LMFDB - Embedded newform 378.2.v.b.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8, 12]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			67.5
Character	$\chi$	$=$	378.67
Dual form			378.2.v.b.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-0.402772 + 1.68457i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.366960 + 2.08113i) q^{5} +(0.774279 + 1.54935i) q^{6} +(1.84638 + 1.89496i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.67555 - 1.35699i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.402772 + 1.68457i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.366960 + 2.08113i) q^{5} +(0.774279 + 1.54935i) q^{6} +(1.84638 + 1.89496i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.67555 - 1.35699i) q^{9} +(1.05662 + 1.83012i) q^{10} +(-0.394893 - 2.23955i) q^{11} +(1.58904 + 0.689175i) q^{12} +(-0.774677 + 4.39341i) q^{13} +(2.63247 + 0.264792i) q^{14} +(-3.35801 - 1.45639i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.550487 + 0.953472i) q^{17} +(-2.92185 + 0.680293i) q^{18} +(-3.27751 + 5.67682i) q^{19} +(1.98579 + 0.722770i) q^{20} +(-3.93586 + 2.34712i) q^{21} +(-1.74206 - 1.46176i) q^{22} +(4.32780 + 3.63145i) q^{23} +(1.66027 - 0.493474i) q^{24} +(0.502011 + 0.182717i) q^{25} +(2.23059 + 3.86350i) q^{26} +(3.36359 - 3.96059i) q^{27} +(2.18679 - 1.48928i) q^{28} +(-0.886000 - 5.02476i) q^{29} +(-3.50854 + 1.04283i) q^{30} +(1.23018 - 6.97669i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(3.93173 + 0.236802i) q^{33} +(1.03458 + 0.376555i) q^{34} +(-4.62121 + 3.14719i) q^{35} +(-1.80098 + 2.39926i) q^{36} +11.0055 q^{37} +(1.13827 + 6.45544i) q^{38} +(-7.08899 - 3.07454i) q^{39} +(1.98579 - 0.722770i) q^{40} +(1.28738 - 7.30109i) q^{41} +(-1.50634 + 4.32792i) q^{42} +(-4.90452 + 4.11538i) q^{43} -2.27410 q^{44} +(3.80590 - 5.07021i) q^{45} +5.64954 q^{46} +(-1.25382 - 7.11077i) q^{47} +(0.954638 - 1.44522i) q^{48} +(-0.181745 + 6.99764i) q^{49} +(0.502011 - 0.182717i) q^{50} +(-1.82791 + 0.543303i) q^{51} +(4.19214 + 1.52582i) q^{52} +(2.35202 - 4.07382i) q^{53} +(0.0308378 - 5.19606i) q^{54} +4.80571 q^{55} +(0.717892 - 2.54649i) q^{56} +(-8.24290 - 7.80766i) q^{57} +(-3.90857 - 3.27968i) q^{58} +(-3.22478 + 1.17372i) q^{59} +(-2.01738 + 3.05410i) q^{60} +(-0.248045 - 1.40673i) q^{61} +(-3.54216 - 6.13519i) q^{62} +(-2.36864 - 7.57559i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-8.85899 - 3.22441i) q^{65} +(3.16409 - 2.34586i) q^{66} +(-5.47003 - 4.58990i) q^{67} +(1.03458 - 0.376555i) q^{68} +(-7.86055 + 5.82783i) q^{69} +(-1.51708 + 5.38135i) q^{70} +(-2.73928 + 4.74457i) q^{71} +(0.162584 + 2.99559i) q^{72} +13.0625 q^{73} +(8.43070 - 7.07419i) q^{74} +(-0.509995 + 0.772079i) q^{75} +(5.02144 + 4.21349i) q^{76} +(3.51473 - 4.88337i) q^{77} +(-7.40675 + 2.20148i) q^{78} +(4.38906 - 3.68286i) q^{79} +(1.05662 - 1.83012i) q^{80} +(5.31713 + 7.26141i) q^{81} +(-3.70686 - 6.42047i) q^{82} +(-0.173835 - 0.985869i) q^{83} +(1.62801 + 4.28364i) q^{84} +(-2.18631 + 0.795751i) q^{85} +(-1.11176 + 6.30513i) q^{86} +(8.82141 + 0.531301i) q^{87} +(-1.74206 + 1.46176i) q^{88} +(4.05995 - 7.03203i) q^{89} +(-0.343578 - 6.33039i) q^{90} +(-9.75568 + 6.64393i) q^{91} +(4.32780 - 3.63145i) q^{92} +(11.2572 + 4.88233i) q^{93} +(-5.53120 - 4.64123i) q^{94} +(-10.6115 - 8.90410i) q^{95} +(-0.197675 - 1.72073i) q^{96} +(0.607697 - 0.509919i) q^{97} +(4.35877 + 5.47733i) q^{98} +(-1.98250 + 6.52789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	$ 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−0.402772	+	1.68457i	−0.232540	+	0.972587i
$3$	−0.402772	+	1.68457i	−0.232540	+	0.972587i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.366960	+	2.08113i	−0.164109	+	0.930711i	0.785869	+	0.618394i	$0.212216\pi$
$5$	−0.366960	+	2.08113i	−0.164109	+	0.930711i	−0.949978	+	0.312317i	$0.898895\pi$
$6$	0.774279	+	1.54935i	0.316098	+	0.632520i
$7$	1.84638	+	1.89496i	0.697867	+	0.716227i
$7$	1.84638	+	1.89496i	0.697867	+	0.716227i
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.67555	−	1.35699i	−0.891850	−	0.452331i
$10$	1.05662	+	1.83012i	0.334132	+	0.578734i
$11$	−0.394893	−	2.23955i	−0.119065	−	0.675249i	−0.984657	−	0.174500i	$-0.944169\pi$
$11$	−0.394893	−	2.23955i	−0.119065	−	0.675249i	0.865592	−	0.500749i	$-0.166942\pi$
$12$	1.58904	+	0.689175i	0.458715	+	0.198948i
$13$	−0.774677	+	4.39341i	−0.214857	+	1.21851i	0.666298	+	0.745685i	$0.267878\pi$
$13$	−0.774677	+	4.39341i	−0.214857	+	1.21851i	−0.881155	+	0.472827i	$0.843233\pi$
$14$	2.63247	+	0.264792i	0.703557	+	0.0707686i
$15$	−3.35801	−	1.45639i	−0.867035	−	0.376038i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.550487	+	0.953472i	0.133513	+	0.231251i	0.925028	−	0.379898i	$-0.124041\pi$
$17$	0.550487	+	0.953472i	0.133513	+	0.231251i	−0.791516	+	0.611149i	$0.790708\pi$
$18$	−2.92185	+	0.680293i	−0.688686	+	0.160347i
$19$	−3.27751	+	5.67682i	−0.751913	+	1.30235i	0.194982	+	0.980807i	$0.437535\pi$
$19$	−3.27751	+	5.67682i	−0.751913	+	1.30235i	−0.946895	+	0.321544i	$0.895798\pi$
$20$	1.98579	+	0.722770i	0.444037	+	0.161616i
$21$	−3.93586	+	2.34712i	−0.858876	+	0.512184i
$22$	−1.74206	−	1.46176i	−0.371408	−	0.311649i
$23$	4.32780	+	3.63145i	0.902408	+	0.757210i	0.970660	−	0.240458i	$-0.0772976\pi$
$23$	4.32780	+	3.63145i	0.902408	+	0.757210i	−0.0682515	+	0.997668i	$0.521742\pi$
$24$	1.66027	−	0.493474i	0.338900	−	0.100730i
$25$	0.502011	+	0.182717i	0.100402	+	0.0365434i
$26$	2.23059	+	3.86350i	0.437455	+	0.757695i
$27$	3.36359	−	3.96059i	0.647323	−	0.762216i
$28$	2.18679	−	1.48928i	0.413265	−	0.281447i
$29$	−0.886000	−	5.02476i	−0.164526	−	0.933074i	−0.949552	−	0.313610i	$-0.898461\pi$
$29$	−0.886000	−	5.02476i	−0.164526	−	0.933074i	0.785026	−	0.619463i	$-0.212650\pi$
$30$	−3.50854	+	1.04283i	−0.640568	+	0.190394i
$31$	1.23018	−	6.97669i	0.220946	−	1.25305i	−0.649338	−	0.760500i	$-0.724954\pi$
$31$	1.23018	−	6.97669i	0.220946	−	1.25305i	0.870284	−	0.492550i	$-0.163935\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	3.93173	+	0.236802i	0.684426	+	0.0412220i
$34$	1.03458	+	0.376555i	0.177429	+	0.0645787i
$35$	−4.62121	+	3.14719i	−0.781127	+	0.531973i
$36$	−1.80098	+	2.39926i	−0.300164	+	0.399877i
$37$	11.0055			1.80929			0.904646	−	0.426164i	$-0.140135\pi$
$37$	11.0055			1.80929			0.904646	+	0.426164i	$0.140135\pi$
$38$	1.13827	+	6.45544i	0.184651	+	1.04721i
$39$	−7.08899	−	3.07454i	−1.13515	−	0.492320i
$40$	1.98579	−	0.722770i	0.313982	−	0.114280i
$41$	1.28738	−	7.30109i	0.201055	−	1.14024i	−0.702474	−	0.711710i	$-0.747921\pi$
$41$	1.28738	−	7.30109i	0.201055	−	1.14024i	0.903528	−	0.428528i	$-0.140968\pi$
$42$	−1.50634	+	4.32792i	−0.232434	+	0.667813i
$43$	−4.90452	+	4.11538i	−0.747932	+	0.627589i	−0.934955	−	0.354766i	$-0.884560\pi$
$43$	−4.90452	+	4.11538i	−0.747932	+	0.627589i	0.187023	+	0.982356i	$0.440116\pi$
$44$	−2.27410			−0.342833
$45$	3.80590	−	5.07021i	0.567351	−	0.755822i
$46$	5.64954			0.832979
$47$	−1.25382	−	7.11077i	−0.182889	−	1.03721i	−0.928638	−	0.370987i	$-0.879020\pi$
$47$	−1.25382	−	7.11077i	−0.182889	−	1.03721i	0.745750	−	0.666226i	$-0.232092\pi$
