0.729861i
$513$	−9.51289	+	6.91152i	−0.420004	+	0.305151i
$514$	−6.63737	−	20.4277i	−0.292762	−	0.901028i
$515$		0			0
$516$	−9.47483	−	6.88387i	−0.417106	−	0.303045i
$517$	1.46514	−	4.50923i	0.0644367	−	0.198316i
$518$	34.6350	−	25.1638i	1.52178	−	1.10563i
$519$	−9.48373	+	6.89033i	−0.416289	+	0.302452i
$520$		0			0
$521$	−5.07858			−0.222497			−0.111248	−	0.993793i	$-0.535485\pi$
$521$	−5.07858			−0.222497			−0.111248	+	0.993793i	$0.535485\pi$
$522$	−3.81106			−0.166806
$523$	13.2479	+	9.62516i	0.579290	+	0.420879i	0.838468	−	0.544951i	$-0.183452\pi$
$523$	13.2479	+	9.62516i	0.579290	+	0.420879i	−0.259178	+	0.965830i	$0.583452\pi$
$524$	0.990410	+	3.04817i	0.0432663	+	0.133160i
$525$		0			0
$526$	0.0884181			0.00385521
$527$	1.34669	−	13.2937i	0.0586628	−	0.579082i
$528$	−6.39026			−0.278100
$529$	10.0565	−	30.9507i	0.437239	−	1.34568i
$530$		0			0
$531$	−13.8520	−	10.0640i	−0.601125	−	0.436743i
$532$	−11.3567			−0.492374
$533$	4.55609			0.197346
$534$	−23.9244	−	17.3821i	−1.03531	−	0.752198i
$535$		0			0
$536$	−8.27654	+	6.01326i	−0.357492	+	0.259733i
$537$	−2.50324	+	7.70417i	−0.108023	+	0.332460i
$538$	−10.2058	−	7.41497i	−0.440005	−	0.319682i
$539$	7.79579	−	23.9930i	0.335789	−	1.03345i
$540$		0			0
$541$	34.4222	−	25.0092i	1.47993	−	1.07523i	0.502347	−	0.864666i	$-0.332470\pi$
$541$	34.4222	−	25.0092i	1.47993	−	1.07523i	0.977580	−	0.210563i	$-0.0675299\pi$
$542$	−2.40409	−	7.39904i	−0.103265	−	0.317816i
$543$	0.378477	+	1.16483i	0.0162420	+	0.0499878i
$544$	8.39377	−	6.09843i	0.359880	−	0.261468i
$545$		0			0
$546$	2.93113	−	9.02108i	0.125441	−	0.386066i
$547$	8.55006	+	6.21198i	0.365574	+	0.265605i	0.755373	−	0.655295i	$-0.227456\pi$
$547$	8.55006	+	6.21198i	0.365574	+	0.265605i	−0.389799	+	0.920900i	$0.627456\pi$
$548$	−5.59412	+	17.2169i	−0.238969	+	0.735470i
$549$	22.7141	−	16.5027i	0.969412	−	0.704319i
$550$		0			0
$551$	−1.71383	−	1.24517i	−0.0730116	−	0.0530460i
$552$	62.7349			2.67018
$553$	36.4003			1.54790
$554$	13.6833	+	9.94147i	0.581346	+	0.422372i
$555$		0			0
$556$	−1.36889	+	4.21301i	−0.0580539	+	0.178671i
$557$	23.2668			0.985845			0.492923	−	0.870073i	$-0.335929\pi$
$557$	23.2668			0.985845			0.492923	+	0.870073i	$0.335929\pi$
$558$	25.1541	+	11.0862i	1.06486	+	0.469315i
$559$	3.27917			0.138694
$560$		0			0
$561$	2.85103	+	8.77456i	0.120371	+	0.370462i
$562$	−10.6345	−	7.72643i	−0.448590	−	0.325920i
$563$	−4.65782			−0.196304			−0.0981519	−	0.995171i	$-0.531293\pi$
$563$	−4.65782			−0.196304			−0.0981519	+	0.995171i	$0.531293\pi$
$564$	−7.70869			−0.324594
$565$		0			0
$566$	−4.95331	+	3.59879i	−0.208203	+	0.151269i
$567$	7.67470	−	5.57600i	0.322307	−	0.234170i
$568$	−1.98293	+	6.10283i	−0.0832018	+	0.256069i
$569$	4.77950	+	3.47251i	0.200367	+	0.145575i	0.683445	−	0.730002i	$-0.260481\pi$
$569$	4.77950	+	3.47251i	0.200367	+	0.145575i	−0.483078	+	0.875578i	$0.660481\pi$
$570$		0			0
$571$	14.4553	+	44.4889i	0.604936	+	1.86180i	0.497229	+	0.867620i	$0.334351\pi$
$571$	14.4553	+	44.4889i	0.604936	+	1.86180i	0.107708	+	0.994183i	$0.465649\pi$
$572$	−0.595556	+	0.432696i	−0.0249014	+	0.0180919i
$573$	−20.0978	−	61.8545i	−0.839596	−	2.58401i
$574$	11.9867	+	36.8912i	0.500315	+	1.53981i
$575$		0			0
$576$	11.2788	+	34.7125i	0.469949	+	1.44636i
$577$	−5.40567	+	16.6370i	−0.225041	+	0.692605i	0.773246	+	0.634106i	$0.218632\pi$
$577$	−5.40567	+	16.6370i	−0.225041	+	0.692605i	−0.998287	+	0.0584996i	$0.981368\pi$
$578$	−9.84940	−	7.15601i	−0.409681	−	0.297651i
$579$	16.4827	−	50.7285i	0.684998	−	2.10821i
$580$		0			0
$581$	−35.1373	+	25.5287i	−1.45774	+	1.05911i
$582$	41.5396	+	30.1802i	1.72187	+	1.25101i
$583$	1.87481			0.0776466
$584$	−33.6619			−1.39294
$585$		0			0
$586$	5.54903	+	17.0781i	0.229228	+	0.705492i
$587$	10.3838	−	31.9580i	0.428584	−	1.31905i	−0.470936	−	0.882167i	$-0.656084\pi$
$587$	10.3838	−	31.9580i	0.428584	−	1.31905i	0.899520	−	0.436879i	$-0.143916\pi$
$588$	−41.0169			−1.69151
$589$	7.68964	+	13.2039i	0.316846	+	0.544058i
$590$		0			0
$591$	−9.32171	+	28.6893i	−0.383444	+	1.18012i
$592$	−4.05734	−	12.4872i	−0.166756	−	0.513221i
$593$	18.9442	+	13.7638i	0.777946	+	0.565211i	0.904362	−	0.426767i	$-0.140347\pi$
$593$	18.9442	+	13.7638i	0.777946	+	0.565211i	−0.126416	+	0.991977i	$0.540347\pi$
$594$	−6.48922			−0.266256
$595$		0			0
$596$	−1.05330	−	0.765268i	−0.0431449	−	0.0313466i
$597$	−23.0110	+	16.7184i	−0.941776	+	0.684240i
$598$	−4.15704	+	3.02027i	−0.169994	+	0.123508i
$599$	1.12006	−	3.44720i	0.0457645	−	0.140849i	−0.925563	−	0.378593i	$-0.876408\pi$
$599$	1.12006	−	3.44720i	0.0457645	−	0.140849i	0.971328	+	0.237744i	$0.0764080\pi$
$600$		0			0
$601$	−8.53432	+	26.2659i	−0.348122	+	1.07141i	0.611769	+	0.791036i	$0.290458\pi$
$601$	−8.53432	+	26.2659i	−0.348122	+	1.07141i	−0.959891	+	0.280373i	$0.909542\pi$
$602$	8.62721	+	26.5518i	0.351619	+	1.08217i
$603$	−12.3223	+	8.95269i	−0.501804	+	0.364582i
$604$	2.19451	+	6.75402i	0.0892935	+	0.274817i
$605$		0			0
$606$	−8.40784	+	6.10865i	−0.341545	+	0.248147i
$607$	8.43114	+	25.9484i	0.342209	+	1.05321i	0.963061	+	0.269284i	$0.0867870\pi$
$607$	8.43114	+	25.9484i	0.342209	+	1.05321i	−0.620851	+	0.783928i	$0.713213\pi$
$608$	−3.66639	+	11.2840i	−0.148692	+	0.457626i
$609$	−8.59154	−	6.24212i	−0.348147	−	0.252943i
$610$		0			0
$611$	1.74618	−	1.26867i	0.0706428	−	0.0513250i
$612$	7.31892	−	5.31750i	0.295850	−	0.214947i
$613$	37.2047	+	27.0308i	1.50268	+	1.09176i	0.969297	+	0.245892i	$0.0790809\pi$
$613$	37.2047	+	27.0308i	1.50268	+	1.09176i	0.533387	+	0.845872i	$0.320919\pi$
$614$	−1.15567			−0.0466392
$615$		0			0
$616$	−17.3332	−	12.5933i	−0.698375	−	0.507399i
$617$	−5.04636	−	15.5311i	−0.203159	−	0.625259i	−0.999784	−	0.0207851i	$-0.993383\pi$
$617$	−5.04636	−	15.5311i	−0.203159	−	0.625259i	0.796625	−	0.604474i	$-0.206617\pi$
$618$	−7.57241	+	23.3055i	−0.304607	+	0.937484i
$619$	7.49401			0.301210			0.150605	−	0.988594i	$-0.451878\pi$
$619$	7.49401			0.301210			0.150605	+	0.988594i	$0.451878\pi$
$620$		0			0
$621$	31.9325			1.28141
$622$	6.70096	−	20.6234i	0.268684	−	0.826925i
$623$	−15.3574	−	47.2653i	−0.615283	−	1.89365i
$624$	−2.35348	−	1.70990i	−0.0942147	−	0.0684510i
$625$		0			0
$626$	−20.8843			−0.834705
$627$	−8.53559	−	6.20147i	−0.340879	−	0.247663i
$628$	5.62901	−	4.08972i	0.224622	−	0.163197i
$629$	−15.3362	+	11.1424i	−0.611493	+	0.444276i
$630$		0			0
$631$	−3.09596	−	2.24935i	−0.123248	−	0.0895452i	0.524453	−	0.851439i	$-0.324270\pi$
$631$	−3.09596	−	2.24935i	−0.123248	−	0.0895452i	−0.647702	+	0.761894i	$0.724270\pi$
$632$	6.88238	−	21.1818i	0.273766	−	0.842566i
$633$	−12.5984	−	38.7739i	−0.500742	−	1.54112i
$634$	−20.4981	+	14.8928i	−0.814085	+	0.591468i
$635$		0			0
$636$	−0.941941	−	2.89900i	−0.0373504	−	0.114953i
$637$	9.29117	−	6.75043i	0.368129	−	0.267462i
$638$	−0.361268	−	1.11187i	−0.0143027	−	0.0440193i
$639$	−2.95223	+	9.08604i	−0.116789	+	0.359438i
$640$		0			0
$641$	8.53249	−	26.2603i	0.337013	−	1.03722i	−0.628709	−	0.777641i	$-0.716416\pi$
$641$	8.53249	−	26.2603i	0.337013	−	1.03722i	0.965722	−	0.259579i	$-0.0835837\pi$
$642$	14.3057	−	10.3937i	0.564600	−	0.410206i
$643$	−25.2916	+	18.3754i	−0.997401	+	0.724655i	−0.961529	−	0.274702i	$-0.911421\pi$
$643$	−25.2916	+	18.3754i	−0.997401	+	0.724655i	−0.0358720	+	0.999356i	$0.511421\pi$
$644$	24.9510	+	18.1279i	0.983205	+	0.714341i
$645$		0			0
$646$	−7.13304			−0.280646
$647$	26.6173	+	19.3386i	1.04644	+	0.760280i	0.971531	−	0.236911i	$-0.0761349\pi$
$647$	26.6173	+	19.3386i	1.04644	+	0.760280i	0.0749042	+	0.997191i	$0.476135\pi$
$648$	−1.79365	−	5.52028i	−0.0704612	−	0.216857i