$48$	0.954638	−	1.44522i	0.137790	−	0.208600i
$49$	−0.181745	+	6.99764i	−0.0259635	+	0.999663i
$50$	0.502011	−	0.182717i	0.0709950	−	0.0258401i
$51$	−1.82791	+	0.543303i	−0.255959	+	0.0760776i
$52$	4.19214	+	1.52582i	0.581346	+	0.211592i
$53$	2.35202	−	4.07382i	0.323075	−	0.559582i	−0.658046	−	0.752978i	$-0.728617\pi$
$53$	2.35202	−	4.07382i	0.323075	−	0.559582i	0.981121	+	0.193396i	$0.0619501\pi$
$54$	0.0308378	−	5.19606i	0.00419649	−	0.707094i
$55$	4.80571			0.648001
$56$	0.717892	−	2.54649i	0.0959324	−	0.340290i
$57$	−8.24290	−	7.80766i	−1.09180	−	1.03415i
$58$	−3.90857	−	3.27968i	−0.513220	−	0.430643i
$59$	−3.22478	+	1.17372i	−0.419831	+	0.152806i	−0.543293	−	0.839543i	$-0.682823\pi$
$59$	−3.22478	+	1.17372i	−0.419831	+	0.152806i	0.123462	+	0.992349i	$0.460600\pi$
$60$	−2.01738	+	3.05410i	−0.260442	+	0.394282i
$61$	−0.248045	−	1.40673i	−0.0317589	−	0.180113i	0.964802	−	0.262977i	$-0.0847044\pi$
$61$	−0.248045	−	1.40673i	−0.0317589	−	0.180113i	−0.996561	+	0.0828639i	$0.973593\pi$
$62$	−3.54216	−	6.13519i	−0.449854	−	0.779171i
$63$	−2.36864	−	7.57559i	−0.298420	−	0.954434i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−8.85899	−	3.22441i	−1.09882	−	0.399939i
$66$	3.16409	−	2.34586i	0.389473	−	0.288756i
$67$	−5.47003	−	4.58990i	−0.668271	−	0.560746i	0.244282	−	0.969704i	$-0.421448\pi$
$67$	−5.47003	−	4.58990i	−0.668271	−	0.560746i	−0.912553	+	0.408958i	$0.865892\pi$
$68$	1.03458	−	0.376555i	0.125461	−	0.0456640i
$69$	−7.86055	+	5.82783i	−0.946299	+	0.701588i
$70$	−1.51708	+	5.38135i	−0.181325	+	0.643194i
$71$	−2.73928	+	4.74457i	−0.325093	+	0.563077i	−0.981531	−	0.191302i	$-0.938729\pi$
$71$	−2.73928	+	4.74457i	−0.325093	+	0.563077i	0.656438	+	0.754380i	$0.272062\pi$
$72$	0.162584	+	2.99559i	0.0191607	+	0.353034i
$73$	13.0625			1.52885			0.764427	−	0.644711i	$-0.223022\pi$
$73$	13.0625			1.52885			0.764427	+	0.644711i	$0.223022\pi$
$74$	8.43070	−	7.07419i	0.980049	−	0.822358i
$75$	−0.509995	+	0.772079i	−0.0588892	+	0.0891520i
$76$	5.02144	+	4.21349i	0.575998	+	0.483320i
$77$	3.51473	−	4.88337i	0.400541	−	0.556512i
$78$	−7.40675	+	2.20148i	−0.838650	+	0.249269i
$79$	4.38906	−	3.68286i	0.493808	−	0.414354i	−0.361581	−	0.932341i	$-0.617763\pi$
$79$	4.38906	−	3.68286i	0.493808	−	0.414354i	0.855389	+	0.517987i	$0.173318\pi$
$80$	1.05662	−	1.83012i	0.118134	−	0.204613i
$81$	5.31713	+	7.26141i	0.590793	+	0.806823i
$82$	−3.70686	−	6.42047i	−0.409354	−	0.709022i
$83$	−0.173835	−	0.985869i	−0.0190809	−	0.108213i	0.973780	−	0.227492i	$-0.0730527\pi$
$83$	−0.173835	−	0.985869i	−0.0190809	−	0.108213i	−0.992861	+	0.119279i	$0.961942\pi$
$84$	1.62801	+	4.28364i	0.177630	+	0.467384i
$85$	−2.18631	+	0.795751i	−0.237138	+	0.0863113i
$86$	−1.11176	+	6.30513i	−0.119885	+	0.679899i
$87$	8.82141	+	0.531301i	0.945754	+	0.0569614i
$88$	−1.74206	+	1.46176i	−0.185704	+	0.155824i
$89$	4.05995	−	7.03203i	0.430353	−	0.745394i	−0.566550	−	0.824027i	$-0.691722\pi$
$89$	4.05995	−	7.03203i	0.430353	−	0.745394i	0.996904	+	0.0786334i	$0.0250556\pi$
$90$	−0.343578	−	6.33039i	−0.0362163	−	0.667282i
$91$	−9.75568	+	6.64393i	−1.02267	+	0.696473i
$92$	4.32780	−	3.63145i	0.451204	−	0.378605i
$93$	11.2572	+	4.88233i	1.16732	+	0.506274i
$94$	−5.53120	−	4.64123i	−0.570500	−	0.478706i
$95$	−10.6115	−	8.90410i	−1.08872	−	0.913541i
$96$	−0.197675	−	1.72073i	−0.0201751	−	0.175622i
$97$	0.607697	−	0.509919i	0.0617023	−	0.0517744i	−0.611415	−	0.791310i	$-0.709399\pi$
$97$	0.607697	−	0.509919i	0.0617023	−	0.0517744i	0.673117	+	0.739536i	$0.264955\pi$
$98$	4.35877	+	5.47733i	0.440302	+	0.553294i
$99$	−1.98250	+	6.52789i	−0.199249	+	0.656078i
$100$	0.267114	−	0.462656i	0.0267114	−	0.0462656i
$101$	8.43701	−	7.07949i	0.839514	−	0.704436i	−0.117940	−	0.993021i	$-0.537629\pi$
$101$	8.43701	−	7.07949i	0.839514	−	0.704436i	0.957454	+	0.288585i	$0.0931847\pi$
$102$	−1.05103	+	1.59115i	−0.104068	+	0.157548i
$103$	−2.71497	+	15.3974i	−0.267514	+	1.51715i	0.494266	+	0.869310i	$0.335437\pi$
$103$	−2.71497	+	15.3974i	−0.267514	+	1.51715i	−0.761780	+	0.647836i	$0.775674\pi$
$104$	4.19214	−	1.52582i	0.411073	−	0.149618i
$105$	−3.44037	−	9.05235i	−0.335746	−	0.883419i
$106$	−0.816848	−	4.63258i	−0.0793393	−	0.449956i
$107$	5.60715	+	9.71187i	0.542063	+	0.938881i	0.998785	+	0.0492719i	$0.0156901\pi$
$107$	5.60715	+	9.71187i	0.542063	+	0.938881i	−0.456722	+	0.889610i	$0.650977\pi$
$108$	−3.31634	−	4.00024i	−0.319115	−	0.384923i
$109$	3.22127	−	5.57940i	0.308542	−	0.534410i	−0.669502	−	0.742810i	$-0.733492\pi$
$109$	3.22127	−	5.57940i	0.308542	−	0.534410i	0.978044	+	0.208400i	$0.0668257\pi$
$110$	3.68139	−	3.08905i	0.351006	−	0.294529i
$111$	−4.43270	+	18.5395i	−0.420733	+	1.75969i
$112$	−1.08692	−	2.41218i	−0.102704	−	0.227930i
$113$	−9.57952	−	8.03817i	−0.901165	−	0.756167i	0.0692526	−	0.997599i	$-0.477939\pi$
$113$	−9.57952	−	8.03817i	−0.901165	−	0.756167i	−0.970418	+	0.241432i	$0.922383\pi$
$114$	−11.3331	−	0.682576i	−1.06144	−	0.0639291i
$115$	−9.14566	+	7.67412i	−0.852837	+	0.715615i
$116$	−5.10227			−0.473734
$117$	8.03452	−	10.7036i	0.742791	−	0.989544i
$118$	−1.71587	+	2.97197i	−0.157959	+	0.273592i
$119$	−0.790381	+	2.80362i	−0.0724541	+	0.257008i
$120$	0.417735	+	3.63632i	0.0381338	+	0.331949i
$121$	5.47698	−	1.99346i	0.497907	−	0.181223i
$122$	−1.09424	−	0.918179i	−0.0990681	−	0.0831280i
$123$	11.7807	+	5.10935i	1.06223	+	0.460695i
$124$	−6.65708	−	2.42298i	−0.597823	−	0.217590i
$125$	−5.84757	+	10.1283i	−0.523022	+	0.905901i
$126$	−6.68398	−	4.28071i	−0.595456	−	0.381356i
$127$	−9.45707	−	16.3801i	−0.839179	−	1.45350i	−0.890582	−	0.454823i	$-0.849703\pi$
$127$	−9.45707	−	16.3801i	−0.839179	−	1.45350i	0.0514030	−	0.998678i	$-0.483631\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−4.95724	−	9.91956i	−0.436461	−	0.873369i
$130$	−8.85899	+	3.22441i	−0.776985	+	0.282799i
$131$	−10.9325	−	9.17349i	−0.955181	−	0.801492i	0.0249818	−	0.999688i	$-0.492047\pi$
$131$	−10.9325	−	9.17349i	−0.955181	−	0.801492i	−0.980162	+	0.198196i	$0.936492\pi$
$132$	0.915942	−	3.83088i	0.0797225	−	0.333435i
$133$	−16.8089	+	4.27082i	−1.45751	+	0.370327i
$134$	−7.14062			−0.616856
$135$	7.00821	+	8.45345i	0.603171	+	0.727557i
$136$	0.550487	−	0.953472i	0.0472039	−	0.0817595i
$137$	17.3970	+	6.33198i	1.48632	+	0.540977i	0.952479	−	0.304605i	$-0.0985246\pi$
$137$	17.3970	+	6.33198i	1.48632	+	0.540977i	0.533844	+	0.845583i	$0.320747\pi$
$138$	−2.27547	+	9.51704i	−0.193701	+	0.810144i
$139$	−0.894249	+	0.325480i	−0.0758492	+	0.0276069i	−0.379666	−	0.925124i	$-0.623961\pi$
$139$	−0.894249	+	0.325480i	−0.0758492	+	0.0276069i	0.303817	+	0.952730i	$0.401739\pi$
$140$	2.29691	+	5.09751i	0.194125	+	0.430818i
$141$	12.4836	+	0.751869i	1.05131	+	0.0633188i
$142$	0.951342	+	5.39533i	0.0798349	+	0.452766i
$143$	10.1452			0.848382
$144$	2.05008	+	2.19025i	0.170840	+	0.182521i
$145$	10.7823			0.895422
$146$	10.0065	−	8.39643i	0.828142	−	0.694894i
$147$	−11.7148	−	3.12461i	−0.966221	−	0.257714i
$148$	1.91108	−	10.8383i	0.157090	−	0.890902i
$149$	−16.7859	+	6.10955i	−1.37515	+	0.500514i	−0.920705	−	0.390260i	$-0.872385\pi$
$149$	−16.7859	+	6.10955i	−1.37515	+	0.500514i	−0.454446	+	0.890774i	$0.650163\pi$