$649$	1.62307	−	4.99530i	0.0637112	−	0.196083i
$650$		0			0
$651$	38.5487	+	66.1921i	1.51084	+	2.59427i
$652$	2.44283			0.0956686
$653$	−5.98202	+	18.4108i	−0.234095	+	0.720469i	0.763146	+	0.646227i	$0.223654\pi$
$653$	−5.98202	+	18.4108i	−0.234095	+	0.720469i	−0.997240	+	0.0742426i	$0.976346\pi$
$654$	10.2496	+	31.5451i	0.400792	+	1.23351i
$655$		0			0
$656$	11.8965			0.464479
$657$	−50.1167			−1.95524
$658$	14.8666	+	10.8012i	0.579562	+	0.421076i
$659$	2.78409	−	2.02276i	0.108453	−	0.0787957i	−0.532237	−	0.846595i	$-0.678648\pi$
$659$	2.78409	−	2.02276i	0.108453	−	0.0787957i	0.640690	+	0.767800i	$0.278648\pi$
$660$		0			0
$661$	−5.48729	+	16.8881i	−0.213431	+	0.656873i	0.785830	+	0.618442i	$0.212236\pi$
$661$	−5.48729	+	16.8881i	−0.213431	+	0.656873i	−0.999261	+	0.0384307i	$0.987764\pi$
$662$	−18.5794	−	13.4987i	−0.722109	−	0.524643i
$663$	−1.29789	+	3.99448i	−0.0504057	+	0.155133i
$664$	8.21190	+	25.2736i	0.318684	+	0.980807i
$665$		0			0
$666$	−12.0513	−	37.0902i	−0.466979	−	1.43722i
$667$	1.77775	+	5.47135i	0.0688347	+	0.211852i
$668$	7.00601	−	5.09017i	0.271071	−	0.196944i
$669$	−11.4531	−	35.2490i	−0.442803	−	1.36281i
$670$		0			0
$671$	6.96781	+	5.06241i	0.268989	+	0.195432i
$672$	−18.3798	+	56.5673i	−0.709018	+	2.18213i
$673$	−12.5248	+	9.09980i	−0.482795	+	0.350771i	−0.802407	−	0.596777i	$-0.796448\pi$
$673$	−12.5248	+	9.09980i	−0.482795	+	0.350771i	0.319611	+	0.947549i	$0.396448\pi$
$674$	11.2062	−	8.14180i	0.431648	−	0.313610i
$675$		0			0
$676$	10.4155			0.400595
$677$	−26.4473			−1.01645			−0.508227	−	0.861223i	$-0.669699\pi$
$677$	−26.4473			−1.01645			−0.508227	+	0.861223i	$0.669699\pi$
$678$	−29.9177	−	21.7365i	−1.14898	−	0.834786i
$679$	26.6648	+	82.0659i	1.02330	+	3.14940i
$680$		0			0
$681$	60.5575			2.32057
$682$	−0.849890	+	8.38957i	−0.0325440	+	0.321253i
$683$	−35.7929			−1.36958			−0.684789	−	0.728742i	$-0.740106\pi$
$683$	−35.7929			−1.36958			−0.684789	+	0.728742i	$0.740106\pi$
$684$	−3.19690	+	9.83903i	−0.122236	+	0.376205i
$685$		0			0
$686$	48.4105	+	35.1723i	1.84832	+	1.34289i
$687$	−11.7672			−0.448947
$688$	8.56227			0.326434
$689$	0.690477	+	0.501661i	0.0263051	+	0.0191118i
$690$		0			0
$691$	−36.9543	+	26.8488i	−1.40581	+	1.02138i	−0.411891	+	0.911233i	$0.635132\pi$
$691$	−36.9543	+	26.8488i	−1.40581	+	1.02138i	−0.993916	+	0.110145i	$0.964868\pi$
$692$	−1.08962	+	3.35351i	−0.0414211	+	0.127481i
$693$	−25.8061	−	18.7492i	−0.980293	−	0.712224i
$694$	11.4765	−	35.3210i	0.435642	−	1.34077i
$695$		0			0
$696$	−5.25681	+	3.81930i	−0.199259	+	0.144770i
$697$	−5.30763	−	16.3352i	−0.201041	−	0.618741i
$698$	−0.349104	−	1.07443i	−0.0132138	−	0.0406678i
$699$	−36.7882	+	26.7282i	−1.39146	+	1.01095i
$700$		0			0
$701$	−3.29087	+	10.1283i	−0.124295	+	0.382539i	−0.993772	−	0.111433i	$-0.964456\pi$
$701$	−3.29087	+	10.1283i	−0.124295	+	0.382539i	0.869477	+	0.493973i	$0.164456\pi$
$702$	−2.38993	−	1.73638i	−0.0902020	−	0.0655356i
$703$	6.69883	−	20.6169i	0.252651	−	0.777580i
$704$	−9.05814	+	6.58112i	−0.341391	+	0.248035i
$705$		0			0
$706$	2.57953	+	1.87414i	0.0970820	+	0.0705342i
$707$	−17.4654			−0.656855
$708$	−8.53965			−0.320940
$709$	−0.118571	−	0.0861468i	−0.00445303	−	0.00323531i	0.585557	−	0.810632i	$-0.300876\pi$
$709$	−0.118571	−	0.0861468i	−0.00445303	−	0.00323531i	−0.590010	+	0.807396i	$0.700876\pi$
$710$		0			0
$711$	10.2467	−	31.5360i	0.384279	−	1.18269i
$712$	−30.4080			−1.13959
$713$	4.18219	−	41.2839i	0.156624	−	1.54609i
$714$	−35.7584			−1.33822
$715$		0			0
$716$	0.752962	+	2.31738i	0.0281395	+	0.0866046i
$717$	−33.2982	−	24.1925i	−1.24354	−	0.903487i
$718$	−4.16549			−0.155455
$719$	−28.0309			−1.04538			−0.522688	−	0.852524i	$-0.675071\pi$
$719$	−28.0309			−1.04538			−0.522688	+	0.852524i	$0.675071\pi$
$720$		0			0
$721$	−33.3167	+	24.2060i	−1.24078	+	0.901478i
$722$	−10.0490	+	7.30102i	−0.373985	+	0.271716i
$723$	−10.9924	+	33.8310i	−0.408810	+	1.25819i
$724$	0.298048	+	0.216545i	0.0110769	+	0.00804782i
$725$		0			0
$726$	8.32228	+	25.6134i	0.308869	+	0.950601i
$727$	−27.9552	+	20.3106i	−1.03680	+	0.753280i	−0.969659	−	0.244463i	$-0.921388\pi$
$727$	−27.9552	+	20.3106i	−1.03680	+	0.753280i	−0.0671425	+	0.997743i	$0.521388\pi$
$728$	−3.01397	−	9.27603i	−0.111705	−	0.343793i
$729$	−13.5908	−	41.8282i	−0.503363	−	1.54919i
$730$		0			0
$731$	−3.82008	−	11.7570i	−0.141291	−	0.434848i
$732$	4.32718	−	13.3177i	0.159937	−	0.492237i
$733$	13.9267	+	10.1184i	0.514396	+	0.373730i	0.814488	−	0.580180i	$-0.197018\pi$
$733$	13.9267	+	10.1184i	0.514396	+	0.373730i	−0.300093	+	0.953910i	$0.597018\pi$
$734$	1.84506	−	5.67851i	0.0681024	−	0.209597i
$735$		0			0
$736$	26.0671	−	18.9388i	0.960845	−	0.698094i
$737$	−3.78002	−	2.74634i	−0.139239	−	0.101163i
$738$	35.3355			1.30072
$739$	31.0347			1.14163			0.570816	−	0.821078i	$-0.306627\pi$
$739$	31.0347			1.14163			0.570816	+	0.821078i	$0.306627\pi$
$740$		0			0
$741$	−1.48420	−	4.56791i	−0.0545235	−	0.167806i
$742$	−2.24542	+	6.91070i	−0.0824320	+	0.253700i
$743$	31.9364			1.17163			0.585817	−	0.810443i	$-0.300774\pi$
$743$	31.9364			1.17163			0.585817	+	0.810443i	$0.300774\pi$
$744$	45.8066	−	9.91669i	1.67935	−	0.363564i
$745$		0			0
$746$	0.178266	−	0.548647i	0.00652679	−	0.0200874i
$747$	12.2261	+	37.6280i	0.447329	+	1.37674i
$748$	2.24516	+	1.63121i	0.0820914	+	0.0596429i
$749$	29.7169			1.08583
$750$		0			0
$751$	4.73561	+	3.44062i	0.172805	+	0.125550i	0.670826	−	0.741615i	$-0.265940\pi$
$751$	4.73561	+	3.44062i	0.172805	+	0.125550i	−0.498021	+	0.867165i	$0.665940\pi$
$752$	4.55946	−	3.31264i	0.166266	−	0.120800i
$753$	31.9632	−	23.2226i	1.16480	−	0.846279i
$754$	0.164462	−	0.506161i	0.00598934	−	0.0184333i
$755$		0			0
$756$	−5.47913	+	16.8630i	−0.199274	+	0.613303i
$757$	−11.8344	−	36.4227i	−0.430130	−	1.32380i	−0.897996	−	0.440004i	$-0.854977\pi$
$757$	−11.8344	−	36.4227i	−0.430130	−	1.32380i	0.467866	−	0.883800i	$-0.345023\pi$
$758$	−6.44475	+	4.68239i	−0.234084	+	0.170072i
$759$	8.85394	+	27.2496i	0.321378	+	0.989099i
$760$		0			0
$761$	6.46626	−	4.69801i	0.234402	−	0.170303i	−0.464384	−	0.885634i	$-0.653724\pi$
$761$	6.46626	−	4.69801i	0.234402	−	0.170303i	0.698786	+	0.715331i	$0.253724\pi$
$762$	9.75459	+	30.0216i	0.353372	+	1.08757i
$763$	−17.2251	+	53.0133i	−0.623589	+	1.91921i
$764$	−15.8268	−	11.4989i	−0.572595	−	0.416015i
$765$		0			0
$766$	−3.56482	+	2.59000i	−0.128802	+	0.0935804i
$767$	1.93441	−	1.40543i	0.0698474	−	0.0507471i
$768$	35.5568	+	25.8335i	1.28304	+	0.932186i
$769$	4.92944			0.177760			0.0888800	−	0.996042i	$-0.471671\pi$
$769$	4.92944			0.177760			0.0888800	+	0.996042i	$0.471671\pi$
$770$		0			0
$771$	−44.1096	−	32.0475i	−1.58857	−	1.15416i
$772$	−4.95792	−	15.2589i	−0.178440	−	0.549180i
$773$	−13.0969	+	40.3080i	−0.471062	+	1.44978i	0.380135	+	0.924931i	$0.375878\pi$
$773$	−13.0969	+	40.3080i	−0.471062	+	1.44978i	−0.851196	+	0.524848i	$0.824122\pi$
$774$	25.4321			0.914139
$775$		0			0
$776$	52.7968			1.89530
$777$	33.5817	−	103.354i	1.20474	−	3.70779i
$778$	11.5393	+	35.5143i	0.413704	+	1.27325i
$779$	15.8903	+	11.5450i	0.569331	+	0.413643i
$780$		0			0
$781$	−2.93069			−0.104868
$782$	15.6715	+	11.3860i	0.560412	+	0.407163i
$783$	−2.67575	+	1.94405i	−0.0956235	+	0.0694746i
$784$	24.2603	−	17.6261i	0.866438	−	0.629504i
$785$		0			0
$786$	−9.33628	−	6.78321i	−0.333014	−	0.241949i
$787$	−11.3831	+	35.0337i	−0.405765	+	1.24882i	0.514489	+	0.857497i	$0.327982\pi$
$787$	−11.3831	+	35.0337i	−0.405765	+	1.24882i	−0.920255	+	0.391320i	$0.872018\pi$
$788$	2.80393	+	8.62960i	0.0998858	+	0.307417i