$150$	0.105604	+	0.919265i	0.00862251	+	0.0750577i
$151$	1.08833	+	6.17225i	0.0885673	+	0.502290i	0.996530	+	0.0832385i	$0.0265263\pi$
$151$	1.08833	+	6.17225i	0.0885673	+	0.502290i	−0.907962	+	0.419052i	$0.862363\pi$
$152$	6.55502			0.531682
$153$	−0.179000	−	3.29807i	−0.0144713	−	0.266633i
$154$	−0.446529	−	6.00010i	−0.0359823	−	0.483502i
$155$	14.0680	+	5.12033i	1.12997	+	0.411275i
$156$	−4.25882	+	6.44740i	−0.340978	+	0.516205i
$157$	−6.48739	+	2.36122i	−0.517750	+	0.188446i	−0.587660	−	0.809108i	$-0.699951\pi$
$157$	−6.48739	+	2.36122i	−0.517750	+	0.188446i	0.0699103	+	0.997553i	$0.477729\pi$
$158$	0.994920	−	5.64247i	0.0791516	−	0.448891i
$159$	5.91531	+	5.60296i	0.469114	+	0.444344i
$160$	−0.366960	−	2.08113i	−0.0290107	−	0.164528i
$161$	1.10931	+	14.9061i	0.0874260	+	1.17476i
$162$	8.74071	+	2.14477i	0.686735	+	0.168509i
$163$	7.72077	+	13.3728i	0.604737	+	1.04744i	0.992093	+	0.125505i	$0.0400551\pi$
$163$	7.72077	+	13.3728i	0.604737	+	1.04744i	−0.387356	+	0.921930i	$0.626612\pi$
$164$	−6.96662	−	2.53564i	−0.544001	−	0.198000i
$165$	−1.93560	+	8.09555i	−0.150686	+	0.630238i
$166$	−0.766870	−	0.643480i	−0.0595206	−	0.0499437i
$167$	−0.125142	−	0.105007i	−0.00968378	−	0.00812566i	0.637933	−	0.770092i	$-0.279790\pi$
$167$	−0.125142	−	0.105007i	−0.00968378	−	0.00812566i	−0.647617	+	0.761966i	$0.724234\pi$
$168$	4.00060	+	2.23499i	0.308653	+	0.172434i
$169$	−6.48592	−	2.36068i	−0.498917	−	0.181591i
$170$	−1.16331	+	2.01491i	−0.0892218	+	0.154537i
$171$	16.4725	−	10.7410i	1.25969	−	0.821388i
$172$	3.20120	+	5.54463i	0.244089	+	0.422774i
$173$	−15.0954	−	5.49426i	−1.14768	−	0.417721i	−0.302998	−	0.952991i	$-0.597988\pi$
$173$	−15.0954	−	5.49426i	−1.14768	−	0.417721i	−0.844681	+	0.535270i	$0.820210\pi$
$174$	7.09910	−	5.26329i	0.538182	−	0.399009i
$175$	0.580662	+	1.28866i	0.0438940	+	0.0974132i
$176$	−0.394893	+	2.23955i	−0.0297662	+	0.168812i
$177$	−0.678370	−	5.90511i	−0.0509894	−	0.443855i
$178$	−1.41000	−	7.99653i	−0.105684	−	0.599365i
$179$	−2.62566	−	4.54777i	−0.196251	−	0.339916i	0.751059	−	0.660235i	$-0.229543\pi$
$179$	−2.62566	−	4.54777i	−0.196251	−	0.339916i	−0.947310	+	0.320319i	$0.896210\pi$
$180$	−4.33230	−	4.62852i	−0.322910	−	0.344989i
$181$	8.10196	+	14.0330i	0.602214	+	1.04307i	0.992485	+	0.122365i	$0.0390480\pi$
$181$	8.10196	+	14.0330i	0.602214	+	1.04307i	−0.390271	+	0.920700i	$0.627619\pi$
$182$	−3.20265	+	11.3604i	−0.237396	+	0.842087i
$183$	2.46964	+	0.148743i	0.182561	+	0.0109954i
$184$	0.981032	−	5.56371i	0.0723226	−	0.410162i
$185$	−4.03857	+	22.9039i	−0.296922	+	1.68393i
$186$	11.7618	−	3.49593i	0.862420	−	0.256334i
$187$	1.91796	−	1.60936i	0.140255	−	0.117688i
$188$	−7.22047			−0.526607
$189$	13.7156	−	0.938905i	0.997665	−	0.0682953i
$190$	−13.8523			−1.00495
$191$	3.60864	−	3.02801i	0.261112	−	0.219099i	−0.502828	−	0.864387i	$-0.667707\pi$
$191$	3.60864	−	3.02801i	0.261112	−	0.219099i	0.763940	+	0.645288i	$0.223263\pi$
$192$	−1.25749	−	1.19110i	−0.0907518	−	0.0859599i
$193$	1.17376	−	6.65672i	0.0844890	−	0.479161i	−0.912977	−	0.408012i	$-0.866222\pi$
$193$	1.17376	−	6.65672i	0.0844890	−	0.479161i	0.997466	−	0.0711492i	$-0.0226666\pi$
$194$	0.137754	−	0.781241i	0.00989015	−	0.0560898i
$195$	8.99989	−	13.6249i	0.644496	−	0.975699i
$196$	6.85977	+	1.39411i	0.489984	+	0.0995794i
$197$	5.01390	+	8.68433i	0.357226	+	0.618733i	0.987496	−	0.157643i	$-0.0503894\pi$
$197$	5.01390	+	8.68433i	0.357226	+	0.618733i	−0.630271	+	0.776376i	$0.717056\pi$
$198$	2.67737	+	6.27498i	0.190272	+	0.445943i
$199$	2.07010	+	3.58551i	0.146745	+	0.254170i	0.930023	−	0.367502i	$-0.119787\pi$
$199$	2.07010	+	3.58551i	0.146745	+	0.254170i	−0.783277	+	0.621672i	$0.786454\pi$
$200$	−0.0927678	−	0.526112i	−0.00655968	−	0.0372018i
$201$	9.93518	−	7.36597i	0.700774	−	0.519555i
$202$	1.91252	−	10.8464i	0.134564	−	0.763151i
$203$	7.88581	−	10.9566i	0.553476	−	0.768999i
$204$	0.217635	+	1.89448i	0.0152375	+	0.132640i
$205$	14.7221	+	5.35841i	1.02824	+	0.374248i
$206$	7.81744	+	13.5402i	0.544667	+	0.943391i
$207$	−6.65138	−	15.5889i	−0.462303	−	1.08351i
$208$	2.23059	−	3.86350i	0.154664	−	0.267886i
$209$	14.0078	+	5.09841i	0.968938	+	0.352665i
$210$	−8.45422	−	4.72307i	−0.583396	−	0.325923i
$211$	6.04115	+	5.06913i	0.415890	+	0.348973i	0.826597	−	0.562794i	$-0.190274\pi$
$211$	6.04115	+	5.06913i	0.415890	+	0.348973i	−0.410707	+	0.911767i	$0.634718\pi$
$212$	−3.60351	−	3.02370i	−0.247490	−	0.207669i
$213$	−6.88926	−	6.52549i	−0.472044	−	0.447119i
$214$	10.5380	+	3.83552i	0.720362	+	0.262190i
$215$	−6.76489	−	11.7171i	−0.461361	−	0.799102i
$216$	−5.11177	−	0.932656i	−0.347812	−	0.0634592i
$217$	15.4919	−	10.5505i	1.05166	−	0.716214i
$218$	−1.11874	−	6.34466i	−0.0757703	−	0.429715i
$219$	−5.26122	+	22.0047i	−0.355520	+	1.48694i
$220$	0.834502	−	4.73270i	0.0562621	−	0.319078i
$221$	−4.61544	+	1.67988i	−0.310468	+	0.113001i
$222$	8.52133	+	17.0514i	0.571914	+	1.14441i
$223$	−26.9328	−	9.80273i	−1.80355	−	0.656440i	−0.997951	−	0.0639823i	$-0.979620\pi$
$223$	−26.9328	−	9.80273i	−1.80355	−	0.656440i	−0.805602	−	0.592457i	$-0.798158\pi$
$224$	−2.38315	−	1.14918i	−0.159231	−	0.0767828i
$225$	−1.09521	−	1.17009i	−0.0730139	−	0.0780063i
$226$	−12.5052			−0.831832
$227$	2.74928	+	15.5919i	0.182476	+	1.03487i	0.929155	+	0.369689i	$0.120536\pi$
$227$	2.74928	+	15.5919i	0.182476	+	1.03487i	−0.746679	+	0.665184i	$0.768353\pi$
$228$	−9.12041	+	6.76189i	−0.604014	+	0.447817i
$229$	10.9231	−	3.97569i	0.721820	−	0.262721i	0.0451219	−	0.998981i	$-0.485632\pi$
$229$	10.9231	−	3.97569i	0.721820	−	0.262721i	0.676698	+	0.736260i	$0.263410\pi$
$230$	−2.07315	+	11.7574i	−0.136700	+	0.775262i
$231$	6.81074	+	7.88769i	0.448114	+	0.518972i
$232$	−3.90857	+	3.27968i	−0.256610	+	0.215321i
$233$	1.71150			0.112124			0.0560619	−	0.998427i	$-0.482146\pi$
$233$	1.71150			0.112124			0.0560619	+	0.998427i	$0.482146\pi$
$234$	−0.725316	−	13.3639i	−0.0474154	−	0.873625i
$235$	15.2586			0.995359
$236$	0.595915	+	3.37960i	0.0387908	+	0.219994i
$237$	4.43625	+	8.87703i	0.288165	+	0.576625i
$238$	1.19667	+	2.65575i	0.0775685	+	0.172147i
$239$	1.80505	−	0.656984i	0.116759	−	0.0424968i	−0.282980	−	0.959126i	$-0.591323\pi$
$239$	1.80505	−	0.656984i	0.116759	−	0.0424968i	0.399739	+	0.916629i	$0.369101\pi$
$240$	2.65738	+	2.51707i	0.171533	+	0.162476i
$241$	−14.4568	−	5.26183i	−0.931242	−	0.338944i	−0.168540	−	0.985695i	$-0.553905\pi$
$241$	−14.4568	−	5.26183i	−0.931242	−	0.338944i	−0.762702	+	0.646750i	$0.776128\pi$
$242$	2.91424	−	5.04761i	0.187334	−	0.324473i
$243$	−14.3739	+	6.03239i	−0.922089	+	0.386978i
$244$	−1.42843			−0.0914460
$245$	−14.4963	−	2.94609i	−0.926136	−	0.188219i
$246$	12.3087	−	3.65848i	0.784777	−	0.233256i
$247$	−22.4016	−	18.7971i	−1.42538	−	1.19603i
$248$	−6.65708	+	2.42298i	−0.422725	+	0.153859i
$249$	1.73078	+	0.104242i	0.109684	+	0.00660610i
$250$	2.03084	+	11.5175i	0.128442	+	0.728428i
$251$	8.80203	+	15.2456i	0.555579	+	0.962292i	0.997858	+	0.0654140i	$0.0208368\pi$
$251$	8.80203	+	15.2456i	0.555579	+	0.962292i	−0.442279	+	0.896878i	$0.645830\pi$
$252$	−7.87181	+	1.01717i	−0.495877	+	0.0640755i
$253$	6.42380	−	11.1263i	0.403861	−	0.699507i
$254$	−17.7735	−	6.46901i	−1.11521	−	0.405902i
$255$	−0.459915	−	4.00349i	−0.0288010	−	0.250708i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	4.30276	−	1.56608i	0.268399	−	0.0976892i	−0.204315	−	0.978905i	$-0.565497\pi$
$257$	4.30276	−	1.56608i	0.268399	−	0.0976892i	0.472714	+	0.881216i	$0.343274\pi$
$258$	−10.1736	−	4.41237i	−0.633383	−	0.274702i
$259$	20.3203	+	20.8550i	1.26265	+	1.29586i
$260$	−4.71377	+	8.16449i	−0.292336	+	0.506340i
$261$	−4.44803	+	14.6463i	−0.275326	+	0.906582i
$262$	−14.2714			−0.881691
$263$	−16.3333	+	13.7053i	−1.00716	+	0.845105i	−0.987960	−	0.154711i	$-0.950555\pi$
$263$	−16.3333	+	13.7053i	−1.00716	+	0.845105i	−0.0191967	+	0.999816i	$0.506111\pi$
$264$	−1.76079	−	3.52338i	−0.108369	−	0.216849i
$265$	7.61506	+	6.38980i	0.467790	+	0.392522i
$266$	−10.1311	+	14.0762i	−0.621178	+	0.863066i
$267$	10.2107	+	9.67156i	0.624886	+	0.591890i
$268$	−5.47003	+	4.58990i	−0.334135	+	0.280373i
$269$	−11.0845	+	19.1990i	−0.675836	+	1.17058i	0.300387	+	0.953817i	$0.402884\pi$
$269$	−11.0845	+	19.1990i	−0.675836	+	1.17058i	−0.976224	+	0.216766i	$0.930449\pi$
$270$	10.8024	+	1.97092i	0.657412	+	0.119947i
$271$	−10.0283	−	17.3695i	−0.609175	−	1.05512i	−0.991377	−	0.131044i	$-0.958167\pi$
$271$	−10.0283	−	17.3695i	−0.609175	−	1.05512i	0.382201	−	0.924079i	$-0.375166\pi$
$272$	−0.191182	−	1.08425i	−0.0115921	−	0.0657422i
$273$	−7.26285	−	19.1101i	−0.439568	−	1.15660i
$274$	17.3970	−	6.33198i	1.05099	−	0.382529i
$275$	0.210963	−	1.19643i	0.0127216	−	0.0721475i
$276$	4.37432	+	8.75312i	0.263303	+	0.526876i
$277$	−4.50657	+	3.78146i	−0.270774	+	0.227206i	−0.768056	−	0.640383i	$-0.778776\pi$
$277$	−4.50657	+	3.78146i	−0.270774	+	0.227206i	0.497282	+	0.867589i	$0.334331\pi$
$278$	−0.475820	+	0.824144i	−0.0285378	+	0.0494289i
$279$	−12.7587	+	16.9971i	−0.763845	+	1.01759i
$280$	5.03615	+	2.42849i	0.300968	+	0.145130i
$281$	−23.2653	+	19.5219i	−1.38789	+	1.16458i	−0.421706	+	0.906733i	$0.638569\pi$
$281$	−23.2653	+	19.5219i	−1.38789	+	1.16458i	−0.966186	+	0.257847i	$0.916987\pi$
$282$	10.0463	−	7.44834i	0.598247	−	0.443542i
$283$	0.119444	+	0.100226i	0.00710023	+	0.00595780i	0.646331	−	0.763057i	$-0.276303\pi$
$283$	0.119444	+	0.100226i	0.00710023	+	0.00595780i	−0.639231	+	0.769015i	$0.720747\pi$
$284$	4.19682	+	3.52155i	0.249036	+	0.208966i
$285$	19.2736	−	14.2895i	1.14167	−	0.846435i
$286$	7.77165	−	6.52119i	0.459547	−	0.385606i
$287$	16.2123	−	11.0411i	0.956979	−	0.651734i
$288$	2.97831	+	0.360065i	0.175499	+	0.0212170i
$289$	7.89393	−	13.6727i	0.464349	−	0.804276i
$290$	8.25973	−	6.93073i	0.485028	−	0.406987i
$291$	0.614230	+	1.22909i	0.0360068	+	0.0720505i
$292$	2.26828	−	12.8641i	0.132741	−	0.752813i
$293$	5.17996	−	1.88535i	0.302617	−	0.110143i	−0.186249	−	0.982503i	$-0.559633\pi$
$293$	5.17996	−	1.88535i	0.302617	−	0.110143i	0.488866	+	0.872359i	$0.337411\pi$
$294$	−10.9825	+	5.13654i	−0.640514	+	0.299569i
$295$	−1.25931	−	7.14191i	−0.0733199	−	0.415818i
$296$	−5.50275	−	9.53104i	−0.319841	−	0.553980i
$297$	−10.1982	−	5.96891i	−0.591759	−	0.346351i
$298$	−8.93157	+	15.4699i	−0.517392	+	0.896149i
$299$	−19.3071	+	16.2006i	−1.11656	+	0.936904i
$300$	0.671789	+	0.636317i	0.0387858	+	0.0367378i
$301$	−16.8541	−	1.69530i	−0.971454	−	0.0977155i
$302$	4.80116	+	4.02865i	0.276275	+	0.231823i
$303$	8.52771	+	17.0642i	0.489904	+	0.980310i
$304$	5.02144	−	4.21349i	0.287999	−	0.241660i
$305$	3.01862			0.172845
$306$	−2.25708	−	2.41141i	−0.129029	−	0.137851i
$307$	−6.56559	+	11.3719i	−0.374718	+	0.649031i	−0.990285	−	0.139054i	$-0.955594\pi$
$307$	−6.56559	+	11.3719i	−0.374718	+	0.649031i	0.615567	+	0.788085i	$0.288927\pi$
$308$	−4.19885	−	4.30932i	−0.239252	−	0.245546i
$309$	−24.8444	−	10.7752i	−1.41335	−	0.612978i
$310$	14.0680	−	5.12033i	0.799008	−	0.290815i
$311$	−5.34788	−	4.48740i	−0.303250	−	0.254457i	0.478445	−	0.878117i	$-0.341200\pi$
$311$	−5.34788	−	4.48740i	−0.303250	−	0.254457i	−0.781696	+	0.623660i	$0.785645\pi$
$312$	0.881866	+	7.67651i	0.0499258	+	0.434597i
$313$	−9.27538	−	3.37596i	−0.524276	−	0.190821i	0.0663049	−	0.997799i	$-0.478879\pi$
$313$	−9.27538	−	3.37596i	−0.524276	−	0.190821i	−0.590581	+	0.806979i	$0.701101\pi$
$314$	−3.45187	+	5.97881i	−0.194800	+	0.337404i
$315$	16.6350	−	2.14952i	0.937276	−	0.121111i
$316$	−2.86476	−	4.96190i	−0.161155	−	0.279129i
$317$	−4.20287	−	23.8357i	−0.236057	−	1.33874i	−0.840377	−	0.542002i	$-0.817666\pi$
$317$	−4.20287	−	23.8357i	−0.236057	−	1.33874i	0.604320	−	0.796742i	$-0.293445\pi$
$318$	8.13290	+	0.489833i	0.456071	+	0.0274685i
$319$	−10.9033	+	3.96848i	−0.610468	+	0.222192i
$320$	−1.61883	−	1.35836i	−0.0904955	−	0.0759348i
$321$	−18.6187	+	5.53397i	−1.03920	+	0.308876i
$322$	10.4312	+	10.7056i	0.581308	+	0.596602i
$323$	−7.21691			−0.401560
$324$	8.07440	−	3.97542i	0.448578	−	0.220857i
$325$	−1.19165	+	2.06399i	−0.0661006	+	0.114490i
$326$	14.5103	+	5.28132i	0.803651	+	0.292505i
$327$	8.10146	+	7.67368i	0.448012	+	0.424355i
$328$	−6.96662	+	2.53564i	−0.384667	+	0.140007i
$329$	11.1596	−	15.5051i	0.615248	−	0.854826i
$330$	3.72096	+	7.44573i	0.204832	+	0.409874i
$331$	−4.39867	−	24.9461i	−0.241773	−	1.37116i	−0.827869	−	0.560921i	$-0.810447\pi$
$331$	−4.39867	−	24.9461i	−0.241773	−	1.37116i	0.586096	−	0.810241i	$-0.300664\pi$
$332$	−1.00108			−0.0549413
$333$	−29.4457	−	14.9344i	−1.61362	−	0.818399i
$334$	−0.163361			−0.00893873
$335$	11.5595	−	9.69955i	0.631562	−	0.529943i
$336$	4.50126	−	0.859430i	0.245564	−	0.0468858i
$337$	3.37701	−	19.1520i	0.183958	−	1.04328i	−0.743330	−	0.668925i	$-0.766755\pi$
$337$	3.37701	−	19.1520i	0.183958	−	1.04328i	0.927287	−	0.374350i	$-0.122134\pi$
$338$	−6.48592	+	2.36068i	−0.352788	+	0.128404i
$339$	17.3992	−	12.8998i	0.944996	−	0.700622i
$340$	0.404013	+	2.29127i	0.0219107	+	0.124262i
$341$	−16.1104			−0.872428
$342$	5.71450	−	18.8165i	0.309005	−	1.01748i
$343$	−13.5958	+	12.5759i	−0.734105	+	0.679036i
$344$	6.01628	+	2.18975i	0.324376	+	0.118063i
$345$	−9.24398	−	18.4974i	−0.497679	−	0.995868i
$346$	−15.0954	+	5.49426i	−0.811532	+	0.295373i
$347$	2.95191	−	16.7411i	0.158467	−	0.898711i	−0.797080	−	0.603873i	$-0.793623\pi$
$347$	2.95191	−	16.7411i	0.158467	−	0.898711i	0.955547	−	0.294838i	$-0.0952655\pi$
$348$	2.05505	−	8.59513i	0.110162	−	0.460747i
$349$	−3.12520	−	17.7239i	−0.167288	−	0.948737i	−0.946674	−	0.322193i	$-0.895580\pi$
$349$	−3.12520	−	17.7239i	−0.167288	−	0.948737i	0.779386	−	0.626544i	$-0.215531\pi$
$350$	1.27314	+	0.613925i	0.0680525	+	0.0328157i
$351$	14.7948	+	17.8458i	0.789688	+	0.952538i
$352$	1.13705	+	1.96943i	0.0606049	+	0.104971i
$353$	31.4637	+	11.4519i	1.67465	+	0.609521i	0.992561	−	0.121752i	$-0.0388513\pi$
$353$	31.4637	+	11.4519i	1.67465	+	0.609521i	0.682085	+	0.731273i	$0.261074\pi$
$354$	−4.31539	−	4.08753i	−0.229361	−	0.217250i
$355$	−8.86888	−	7.44187i	−0.470711	−	0.394974i
$356$	−6.22020	−	5.21936i	−0.329670	−	0.276626i
$357$	−4.40456	−	2.46067i	−0.233114	−	0.130233i
$358$	−4.93462	−	1.79606i	−0.260803	−	0.0949245i
$359$	9.60803	−	16.6416i	0.507092	−	0.878310i	−0.492874	−	0.870101i	$-0.664054\pi$