$789$	0.181577	−	0.131923i	0.00646431	−	0.00469660i
$790$		0			0
$791$	−19.2046	−	59.1058i	−0.682838	−	2.10156i
$792$	−15.7897	+	11.4719i	−0.561062	+	0.407636i
$793$	1.21159	+	3.72889i	0.0430248	+	0.132417i
$794$	−0.631635	+	1.94397i	−0.0224159	+	0.0689890i
$795$		0			0
$796$	−2.64381	+	8.13682i	−0.0937075	+	0.288402i
$797$	27.4325	−	19.9309i	0.971710	−	0.705989i	0.0158697	−	0.999874i	$-0.494948\pi$
$797$	27.4325	−	19.9309i	0.971710	−	0.705989i	0.955841	+	0.293885i	$0.0949483\pi$
$798$	33.0821	−	24.0355i	1.17109	−	0.850848i
$799$	−6.58285	−	4.78272i	−0.232885	−	0.169201i
$800$		0			0
$801$	−45.2722			−1.59961
$802$	17.6211	+	12.8025i	0.622223	+	0.452071i
$803$	−4.75079	−	14.6214i	−0.167652	−	0.515980i
$804$	−2.34749	+	7.22482i	−0.0827895	+	0.254800i
$805$		0			0
$806$	−2.55789	+	2.86240i	−0.0900977	+	0.100824i
$807$	−32.0223			−1.12724
$808$	−3.30227	+	10.1633i	−0.116174	+	0.357545i
$809$	−14.0661	−	43.2912i	−0.494539	−	1.52204i	−0.817673	−	0.575683i	$-0.804736\pi$
$809$	−14.0661	−	43.2912i	−0.494539	−	1.52204i	0.323134	−	0.946353i	$-0.395264\pi$
$810$		0			0
$811$	−50.5430			−1.77480			−0.887402	−	0.460997i	$-0.847492\pi$
$811$	−50.5430			−1.77480			−0.887402	+	0.460997i	$0.847492\pi$
$812$	−3.19437			−0.112100
$813$	−15.9768	−	11.6078i	−0.560329	−	0.407103i
$814$	9.67858	−	7.03190i	0.339234	−	0.246468i
$815$		0			0
$816$	−3.38892	+	10.4300i	−0.118636	+	0.365124i
$817$	11.4368	+	8.30932i	0.400123	+	0.290706i
$818$	3.97144	−	12.2228i	0.138858	−	0.427362i
$819$	−4.48727	−	13.8104i	−0.156798	−	0.482574i
$820$		0			0
$821$	−6.25705	−	19.2572i	−0.218372	−	0.672081i	−0.998897	−	0.0469561i	$-0.985048\pi$
$821$	−6.25705	−	19.2572i	−0.218372	−	0.672081i	0.780525	−	0.625125i	$-0.214952\pi$
$822$	−20.1426	−	61.9925i	−0.702553	−	2.16224i
$823$	20.5894	−	14.9590i	0.717700	−	0.521440i	−0.167948	−	0.985796i	$-0.553714\pi$
$823$	20.5894	−	14.9590i	0.717700	−	0.521440i	0.885649	+	0.464356i	$0.153714\pi$
$824$	7.78642	+	23.9641i	0.271253	+	0.834830i
$825$		0			0
$826$	16.4692	+	11.9656i	0.573036	+	0.416335i
$827$	6.87427	−	21.1568i	0.239042	−	0.735695i	−0.757518	−	0.652815i	$-0.773588\pi$
$827$	6.87427	−	21.1568i	0.239042	−	0.735695i	0.996559	−	0.0828805i	$-0.0264120\pi$
$828$	22.7291	−	16.5136i	0.789890	−	0.573889i
$829$	−11.9991	+	8.71789i	−0.416747	+	0.302785i	−0.776328	−	0.630329i	$-0.782920\pi$
$829$	−11.9991	+	8.71789i	−0.416747	+	0.302785i	0.359580	+	0.933114i	$0.382920\pi$
$830$		0			0
$831$	42.9333			1.48934
$832$	−5.09701			−0.176707
$833$	−35.0264	−	25.4482i	−1.21359	−	0.881728i
$834$	−4.92892	−	15.1697i	−0.170675	−	0.525283i
$835$		0			0
$836$	−3.17357			−0.109760
$837$	23.3158	−	5.04766i	0.805914	−	0.174473i
$838$	−15.9809			−0.552052
$839$	−9.12565	+	28.0859i	−0.315052	+	0.969632i	0.660680	+	0.750667i	$0.270268\pi$
$839$	−9.12565	+	28.0859i	−0.315052	+	0.969632i	−0.975733	+	0.218964i	$0.929732\pi$
$840$		0			0
$841$	22.9794	+	16.6955i	0.792394	+	0.575708i
$842$	10.9897			0.378729
$843$	−33.3674			−1.14923
$844$	−9.92115	−	7.20814i	−0.341500	−	0.248114i
$845$		0			0
$846$	13.5428	−	9.83939i	0.465610	−	0.338285i
$847$	−13.9860	+	43.0446i	−0.480566	+	1.47903i
$848$	1.80291	+	1.30989i	0.0619122	+	0.0449819i
$849$	−4.80267	+	14.7811i	−0.164827	+	0.507286i
$850$		0			0
$851$	−47.6269	+	34.6030i	−1.63263	+	1.18617i
$852$	1.47244	+	4.53169i	0.0504449	+	0.155253i
$853$	−6.23811	−	19.1989i	−0.213589	−	0.657359i	−0.999251	−	0.0387029i	$-0.987677\pi$
$853$	−6.23811	−	19.1989i	−0.213589	−	0.657359i	0.785662	−	0.618656i	$-0.212323\pi$
$854$	−27.0057	+	19.6208i	−0.924115	+	0.671409i
$855$		0			0
$856$	5.61871	−	17.2926i	0.192044	−	0.591050i
$857$	21.6920	+	15.7602i	0.740984	+	0.538357i	0.893019	−	0.450019i	$-0.148583\pi$
$857$	21.6920	+	15.7602i	0.740984	+	0.538357i	−0.152035	+	0.988375i	$0.548583\pi$