$359$	9.60803	−	16.6416i	0.507092	−	0.878310i	0.999966	−	0.00820914i	$-0.00261308\pi$
$360$	−6.29388	−	0.760903i	−0.331717	−	0.0401031i
$361$	−11.9842	−	20.7572i	−0.630745	−	1.09248i
$362$	15.2267	+	5.54207i	0.800298	+	0.291285i
$363$	1.15215	+	10.0293i	0.0604720	+	0.526400i
$364$	4.84894	+	10.7612i	0.254154	+	0.564039i
$365$	−4.79342	+	27.1848i	−0.250899	+	1.42292i
$366$	1.98747	−	1.47351i	0.103887	−	0.0770217i
$367$	−3.22893	−	18.3122i	−0.168549	−	0.955887i	−0.945330	−	0.326116i	$-0.894260\pi$
$367$	−3.22893	−	18.3122i	−0.168549	−	0.955887i	0.776781	−	0.629771i	$-0.216851\pi$
$368$	−2.82477	−	4.89264i	−0.147251	−	0.255047i
$369$	−13.3520	+	17.7875i	−0.695076	+	0.925978i
$370$	11.6286	+	20.1413i	0.604543	+	1.04710i
$371$	12.0625	−	3.06484i	0.626252	−	0.159119i
$372$	6.76296	−	10.2384i	0.350643	−	0.530836i
$373$	4.11853	−	23.3573i	0.213249	−	1.20940i	−0.670670	−	0.741756i	$-0.733993\pi$
$373$	4.11853	−	23.3573i	0.213249	−	1.20940i	0.883919	−	0.467640i	$-0.154896\pi$
$374$	0.434767	−	2.46569i	0.0224813	−	0.127498i
$375$	−14.7066	−	13.9300i	−0.759444	−	0.719343i
$376$	−5.53120	+	4.64123i	−0.285250	+	0.239353i
$377$	22.7622			1.17231
$378$	9.90326	−	9.53548i	0.509369	−	0.490452i
$379$	−2.81922			−0.144814			−0.0724069	−	0.997375i	$-0.523068\pi$
$379$	−2.81922			−0.144814			−0.0724069	+	0.997375i	$0.523068\pi$
$380$	−10.6115	+	8.90410i	−0.544358	+	0.456771i
$381$	31.4025	−	9.33364i	1.60880	−	0.478177i
$382$	0.818012	−	4.63918i	0.0418531	−	0.237361i
$383$	1.08220	−	6.13744i	0.0552977	−	0.313609i	−0.944595	−	0.328237i	$-0.893545\pi$
$383$	1.08220	−	6.13744i	0.0552977	−	0.313609i	0.999893	+	0.0146286i	$0.00465659\pi$
$384$	−1.72892	−	0.104130i	−0.0882285	−	0.00531387i
$385$	8.87317	+	9.10662i	0.452219	+	0.464116i
$386$	−3.37970	−	5.85382i	−0.172022	−	0.297951i
$387$	18.7068	−	4.35550i	0.950921	−	0.221403i
$388$	−0.396646	−	0.687012i	−0.0201367	−	0.0348777i
$389$	4.14974	+	23.5343i	0.210400	+	1.19324i	0.888712	+	0.458465i	$0.151601\pi$
$389$	4.14974	+	23.5343i	0.210400	+	1.19324i	−0.678312	+	0.734774i	$0.737288\pi$
$390$	−1.86359	−	16.2223i	−0.0943666	−	0.821448i
$391$	−1.08009	+	6.12550i	−0.0546225	+	0.309780i
$392$	6.15101	−	3.34142i	0.310673	−	0.168767i
$393$	19.8567	−	14.7218i	1.00164	−	0.742617i
$394$	9.42305	+	3.42971i	0.474727	+	0.172786i
$395$	6.05391	+	10.4857i	0.304605	+	0.527592i
$396$	6.08446	+	3.08594i	0.305756	+	0.155074i
$397$	−4.31954	+	7.48166i	−0.216791	+	0.375494i	−0.953825	−	0.300362i	$-0.902892\pi$
$397$	−4.31954	+	7.48166i	−0.216791	+	0.375494i	0.737034	+	0.675856i	$0.236226\pi$
$398$	3.89051	+	1.41603i	0.195014	+	0.0709792i
$399$	−0.424356	−	30.0359i	−0.0212444	−	1.50368i
$400$	−0.409243	−	0.343396i	−0.0204621	−	0.0171698i
$401$	4.32069	+	3.62549i	0.215765	+	0.181048i	0.744264	−	0.667886i	$-0.232800\pi$
$401$	4.32069	+	3.62549i	0.215765	+	0.181048i	−0.528499	+	0.848934i	$0.677245\pi$
$402$	2.87604	−	12.0289i	0.143444	−	0.599946i
$403$	29.6985	+	10.8094i	1.47939	+	0.538452i
$404$	−5.50687	−	9.53817i	−0.273977	−	0.474542i
$405$	−17.0631	+	8.40102i	−0.847874	+	0.417450i
$406$	−1.00185	−	13.4621i	−0.0497211	−	0.668113i
$407$	−4.34599	−	24.6473i	−0.215423	−	1.22172i
$408$	1.38447	+	1.31137i	0.0685414	+	0.0649223i
$409$	1.94279	−	11.0181i	0.0960647	−	0.544810i	−0.898351	−	0.439278i	$-0.855234\pi$
$409$	1.94279	−	11.0181i	0.0960647	−	0.544810i	0.994416	−	0.105532i	$-0.0336545\pi$
$410$	14.7221	−	5.35841i	0.727073	−	0.264633i
$411$	−17.6737	+	26.7561i	−0.871777	+	1.31978i
$412$	14.6920	+	5.34744i	0.723822	+	0.263450i
$413$	−8.17834	−	3.94369i	−0.402430	−	0.194056i
$414$	−15.1156	−	7.66639i	−0.742892	−	0.376782i
$415$	2.11551			0.103846
$416$	−0.774677	−	4.39341i	−0.0379816	−	0.215405i
$417$	−0.188116	−	1.63752i	−0.00921206	−	0.0801897i
$418$	14.0078	−	5.09841i	0.685142	−	0.249371i
$419$	6.33507	−	35.9280i	0.309488	−	1.75520i	−0.292098	−	0.956388i	$-0.594353\pi$
$419$	6.33507	−	35.9280i	0.309488	−	1.75520i	0.601587	−	0.798808i	$-0.294535\pi$
$420$	−9.51224	+	1.81618i	−0.464150	+	0.0886205i
$421$	7.37289	−	6.18659i	0.359333	−	0.301516i	−0.445192	−	0.895435i	$-0.646865\pi$
$421$	7.37289	−	6.18659i	0.359333	−	0.301516i	0.804525	+	0.593919i	$0.202420\pi$
$422$	7.88616			0.383892
$423$	−6.29462	+	20.7267i	−0.306055	+	1.00776i
$424$	−4.70404			−0.228449
$425$	0.102135	+	0.579236i	0.00495427	+	0.0280971i
$426$	−9.47198	−	0.570484i	−0.458919	−	0.0276400i
$427$	2.20771	−	3.06740i	0.106839	−	0.148442i
$428$	10.5380	−	3.83552i	0.509373	−	0.185397i
$429$	−4.08619	+	17.0902i	−0.197283	+	0.825125i
$430$	−12.7138	−	4.62746i	−0.613115	−	0.223156i
$431$	−10.4177	+	18.0440i	−0.501802	+	0.869147i	0.498195	+	0.867065i	$0.333996\pi$
$431$	−10.4177	+	18.0440i	−0.501802	+	0.869147i	−0.999998	+	0.00208252i	$0.999337\pi$
$432$	−4.51534	+	2.57132i	−0.217244	+	0.123713i
$433$	−5.88744			−0.282932			−0.141466	−	0.989943i	$-0.545182\pi$
$433$	−5.88744			−0.282932			−0.141466	+	0.989943i	$0.545182\pi$
$434$	5.08577	−	18.0402i	0.244125	−	0.865955i
$435$	−4.34281	+	18.1635i	−0.208222	+	0.870875i
$436$	−4.93527	−	4.14118i	−0.236357	−	0.198327i
$437$	−34.7995	+	12.6660i	−1.66469	+	0.605896i
$438$	10.1140	+	20.2385i	0.483268	+	0.967031i
$439$	1.90087	+	10.7803i	0.0907234	+	0.514518i	0.995974	+	0.0896403i	$0.0285717\pi$
$439$	1.90087	+	10.7803i	0.0907234	+	0.514518i	−0.905251	+	0.424878i	$0.860317\pi$
$440$	−2.40285	−	4.16186i	−0.114552	−	0.198409i
$441$	9.98202	−	18.4759i	0.475334	−	0.879805i
$442$	−2.45583	+	4.25361i	−0.116812	+	0.202324i
$443$	−8.97627	−	3.26710i	−0.426476	−	0.155224i	0.119860	−	0.992791i	$-0.461755\pi$
$443$	−8.97627	−	3.26710i	−0.426476	−	0.155224i	−0.546336	+	0.837566i	$0.683978\pi$
$444$	17.4881	+	7.58471i	0.829950	+	0.359955i
$445$	13.1448	+	11.0298i	0.623121	+	0.522861i
$446$	−26.9328	+	9.80273i	−1.27530	+	0.464173i
$447$	−3.53110	−	30.7377i	−0.167015	−	1.45384i
$448$	−2.56427	+	0.651534i	−0.121151	+	0.0307821i
$449$	11.1673	−	19.3423i	0.527016	−	0.912818i	−0.472488	−	0.881337i	$-0.656644\pi$
$449$	11.1673	−	19.3423i	0.527016	−	0.912818i	0.999504	−	0.0314814i	$-0.0100225\pi$
$450$	−1.59110	−	0.192357i	−0.0750052	−	0.00906780i
$451$	−16.8595			−0.793884
$452$	−9.57952	+	8.03817i	−0.450583	+	0.378084i
$453$	−10.8359	−	0.652632i	−0.509116	−	0.0306633i
$454$	12.1284	+	10.1769i	0.569213	+	0.477626i
$455$	−10.2470	−	22.7409i	−0.480385	−	1.06611i
$456$	−2.64018	+	11.0424i	−0.123638	+	0.517107i
$457$	−18.4967	+	15.5206i	−0.865239	+	0.726021i	−0.963090	−	0.269180i	$-0.913247\pi$
$457$	−18.4967	+	15.5206i	−0.865239	+	0.726021i	0.0978513	+	0.995201i	$0.468803\pi$
$458$	5.81207	−	10.0668i	0.271580	−	0.470391i
$459$	5.62792	+	1.02683i	0.262689	+	0.0479283i
$460$	5.96941	+	10.3393i	0.278325	+	0.482073i
$461$	−2.93414	−	16.6404i	−0.136657	−	0.775019i	−0.973692	−	0.227869i	$-0.926824\pi$
$461$	−2.93414	−	16.6404i	−0.136657	−	0.775019i	0.837035	−	0.547149i	$-0.184287\pi$
$462$	10.2874	+	1.66446i	0.478615	+	0.0774378i
$463$	−19.7896	+	7.20282i	−0.919701	+	0.334744i	−0.758119	−	0.652116i	$-0.773882\pi$
$463$	−19.7896	+	7.20282i	−0.919701	+	0.334744i	−0.161581	+	0.986859i	$0.551659\pi$
$464$	−0.886000	+	5.02476i	−0.0411315	+	0.233268i
$465$	−14.2917	+	21.6362i	−0.662763	+	1.00335i
$466$	1.31108	−	1.10013i	0.0607347	−	0.0509625i
$467$	−13.0994	+	22.6888i	−0.606167	+	1.04991i	0.385698	+	0.922625i	$0.373961\pi$
$467$	−13.0994	+	22.6888i	−0.606167	+	1.04991i	−0.991866	+	0.127288i	$0.959373\pi$
$468$	−9.14577	−	9.77111i	−0.422763	−	0.451670i
$469$	−1.40209	−	18.8402i	−0.0647426	−	0.869960i
$470$	11.6887	−	9.80801i	0.539161	−	0.452410i
$471$	−1.36470	−	11.8795i	−0.0628819	−	0.547378i
$472$	2.62887	+	2.20588i	0.121003	+	0.101534i
$473$	11.1534	+	9.35877i	0.512832	+	0.430317i
$474$	9.10441	+	3.94864i	0.418179	+	0.181367i
$475$	−2.68260	+	2.25097i	−0.123086	+	0.103281i
$476$	2.62378	+	1.26522i	0.120261	+	0.0579911i
$477$	−11.8211	+	7.70803i	−0.541251	+	0.352927i
$478$	0.960447	−	1.66354i	0.0439298	−	0.0760887i
$479$	−19.9626	+	16.7506i	−0.912115	+	0.765355i	−0.972520	−	0.232819i	$-0.925205\pi$
$479$	−19.9626	+	16.7506i	−0.912115	+	0.765355i	0.0604055	+	0.998174i	$0.480761\pi$
$480$	3.65361	+	0.220052i	0.166764	+	0.0100439i
$481$	−8.52570	+	48.3516i	−0.388738	+	2.20465i
$482$	−14.4568	+	5.26183i	−0.658487	+	0.239670i
$483$	−25.5571	−	4.13502i	−1.16289	−	0.188150i
$484$	−1.01211	−	5.73993i	−0.0460048	−	0.260906i
$485$	0.838208	+	1.45182i	0.0380611	+	0.0659237i
$486$	−7.13353	+	13.8605i	−0.323584	+	0.628724i
$487$	5.52175	−	9.56395i	0.250214	−	0.433384i	−0.713370	−	0.700787i	$-0.752832\pi$
$487$	5.52175	−	9.56395i	0.250214	−	0.433384i	0.963585	+	0.267403i	$0.0861655\pi$
$488$	−1.09424	+	0.918179i	−0.0495340	+	0.0415640i
$489$	−25.6371	+	7.62000i	−1.15935	+	0.344588i
$490$	−12.9985	+	7.06122i	−0.587214	+	0.318994i
$491$	5.21300	+	4.37422i	0.235259	+	0.197406i	0.752794	−	0.658256i	$-0.228706\pi$
$491$	5.21300	+	4.37422i	0.235259	+	0.197406i	−0.517535	+	0.855662i	$0.673150\pi$
$492$	7.07742	−	10.7145i	0.319075	−	0.483045i
$493$	4.30323	−	3.61084i	0.193808	−	0.162624i
$494$	−29.2432			−1.31571
$495$	−12.8579	−	6.52132i	−0.577920	−	0.293111i
$496$	−3.54216	+	6.13519i	−0.159048	+	0.275478i
$497$	−14.0485	+	3.56947i	−0.630163	+	0.160113i
$498$	1.39286	−	1.03267i	0.0624156	−	0.0462750i
$499$	32.5393	−	11.8433i	1.45666	−	0.530180i	0.512216	−	0.858857i	$-0.328825\pi$
$499$	32.5393	−	11.8433i	1.45666	−	0.530180i	0.944443	+	0.328677i	$0.106603\pi$
$500$	8.95900	+	7.51749i	0.400658	+	0.336192i
$501$	0.227295	−	0.168517i	0.0101548	−	0.00752877i
$502$	16.5424	+	6.02094i	0.738324	+	0.268728i
$503$	17.7568	−	30.7556i	0.791735	−	1.37133i	−0.133157	−	0.991095i	$-0.542511\pi$
$503$	17.7568	−	30.7556i	0.791735	−	1.37133i	0.924892	−	0.380231i	$-0.124155\pi$
$504$	−5.37633	+	5.83910i	−0.239481	+	0.260094i
$505$	11.6373	+	20.1564i	0.517854	+	0.896949i
$506$	−2.23096	−	12.6524i	−0.0991784	−	0.562468i
$507$	6.58908	−	9.97517i	0.292631	−	0.443013i
$508$	−17.7735	+	6.46901i	−0.788570	+	0.287016i
$509$	22.2248	+	18.6488i	0.985096	+	0.826593i	0.984850	−	0.173407i	$-0.0554775\pi$
$509$	22.2248	+	18.6488i	0.985096	+	0.826593i	0.000245309		1.00000i	$0.499922\pi$
$510$	−2.92571	−	2.77123i	−0.129553	−	0.122712i
$511$	24.1184	+	24.7530i	1.06694	+	1.09501i
$512$	1.00000			0.0441942
$513$	11.4594	+	32.0753i	0.505943	+	1.41616i
$514$	2.28945	−	3.96545i	0.100983	−	0.174908i
$515$	−31.0476	−	11.3004i	−1.36812	−	0.497956i
$516$	−10.6297	+	3.15942i	−0.467945	+	0.139086i
$517$	−15.4298	+	5.61599i	−0.678602	+	0.246991i
$518$	28.9716	+	2.91416i	1.27294	+	0.128041i
$519$	15.3355	−	23.2163i	0.673152	−	1.01908i
$520$	1.63708	+	9.28432i	0.0717905	+	0.407144i
$521$	35.9617			1.57551			0.787754	−	0.615989i	$-0.211244\pi$
$521$	35.9617			1.57551			0.787754	+	0.615989i	$0.211244\pi$
$522$	6.00706	+	14.0788i	0.262922	+	0.616214i
$523$	−2.17303			−0.0950199			−0.0475100	−	0.998871i	$-0.515129\pi$
$523$	−2.17303			−0.0950199			−0.0475100	+	0.998871i	$0.515129\pi$
$524$	−10.9325	+	9.17349i	−0.477590	+	0.400746i
$525$	−2.40470	+	0.459132i	−0.104950	+	0.0200382i
$526$	−3.70247	+	20.9977i	−0.161435	+	0.915544i
$527$	7.32927	−	2.66764i	0.319268	−	0.116204i
$528$	−3.61362	−	1.56725i	−0.157263	−	0.0682059i
$529$	1.54847	+	8.78180i	0.0673247	+	0.381817i
$530$	9.94076			0.431799
$531$	10.2208	+	1.23565i	0.443545	+	0.0536227i
$532$	1.28711	+	17.2951i	0.0558032	+	0.749839i
$533$	31.0794	+	11.3120i	1.34620	+	0.489976i
$534$	14.0386	+	0.845526i	0.607511	+	0.0365895i
$535$	−22.2693	+	8.10535i	−0.962785	+	0.350425i
$536$	−1.23996	+	7.03214i	−0.0535579	+	0.303742i
$537$	8.71858	−	2.59139i	0.376234	−	0.111827i
$538$	3.84962	+	21.8323i	0.165969	+	0.941256i
$539$	15.7433	−	2.35629i	0.678113	−	0.101493i
$540$	9.54198	−	5.43382i	0.410622	−	0.233834i
$541$	9.39992	+	16.2811i	0.404134	+	0.699981i	0.994220	−	0.107359i	$-0.0342395\pi$
$541$	9.39992	+	16.2811i	0.404134	+	0.699981i	−0.590086	+	0.807340i	$0.700906\pi$
$542$	−18.8470	−	6.85976i	−0.809549	−	0.294652i
$543$	−26.9028	+	7.99622i	−1.15451	+	0.343151i
$544$	−0.843395	−	0.707693i	−0.0361603	−	0.0303421i
$545$	10.4294	+	8.75130i	0.446746	+	0.374865i
$546$	−17.8474	−	9.97073i	−0.763799	−	0.426708i
$547$	8.86581	+	3.22689i	0.379075	+	0.137972i	0.524528	−	0.851393i	$-0.324242\pi$
$547$	8.86581	+	3.22689i	0.379075	+	0.137972i	−0.145453	+	0.989365i	$0.546464\pi$
$548$	9.25673	−	16.0331i	0.395428	−	0.684901i
$549$	−1.24527	+	4.10038i	−0.0531468	+	0.175000i
$550$	−0.607444	−	1.05212i	−0.0259015	−	0.0448627i
$551$	31.4285	+	11.4390i	1.33890	+	0.487319i
$552$	8.97732	+	3.89352i	0.382100	+	0.165719i
$553$	15.0828	+	1.51713i	0.641384	+	0.0645148i
$554$	−1.02156	+	5.79353i	−0.0434018	+	0.246144i
$555$	−36.9566	−	16.0283i	−1.56872	−	0.680363i
$556$	0.165251	+	0.937182i	0.00700818	+	0.0397454i
$557$	−22.7094	−	39.3339i	−0.962229	−	1.66663i	−0.716882	−	0.697194i	$-0.754431\pi$
$557$	−22.7094	−	39.3339i	−0.962229	−	1.66663i	−0.245347	−	0.969435i	$-0.578902\pi$
$558$	1.15179	+	21.2217i	0.0487593	+	0.898386i
$559$	−14.2811	−	24.7356i	−0.604027	−	1.04621i
$560$	5.41892	−	1.37685i	0.228991	−	0.0581824i
$561$	1.93858	+	3.87915i	0.0818470	+	0.163778i
$562$	−5.27382	+	29.9093i	−0.222463	+	1.26165i
$563$	3.47345	−	19.6989i	0.146388	−	0.830210i	−0.819853	−	0.572573i	$-0.805945\pi$
$563$	3.47345	−	19.6989i	0.146388	−	0.830210i	0.966242	−	0.257637i	$-0.0829437\pi$
$564$	2.90820	−	12.1634i	0.122457	−	0.512171i
$565$	20.2438	−	16.9866i	0.851663	−	0.714630i
$566$	0.155924			0.00655396
$567$	−3.94262	+	23.4831i	−0.165574	+	0.986197i
$568$	5.47856			0.229875
$569$	−27.3530	+	22.9519i	−1.14670	+	0.962193i	−0.999637	−	0.0269341i	$-0.991426\pi$
$569$	−27.3530	+	22.9519i	−1.14670	+	0.962193i	−0.147060	+	0.989128i	$0.546981\pi$
$570$	5.57932	−	23.3352i	0.233692	−	0.977404i
$571$	0.743872	−	4.21871i	0.0311301	−	0.176547i	−0.965279	−	0.261223i	$-0.915874\pi$
$571$	0.743872	−	4.21871i	0.0311301	−	0.176547i	0.996409	+	0.0846754i	$0.0269853\pi$
$572$	1.76169	−	9.99104i	0.0736600	−	0.417746i
$573$	3.64743	+	7.29860i	0.152374	+	0.304903i
$574$	5.32225	−	18.8790i	0.222146	−	0.787994i
$575$	1.50907	+	2.61379i	0.0629327	+	0.109003i
$576$	2.51297	−	1.63860i	0.104707	−	0.0682749i
$577$	−4.15106	−	7.18985i	−0.172811	−	0.299317i	0.766591	−	0.642136i	$-0.221952\pi$