$858$	0.819088	−	2.52089i	0.0279632	−	0.0860619i
$859$	37.3251	−	27.1183i	1.27352	−	0.925263i	0.274179	−	0.961679i	$-0.411594\pi$
$859$	37.3251	−	27.1183i	1.27352	−	0.925263i	0.999337	+	0.0364157i	$0.0115941\pi$
$860$		0			0
$861$	79.6593	+	57.8759i	2.71478	+	1.97240i
$862$	−26.7123			−0.909825
$863$	−9.35901			−0.318585			−0.159292	−	0.987231i	$-0.550921\pi$
$863$	−9.35901			−0.318585			−0.159292	+	0.987231i	$0.550921\pi$
$864$	14.9862	+	10.8881i	0.509841	+	0.370421i
$865$		0			0
$866$	−5.31327	+	16.3526i	−0.180552	+	0.555682i
$867$	−30.9039			−1.04955
$868$	21.0837	+	9.29223i	0.715629	+	0.315399i
$869$	10.1719			0.345057
$870$		0			0
$871$	−0.657284	−	2.02291i	−0.0222712	−	0.0685438i
$872$	27.5923	+	20.0469i	0.934392	+	0.678875i
$873$	78.6052			2.66038
$874$	−22.1518			−0.749297
$875$		0			0
$876$	−20.2221	+	14.6922i	−0.683241	+	0.496404i
$877$	−35.6378	+	25.8923i	−1.20340	+	0.874322i	−0.994615	−	0.103639i	$-0.966951\pi$
$877$	−35.6378	+	25.8923i	−1.20340	+	0.874322i	−0.208787	+	0.977961i	$0.566951\pi$
$878$	0.551083	−	1.69606i	0.0185981	−	0.0572392i
$879$	36.8769	+	26.7926i	1.24383	+	0.903692i
$880$		0			0
$881$	3.08166	+	9.48436i	0.103824	+	0.319536i	0.989453	−	0.144857i	$-0.0462723\pi$
$881$	3.08166	+	9.48436i	0.103824	+	0.319536i	−0.885629	+	0.464394i	$0.846272\pi$
$882$	72.0592	−	52.3540i	2.42636	−	1.76285i
$883$	7.72270	+	23.7680i	0.259890	+	0.799858i	0.992827	+	0.119562i	$0.0381489\pi$
$883$	7.72270	+	23.7680i	0.259890	+	0.799858i	−0.732937	+	0.680296i	$0.761851\pi$
$884$	0.390398	+	1.20152i	0.0131305	+	0.0404115i
$885$		0			0
$886$	−6.03281	−	18.5671i	−0.202676	−	0.623773i
$887$	−2.54103	+	7.82050i	−0.0853196	+	0.262587i	−0.984610	−	0.174765i	$-0.944083\pi$
$887$	−2.54103	+	7.82050i	−0.0853196	+	0.262587i	0.899291	+	0.437352i	$0.144083\pi$
$888$	−53.7934	−	39.0832i	−1.80519	−	1.31154i
$889$	−16.3931	+	50.4528i	−0.549808	+	1.69213i
$890$		0			0
$891$	2.14466	−	1.55818i	0.0718487	−	0.0522011i
$892$	−9.01924	−	6.55286i	−0.301987	−	0.219406i
$893$	9.30494			0.311378
$894$	4.68790			0.156787
$895$		0			0
$896$	−0.0390842	−	0.120289i	−0.00130571	−	0.00401857i
$897$	−4.03062	+	12.4050i	−0.134578	+	0.414190i
$898$	−5.25327			−0.175304
$899$	2.16291	+	3.71395i	0.0721372	+	0.123867i
$900$		0			0
$901$	0.994259	−	3.06002i	0.0331236	−	0.101944i
$902$	3.34962	+	10.3091i	0.111530	+	0.343254i
$903$	57.3334	+	41.6551i	1.90794	+	1.38620i
$904$	−38.0255			−1.26471
$905$		0			0
$906$	−20.6870	−	15.0300i	−0.687279	−	0.499337i
$907$	13.5543	−	9.84777i	0.450063	−	0.326990i	−0.339558	−	0.940585i	$-0.610277\pi$
$907$	13.5543	−	9.84777i	0.450063	−	0.326990i	0.789621	+	0.613595i	$0.210277\pi$
$908$	14.7366	−	10.7068i	0.489051	−	0.355316i
$909$	−4.91650	+	15.1314i	−0.163070	+	0.501878i
$910$		0			0
$911$	5.47419	−	16.8478i	0.181368	−	0.558193i	−0.818499	−	0.574508i	$-0.805193\pi$
$911$	5.47419	−	16.8478i	0.181368	−	0.558193i	0.999867	+	0.0163147i	$0.00519337\pi$
$912$	−3.87542	−	11.9273i	−0.128328	−	0.394953i
$913$	−9.81893	+	7.13387i	−0.324959	+	0.236097i
$914$	−1.37489	−	4.23147i	−0.0454773	−	0.139965i
$915$		0			0
$916$	−2.86353	+	2.08048i	−0.0946138	+	0.0687410i
$917$	−5.99310	−	18.4449i	−0.197909	−	0.609103i
$918$	−3.44140	+	10.5915i	−0.113583	+	0.349573i
$919$	0.480867	+	0.349370i	0.0158623	+	0.0115247i	0.595688	−	0.803216i	$-0.296879\pi$
$919$	0.480867	+	0.349370i	0.0158623	+	0.0115247i	−0.579826	+	0.814740i	$0.696879\pi$
$920$		0			0
$921$	−2.37331	+	1.72431i	−0.0782033	+	0.0568180i
$922$	20.3648	−	14.7959i	0.670678	−	0.487276i
$923$	−1.07935	−	0.784193i	−0.0355272	−	0.0258120i
$924$	−15.9093			−0.523377
$925$		0			0
$926$	26.9678	+	19.5933i	0.886218	+	0.643875i
$927$	11.5926	+	35.6784i	0.380751	+	1.17183i
$928$	−1.03127	+	3.17392i	−0.0338531	+	0.104189i