$577$	−4.15106	−	7.18985i	−0.172811	−	0.299317i	−0.939402	+	0.342819i	$0.888618\pi$
$578$	−2.74153	−	15.5480i	−0.114033	−	0.646712i
$579$	10.7409	+	4.65842i	0.446378	+	0.193597i
$580$	1.87233	−	10.6185i	0.0777442	−	0.440909i
$581$	1.54722	−	2.14970i	0.0641893	−	0.0891846i
$582$	1.26057	+	0.546718i	0.0522524	+	0.0226622i
$583$	−10.0523	−	3.65874i	−0.416324	−	0.151530i
$584$	−6.53126	−	11.3125i	−0.270266	−	0.468114i
$585$	19.3272	+	20.6487i	0.799080	+	0.853717i
$586$	2.75620	−	4.77388i	0.113858	−	0.197207i
$587$	−17.7914	−	6.47553i	−0.734328	−	0.267274i	−0.0523324	−	0.998630i	$-0.516666\pi$
$587$	−17.7914	−	6.47553i	−0.734328	−	0.267274i	−0.681996	+	0.731356i	$0.738888\pi$
$588$	−5.11140	+	10.9943i	−0.210791	+	0.453395i
$589$	35.5734	+	29.8497i	1.46578	+	1.22993i
$590$	−5.55542	−	4.66155i	−0.228713	−	0.191913i
$591$	−16.6488	+	4.94846i	−0.684841	+	0.203553i
$592$	−10.3418	−	3.76410i	−0.425045	−	0.154704i
$593$	−6.46570	−	11.1989i	−0.265515	−	0.459885i	0.702184	−	0.711996i	$-0.252209\pi$
$593$	−6.46570	−	11.1989i	−0.265515	−	0.459885i	−0.967698	+	0.252111i	$0.918875\pi$
$594$	−11.6490	+	1.98282i	−0.477965	+	0.0813563i
$595$	−5.54468	−	2.67370i	−0.227310	−	0.109611i
$596$	3.10190	+	17.5918i	0.127059	+	0.720586i
$597$	−6.87382	+	2.04308i	−0.281327	+	0.0836177i
$598$	−4.37657	+	24.8207i	−0.178971	+	1.01500i
$599$	20.2194	−	7.35927i	0.826144	−	0.300692i	0.105869	−	0.994380i	$-0.466238\pi$
$599$	20.2194	−	7.35927i	0.826144	−	0.300692i	0.720275	+	0.693688i	$0.244015\pi$
$600$	0.923637	+	0.0556294i	0.0377073	+	0.00227106i
$601$	12.1343	+	4.41654i	0.494970	+	0.180154i	0.577430	−	0.816440i	$-0.304056\pi$
$601$	12.1343	+	4.41654i	0.494970	+	0.180154i	−0.0824604	+	0.996594i	$0.526278\pi$
$602$	−14.0007	+	9.53493i	−0.570626	+	0.388615i
$603$	8.40687	+	19.7033i	0.342354	+	0.802381i
$604$	6.26746			0.255019
$605$	2.13882	+	12.1298i	0.0869553	+	0.493148i
$606$	17.5012	+	7.59039i	0.710939	+	0.308339i
$607$	19.4004	−	7.06116i	0.787437	−	0.286603i	0.0831665	−	0.996536i	$-0.473497\pi$
$607$	19.4004	−	7.06116i	0.787437	−	0.286603i	0.704270	+	0.709932i	$0.251274\pi$
$608$	1.13827	−	6.45544i	0.0461628	−	0.261803i
$609$	15.2809	+	17.6972i	0.619213	+	0.717126i
$610$	2.31239	−	1.94033i	0.0936261	−	0.0785616i
$611$	32.2118			1.30315
$612$	−3.27905	−	0.396423i	−0.132548	−	0.0160244i
$613$	5.93262			0.239616			0.119808	−	0.992797i	$-0.461772\pi$
$613$	5.93262			0.239616			0.119808	+	0.992797i	$0.461772\pi$
$614$	2.28021	+	12.9317i	0.0920217	+	0.521881i
$615$	−14.9563	+	22.6422i	−0.603095	+	0.913022i
$616$	−5.98649	−	0.602162i	−0.241202	−	0.0242618i
$617$	−26.7010	+	9.71835i	−1.07494	+	0.391246i	−0.818022	−	0.575187i	$-0.804929\pi$
$617$	−26.7010	+	9.71835i	−1.07494	+	0.391246i	−0.256918	+	0.966433i	$0.582707\pi$
$618$	−25.9581	+	7.71541i	−1.04419	+	0.310359i
$619$	−32.7574	−	11.9227i	−1.31663	−	0.479215i	−0.414254	−	0.910161i	$-0.635958\pi$
$619$	−32.7574	−	11.9227i	−1.31663	−	0.479215i	−0.902378	+	0.430946i	$0.858180\pi$
$620$	7.48542	−	12.9651i	0.300622	−	0.520692i
$621$	28.9396	−	4.92593i	1.16131	−	0.197671i
$622$	−6.98116			−0.279919
$623$	20.8216	−	5.29039i	0.834201	−	0.211955i
$624$	5.60991	+	5.31370i	0.224576	+	0.212718i
$625$	−16.8863	−	14.1693i	−0.675451	−	0.566770i
$626$	−9.27538	+	3.37596i	−0.370719	+	0.134931i
$627$	−14.2306	+	21.5436i	−0.568314	+	0.860367i
$628$	1.19882	+	6.79885i	0.0478382	+	0.271304i
$629$	6.05838	+	10.4934i	0.241564	+	0.418400i
$630$	11.3615	−	12.3394i	0.452652	−	0.491613i
$631$	6.04573	−	10.4715i	0.240677	−	0.416865i	−0.720230	−	0.693735i	$-0.755964\pi$
$631$	6.04573	−	10.4715i	0.240677	−	0.416865i	0.960907	+	0.276870i	$0.0892972\pi$
$632$	−5.38398	−	1.95961i	−0.214163	−	0.0779491i
$633$	−10.9725	+	8.13504i	−0.436118	+	0.323339i
$634$	−18.5409	−	15.5576i	−0.736351	−	0.617872i
$635$	37.5596	−	13.6706i	1.49051	−	0.542500i
$636$	6.54502	−	4.85250i	0.259527	−	0.192414i
$637$	−30.6027	−	6.21939i	−1.21252	−	0.246421i
$638$	−5.80153	+	10.0485i	−0.229685	+	0.397826i
$639$	13.7674	−	8.97716i	0.544632	−	0.355131i
$640$	−2.11324			−0.0835330
$641$	−33.4256	+	28.0474i	−1.32023	+	1.10780i	−0.333974	+	0.942582i	$0.608390\pi$
$641$	−33.4256	+	28.0474i	−1.32023	+	1.10780i	−0.986256	+	0.165222i	$0.947166\pi$
$642$	−10.7056	+	16.2071i	−0.422516	+	0.639645i
$643$	18.1099	+	15.1960i	0.714183	+	0.599271i	0.925769	−	0.378089i	$-0.123419\pi$
$643$	18.1099	+	15.1960i	0.714183	+	0.599271i	−0.211587	+	0.977359i	$0.567863\pi$
$644$	14.8722	+	1.49595i	0.586048	+	0.0589487i
$645$	22.4630	−	6.67660i	0.884481	−	0.262891i
$646$	−5.52847	+	4.63894i	−0.217515	+	0.182517i
$647$	5.83538	−	10.1072i	0.229412	−	0.397354i	−0.728222	−	0.685342i	$-0.759653\pi$
$647$	5.83538	−	10.1072i	0.229412	−	0.397354i	0.957634	+	0.287988i	$0.0929862\pi$
$648$	3.63000	−	8.23548i	0.142600	−	0.323520i
$649$	3.90206	+	6.75856i	0.153169	+	0.265297i
$650$	0.413854	+	2.34709i	0.0162327	+	0.0920603i
$651$	11.5333	+	30.3467i	0.452027	+	1.18938i
$652$	14.5103	−	5.28132i	0.568267	−	0.206832i
$653$	3.19388	−	18.1134i	0.124986	−	0.708833i	−0.856330	−	0.516430i	$-0.827261\pi$
$653$	3.19388	−	18.1134i	0.124986	−	0.708833i	0.981316	−	0.192403i	$-0.0616281\pi$
$654$	11.1386	+	0.670863i	0.435555	+	0.0262328i
$655$	23.1031	−	19.3858i	0.902711	−	0.757464i
$656$	−3.70686	+	6.42047i	−0.144729	+	0.250677i
$657$	−34.9494	−	17.7258i	−1.36351	−	0.691548i
$658$	−1.41777	−	19.0509i	−0.0552704	−	0.742681i
$659$	20.4084	−	17.1247i	0.795000	−	0.667084i	−0.151977	−	0.988384i	$-0.548564\pi$
$659$	20.4084	−	17.1247i	0.795000	−	0.667084i	0.946978	+	0.321300i	$0.104120\pi$
$660$	7.63645	+	3.31197i	0.297248	+	0.128918i
$661$	27.2686	+	22.8811i	1.06062	+	0.889970i	0.994170	−	0.107820i	$-0.0343869\pi$
$661$	27.2686	+	22.8811i	1.06062	+	0.889970i	0.0664541	+	0.997789i	$0.478831\pi$
$662$	−19.4046	−	16.2824i	−0.754182	−	0.632834i
$663$	−0.970911	−	8.45164i	−0.0377071	−	0.328235i
$664$	−0.766870	+	0.643480i	−0.0297603	+	0.0249719i
$665$	−2.71996	−	36.5487i	−0.105476	−	1.41730i
$666$	−32.1564	+	7.48696i	−1.24603	+	0.290114i
$667$	14.4127	−	24.9636i	0.558063	−	0.966594i
$668$	−0.125142	+	0.105007i	−0.00484189	+	0.00406283i
$669$	27.3612	−	41.4219i	1.05784	−	1.60146i
$670$	2.62032	−	14.8606i	0.101232	−	0.574114i
$671$	−3.05249	+	1.11102i	−0.117840	+	0.0428903i
$672$	2.89574	−	3.55172i	0.111705	−	0.137011i
$673$	2.95225	+	16.7430i	0.113801	+	0.645397i	0.987337	+	0.158637i	$0.0507101\pi$
$673$	2.95225	+	16.7430i	0.113801	+	0.645397i	−0.873536	+	0.486759i	$0.838179\pi$
$674$	−9.72372	−	16.8420i	−0.374544	−	0.648729i
$675$	2.41222	−	1.37367i	0.0928465	−	0.0528728i
$676$	−3.45109	+	5.97746i	−0.132734	+	0.229902i
$677$	12.5981	−	10.5711i	0.484186	−	0.406280i	−0.367751	−	0.929924i	$-0.619872\pi$
$677$	12.5981	−	10.5711i	0.484186	−	0.406280i	0.851937	+	0.523644i	$0.175428\pi$
$678$	5.03673	−	21.0658i	0.193434	−	0.809028i
$679$	2.08832	+	0.210057i	0.0801423	+	0.00806126i
$680$	1.78229	+	1.49552i	0.0683479	+	0.0573507i
$681$	−27.3730	−	1.64864i	−1.04894	−	0.0631760i
$682$	−12.3413	+	10.3556i	−0.472573	+	0.396536i
$683$	44.8958			1.71789			0.858946	−	0.512066i	$-0.171120\pi$