$929$	−51.7518			−1.69792			−0.848960	−	0.528457i	$-0.822771\pi$
$929$	−51.7518			−1.69792			−0.848960	+	0.528457i	$0.822771\pi$
$930$		0			0
$931$	49.5103			1.62263
$932$	−4.22674	+	13.0086i	−0.138451	+	0.426109i
$933$	−17.0098	−	52.3508i	−0.556876	−	1.71389i
$934$	−14.6354	−	10.6332i	−0.478884	−	0.347930i
$935$		0			0
$936$	−8.88486			−0.290411
$937$	−14.3059	−	10.3939i	−0.467354	−	0.339552i	0.329055	−	0.944311i	$-0.393270\pi$
$937$	−14.3059	−	10.3939i	−0.467354	−	0.339552i	−0.796409	+	0.604758i	$0.793270\pi$
$938$	14.6505	−	10.6442i	0.478356	−	0.347546i
$939$	−42.8884	+	31.1603i	−1.39961	+	1.01688i
$940$		0			0
$941$	18.4855	+	13.4305i	0.602610	+	0.437822i	0.846804	−	0.531904i	$-0.178523\pi$
$941$	18.4855	+	13.4305i	0.602610	+	0.437822i	−0.244194	+	0.969726i	$0.578523\pi$
$942$	−7.74178	+	23.8267i	−0.252241	+	0.776317i
$943$	−16.4830	−	50.7295i	−0.536760	−	1.65198i
$944$	5.05095	−	3.66973i	0.164394	−	0.119440i
$945$		0			0
$946$	2.41083	+	7.41977i	0.0783828	+	0.241238i
$947$	23.6674	−	17.1954i	0.769086	−	0.558774i	−0.132597	−	0.991170i	$-0.542332\pi$
$947$	23.6674	−	17.1954i	0.769086	−	0.558774i	0.901684	+	0.432396i	$0.142332\pi$
$948$	−5.11055	−	15.7287i	−0.165983	−	0.510843i
$949$	2.16272	−	6.65618i	0.0702050	−	0.216069i
$950$		0			0
$951$	−19.8747	+	61.1681i	−0.644482	+	1.98351i
$952$	−29.7467	+	21.6123i	−0.964097	+	0.700458i
$953$	−22.5372	+	16.3742i	−0.730052	+	0.530414i	−0.889580	−	0.456780i	$-0.849003\pi$
$953$	−22.5372	+	16.3742i	−0.730052	+	0.530414i	0.159528	+	0.987193i	$0.449003\pi$
$954$	5.35511	+	3.89071i	0.173378	+	0.125966i
$955$		0			0
$956$	−12.3804			−0.400410
$957$	−2.40086	−	1.74433i	−0.0776088	−	0.0563861i
$958$	1.51661	+	4.66766i	0.0489995	+	0.150805i
$959$	33.8507	−	104.182i	1.09310	−	3.36420i
$960$		0			0
$961$	−3.47219	−	30.8049i	−0.112006	−	0.993708i
$962$	5.44614			0.175591
$963$	8.36528	−	25.7457i	0.269567	−	0.829643i
$964$	3.30645	+	10.1762i	0.106494	+	0.327754i
$965$		0			0
$966$	−111.049			−3.57293
$967$	30.6100			0.984352			0.492176	−	0.870496i	$-0.336202\pi$
$967$	30.6100			0.984352			0.492176	+	0.870496i	$0.336202\pi$
$968$	22.4038	+	16.2773i	0.720085	+	0.523173i
$969$	−14.6485	+	10.6428i	−0.470579	+	0.341896i
$970$		0			0
$971$	13.3831	−	41.1888i	0.429483	−	1.32181i	−0.469153	−	0.883117i	$-0.655441\pi$
$971$	13.3831	−	41.1888i	0.429483	−	1.32181i	0.898636	−	0.438695i	$-0.144559\pi$
$972$	−12.0866	−	8.78145i	−0.387679	−	0.281665i
$973$	8.28332	−	25.4934i	0.265551	−	0.817282i
$974$	5.01979	+	15.4493i	0.160845	+	0.495029i
$975$		0			0
$976$	3.16359	+	9.73654i	0.101264	+	0.311659i
$977$	5.11780	+	15.7510i	0.163733	+	0.503918i	0.998941	−	0.0460166i	$-0.0146527\pi$
$977$	5.11780	+	15.7510i	0.163733	+	0.503918i	−0.835208	+	0.549934i	$0.814653\pi$
$978$	−7.11598	+	5.17006i	−0.227544	+	0.165320i
$979$	−4.29156	−	13.2081i	−0.137159	−	0.422131i
$980$		0			0
$981$	41.0800	+	29.8464i	1.31158	+	0.952922i
$982$	−13.4633	+	41.4358i	−0.429632	+	1.32227i
$983$	−19.6770	+	14.2962i	−0.627598	+	0.455977i	−0.855567	−	0.517692i	$-0.826792\pi$
$983$	−19.6770	+	14.2962i	−0.627598	+	0.455977i	0.227969	+	0.973668i	$0.426792\pi$
$984$	48.7403	−	35.4119i	1.55378	−	1.12889i
$985$		0			0
$986$	−2.00636			−0.0638954
$987$	46.6463			1.48477
$988$	−1.16880	−	0.849182i	−0.0371844	−	0.0270161i
$989$	−11.8633	−	36.5116i	−0.377233	−	1.16100i
$990$		0			0
$991$	25.7566			0.818186			0.409093	−	0.912493i	$-0.365845\pi$
$991$	25.7566			0.818186			0.409093	+	0.912493i	$0.365845\pi$
$992$	16.0394	−	17.9489i	0.509252	−	0.569877i
$993$	−58.2956			−1.84996
$994$	3.51003	−	10.8028i	0.111331	−	0.342643i
$995$		0			0
$996$	15.9643	+	11.5987i	0.505847	+	0.367519i
$997$	27.2866			0.864175			0.432087	−	0.901832i	$-0.357777\pi$
$997$	27.2866			0.864175			0.432087	+	0.901832i	$0.357777\pi$
$998$	44.2086			1.39940
$999$	−27.3812	−	19.8936i	−0.866302	−	0.629405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.k.h.101.5		56
5.2	odd	4		155.2.n.a.39.5	yes	56
5.3	odd	4		155.2.n.a.39.10	yes	56
5.4	even	2	inner	775.2.k.h.101.10		56
31.4	even	5	inner	775.2.k.h.376.5		56
155.4	even	10	inner	775.2.k.h.376.10		56
155.97	odd	20		155.2.n.a.4.10	yes	56
155.128	odd	20		155.2.n.a.4.5	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.n.a.4.5	✓	56	155.128	odd	20
155.2.n.a.4.10	yes	56	155.97	odd	20
155.2.n.a.39.5	yes	56	5.2	odd	4
155.2.n.a.39.10	yes	56	5.3	odd	4
775.2.k.h.101.5		56	1.1	even	1	trivial
775.2.k.h.101.10		56	5.4	even	2	inner
775.2.k.h.376.5		56	31.4	even	5	inner
775.2.k.h.376.10		56	155.4	even	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.334686 + 1.03006i) q^{2} +(0.849570 + 2.61471i) q^{3} +(0.669031 + 0.486079i) q^{4} -2.97764 q^{6} +(-4.04839 - 2.94133i) q^{7} +(-2.47704 + 1.79968i) q^{8} +(-3.68788 + 2.67940i) q^{9} +(-1.13130 - 0.821939i) q^{11} +(-0.702567 + 2.16228i) q^{12} +(-0.196715 - 0.605427i) q^{13} +(4.38467 - 3.18565i) q^{14} +(-0.513645 - 1.58084i) q^{16} +(-1.94151 + 1.41059i) q^{17} +(-1.52566 - 4.69549i) q^{18} +(0.848048 - 2.61002i) q^{19} +(4.25132 - 13.0842i) q^{21} +(1.22527 - 0.890214i) q^{22} +(-6.02940 + 4.38062i) q^{23} +(-6.81005 - 4.94779i) q^{24} +0.689462 q^{26} +(-3.46636 - 2.51846i) q^{27} +(-1.27878 - 3.93568i) q^{28} +(0.238536 - 0.734139i) q^{29} +(-3.70997 + 4.15164i) q^{31} -4.32332 q^{32} +(1.18801 - 3.65632i) q^{33} +(-0.803191 - 2.47197i) q^{34} -3.76971 q^{36} +7.89911 q^{37} +(2.40464 + 1.74708i) q^{38} +(1.41589 - 1.02871i) q^{39} +(-2.21167 + 6.80681i) q^{41} +(12.0546 + 8.75821i) q^{42} +(-1.59181 + 4.89908i) q^{43} +(-0.357348 - 1.09980i) q^{44} +(-2.49433 - 7.67676i) q^{46} +(1.04775 + 3.22464i) q^{47} +(3.69705 - 2.68606i) q^{48} +(5.57493 + 17.1579i) q^{49} +(-5.33772 - 3.87808i) q^{51} +(0.162677 - 0.500668i) q^{52} +(-1.08466 + 0.788052i) q^{53} +(3.75430 - 2.72766i) q^{54} +15.3215 q^{56} +7.54493 q^{57} +(0.676370 + 0.491412i) q^{58} +(1.16069 + 3.57224i) q^{59} -6.15910 q^{61} +(-3.03475 - 5.21098i) q^{62} +22.8110 q^{63} +(2.47425 - 7.61494i) q^{64} +(3.36861 + 2.44744i) q^{66} +3.34130 q^{67} -1.98459 q^{68} +(-16.5764 - 12.0435i) q^{69} +(1.69553 - 1.23188i) q^{71} +(4.31298 - 13.2740i) q^{72} +(8.89448 + 6.46222i) q^{73} +(-2.64372 + 8.13653i) q^{74} +(1.83605 - 1.33397i) q^{76} +(2.16236 + 6.65506i) q^{77} +(0.585747 + 1.80274i) q^{78} +(-5.88488 + 4.27562i) q^{79} +(-0.585816 + 1.80296i) q^{81} +(-6.27119 - 4.55629i) q^{82} +(2.68206 - 8.25452i) q^{83} +(9.20423 - 6.68727i) q^{84} +(-4.51358 - 3.27931i) q^{86} +2.12221 q^{87} +4.28151 q^{88} +(8.03470 + 5.83755i) q^{89} +(-0.984379 + 3.02961i) q^{91} -6.16318 q^{92} +(-14.0072 - 6.17339i) q^{93} -3.67223 q^{94} +(-3.67297 - 11.3042i) q^{96} +(-13.9505 - 10.1356i) q^{97} -19.5394 q^{98} +6.37441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{4} - 4 q^{6} - 8 q^{9} - 14 q^{11} + 16 q^{14} - 22 q^{16} + 2 q^{19} - 38 q^{21} + 30 q^{24} + 12 q^{26} - 20 q^{29} + 26 q^{31} + 2 q^{34} - 44 q^{36} + 18 q^{39} - 20 q^{41} - 62 q^{44} - 70 q^{46}+ \cdots + 52 q^{99}+O(q^{100}) \) 56 * q - 2 * q^4 - 4 * q^6 - 8 * q^9 - 14 * q^11 + 16 * q^14 - 22 * q^16 + 2 * q^19 - 38 * q^21 + 30 * q^24 + 12 * q^26 - 20 * q^29 + 26 * q^31 + 2 * q^34 - 44 * q^36 + 18 * q^39 - 20 * q^41 - 62 * q^44 - 70 * q^46 + 42 * q^49 + 10 * q^51 + 26 * q^54 + 208 * q^56 + 50 * q^59 + 56 * q^61 - 12 * q^64 + 60 * q^66 - 34 * q^69 - 8 * q^71 + 84 * q^74 - 20 * q^76 - 122 * q^79 + 42 * q^81 + 40 * q^84 + 78 * q^86 + 28 * q^89 - 20 * q^91 - 160 * q^94 - 70 * q^96 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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