$683$	44.8958			1.71789			0.858946	+	0.512066i	$0.171120\pi$
$684$	−7.71743	−	18.0875i	−0.295083	−	0.691591i
$685$	−19.5617	+	33.8818i	−0.747413	+	1.29456i
$686$	−2.33135	+	18.3729i	−0.0890115	+	0.701482i
$687$	2.29780	+	20.0021i	0.0876667	+	0.763126i
$688$	6.01628	−	2.18975i	0.229369	−	0.0834833i
$689$	16.0759	+	13.4893i	0.612443	+	0.513901i
$690$	−18.9712	−	8.22793i	−0.722222	−	0.313232i
$691$	−42.6416	−	15.5203i	−1.62216	−	0.590419i	−0.638371	−	0.769729i	$-0.720391\pi$
$691$	−42.6416	−	15.5203i	−1.62216	−	0.590419i	−0.983793	+	0.179309i	$0.942614\pi$
$692$	−8.03208	+	13.9120i	−0.305334	+	0.528854i
$693$	−16.0305	+	8.29623i	−0.608950	+	0.315148i
$694$	−8.49969	−	14.7219i	−0.322644	−	0.558836i
$695$	−0.349214	−	1.98049i	−0.0132464	−	0.0751242i
$696$	−3.95058	−	7.90521i	−0.149746	−	0.299646i
$697$	7.67007	−	2.79168i	0.290524	−	0.105742i
$698$	−13.7867	−	11.5684i	−0.521835	−	0.437872i
$699$	−0.689342	+	2.88314i	−0.0260733	+	0.109050i
$700$	1.36991	−	0.348068i	0.0517777	−	0.0131557i
$701$	−24.0239			−0.907369			−0.453684	−	0.891162i	$-0.649891\pi$
$701$	−24.0239			−0.907369			−0.453684	+	0.891162i	$0.649891\pi$
$702$	22.8045	+	4.16075i	0.860702	+	0.157037i
$703$	−36.0706	+	62.4762i	−1.36043	+	2.35633i
$704$	2.13695	+	0.777787i	0.0805394	+	0.0293140i
$705$	−6.14572	+	25.7041i	−0.231461	+	0.968073i
$706$	31.4637	−	11.4519i	1.18415	−	0.430996i
$707$	28.9933	+	2.91635i	1.09041	+	0.109680i
$708$	−5.93320	−	0.357348i	−0.222983	−	0.0134300i
$709$	3.73973	+	21.2091i	0.140449	+	0.796524i	0.970909	+	0.239447i	$0.0769661\pi$
$709$	3.73973	+	21.2091i	0.140449	+	0.796524i	−0.830461	+	0.557077i	$0.811923\pi$
$710$	−11.5775			−0.434496
$711$	−16.7408	+	3.89775i	−0.627828	+	0.146177i
$712$	−8.11989			−0.304306
$713$	30.6595	−	25.7263i	1.14821	−	0.963459i
$714$	−4.95578	+	0.946211i	−0.185465	+	0.0354111i
$715$	−3.72287	+	21.1134i	−0.139227	+	0.789598i
$716$	−4.93462	+	1.79606i	−0.184415	+	0.0671217i
$717$	0.379713	+	3.30535i	0.0141806	+	0.123440i
$718$	−3.33683	−	18.9241i	−0.124530	−	0.706242i
$719$	−28.9508			−1.07968			−0.539842	−	0.841766i	$-0.681516\pi$
$719$	−28.9508			−1.07968			−0.539842	+	0.841766i	$0.681516\pi$
$720$	−5.31049	+	3.46274i	−0.197910	+	0.129049i
$721$	−34.1902	+	23.2846i	−1.27331	+	0.867165i
$722$	−22.5228	−	8.19764i	−0.838213	−	0.305085i
$723$	14.6867	−	22.2341i	0.546204	−	0.826895i
$724$	15.2267	−	5.54207i	0.565896	−	0.205969i
$725$	0.473326	−	2.68437i	0.0175789	−	0.0996949i
$726$	7.32928	+	6.94228i	0.272015	+	0.257652i
$727$	−3.65752	−	20.7428i	−0.135650	−	0.769309i	−0.974405	−	0.224800i	$-0.927827\pi$
$727$	−3.65752	−	20.7428i	−0.135650	−	0.769309i	0.838755	−	0.544509i	$-0.183284\pi$
$728$	10.6317	+	5.12670i	0.394035	+	0.190008i
$729$	−4.37257	−	26.6436i	−0.161947	−	0.986799i
$730$	13.8021	+	23.9060i	0.510839	+	0.884799i
$731$	−6.62377	−	2.41086i	−0.244989	−	0.0891687i
$732$	0.575332	−	2.40629i	0.0212649	−	0.0889392i
$733$	22.9788	+	19.2815i	0.848742	+	0.712179i	0.959512	−	0.281667i	$-0.0908872\pi$
$733$	22.9788	+	19.2815i	0.848742	+	0.712179i	−0.110770	+	0.993846i	$0.535332\pi$
$734$	−14.2443	−	11.9524i	−0.525768	−	0.441172i
$735$	10.8016	−	23.2335i	0.398423	−	0.856979i
$736$	−5.30883	−	1.93226i	−0.195686	−	0.0712239i
$737$	−8.11923	+	14.0629i	−0.299076	+	0.518014i
$738$	1.20535	+	22.2085i	0.0443695	+	0.817505i
$739$	−11.8669	−	20.5541i	−0.436531	−	0.756094i	0.560888	−	0.827892i	$-0.310460\pi$
$739$	−11.8669	−	20.5541i	−0.436531	−	0.756094i	−0.997419	+	0.0717974i	$0.977127\pi$
$740$	21.8546	+	7.95444i	0.803392	+	0.292411i
$741$	40.6878	−	30.1660i	1.49470	−	1.10818i
$742$	7.27033	−	10.1014i	0.266902	−	0.370834i
$743$	−3.02135	+	17.1349i	−0.110843	+	0.628619i	0.877882	+	0.478876i	$0.158956\pi$
$743$	−3.02135	+	17.1349i	−0.110843	+	0.628619i	−0.988725	+	0.149743i	$0.952155\pi$
$744$	−1.40039	−	12.1902i	−0.0513409	−	0.446915i
$745$	−6.55505	−	37.1755i	−0.240159	−	1.36201i
$746$	−11.8588	−	20.5401i	−0.434182	−	0.752026i
$747$	−0.872713	+	2.87363i	−0.0319309	+	0.105141i
$748$	−1.25186	−	2.16829i	−0.0457726	−	0.0792804i
$749$	−8.05065	+	28.5571i	−0.294165	+	1.04346i
$750$	−20.2199	−	1.21782i	−0.738328	−	0.0444684i
$751$	7.00257	−	39.7135i	0.255527	−	1.44917i	−0.539188	−	0.842185i	$-0.681269\pi$
$751$	7.00257	−	39.7135i	0.255527	−	1.44917i	0.794716	−	0.606982i	$-0.207620\pi$
$752$	−1.25382	+	7.11077i	−0.0457222	+	0.259303i
$753$	−29.2274	+	8.68715i	−1.06511	+	0.316577i
$754$	17.4368	−	14.6312i	0.635012	−	0.532838i
$755$	−13.2446			−0.482022
$756$	1.45705	−	13.6703i	0.0529925	−	0.497184i
$757$	−22.4182			−0.814804			−0.407402	−	0.913249i	$-0.633565\pi$
$757$	−22.4182			−0.814804			−0.407402	+	0.913249i	$0.633565\pi$
$758$	−2.15965	+	1.81216i	−0.0784420	+	0.0658207i
$759$	16.1558	+	15.3027i	0.586418	+	0.555453i
$760$	−2.40543	+	13.6419i	−0.0872541	+	0.494843i
$761$	−4.03195	+	22.8663i	−0.146158	+	0.828903i	0.820272	+	0.571973i	$0.193822\pi$
$761$	−4.03195	+	22.8663i	−0.146158	+	0.828903i	−0.966430	+	0.256929i	$0.917289\pi$
$762$	18.0562	−	27.3351i	0.654106	−	0.990247i
$763$	16.5204	−	4.19753i	0.598080	−	0.151961i
$764$	−2.35537	−	4.07962i	−0.0852144	−	0.147596i
$765$	6.92940	+	0.837735i	0.250533	+	0.0302884i
$766$	−3.11606	−	5.39718i	−0.112588	−	0.195008i
$767$	−2.65849	−	15.0770i	−0.0959925	−	0.544400i
$768$	−1.39136	+	1.03156i	−0.0502064	+	0.0372232i
$769$	−5.33742	+	30.2700i	−0.192472	+

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.402772 + 1.68457i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.366960 + 2.08113i) q^{5} +(0.774279 + 1.54935i) q^{6} +(1.84638 + 1.89496i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.67555 - 1.35699i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.402772 + 1.68457i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.366960 + 2.08113i) q^{5} +(0.774279 + 1.54935i) q^{6} +(1.84638 + 1.89496i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.67555 - 1.35699i) q^{9} +(1.05662 + 1.83012i) q^{10} +(-0.394893 - 2.23955i) q^{11} +(1.58904 + 0.689175i) q^{12} +(-0.774677 + 4.39341i) q^{13} +(2.63247 + 0.264792i) q^{14} +(-3.35801 - 1.45639i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.550487 + 0.953472i) q^{17} +(-2.92185 + 0.680293i) q^{18} +(-3.27751 + 5.67682i) q^{19} +(1.98579 + 0.722770i) q^{20} +(-3.93586 + 2.34712i) q^{21} +(-1.74206 - 1.46176i) q^{22} +(4.32780 + 3.63145i) q^{23} +(1.66027 - 0.493474i) q^{24} +(0.502011 + 0.182717i) q^{25} +(2.23059 + 3.86350i) q^{26} +(3.36359 - 3.96059i) q^{27} +(2.18679 - 1.48928i) q^{28} +(-0.886000 - 5.02476i) q^{29} +(-3.50854 + 1.04283i) q^{30} +(1.23018 - 6.97669i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(3.93173 + 0.236802i) q^{33} +(1.03458 + 0.376555i) q^{34} +(-4.62121 + 3.14719i) q^{35} +(-1.80098 + 2.39926i) q^{36} +11.0055 q^{37} +(1.13827 + 6.45544i) q^{38} +(-7.08899 - 3.07454i) q^{39} +(1.98579 - 0.722770i) q^{40} +(1.28738 - 7.30109i) q^{41} +(-1.50634 + 4.32792i) q^{42} +(-4.90452 + 4.11538i) q^{43} -2.27410 q^{44} +(3.80590 - 5.07021i) q^{45} +5.64954 q^{46} +(-1.25382 - 7.11077i) q^{47} +(0.954638 - 1.44522i) q^{48} +(-0.181745 + 6.99764i) q^{49} +(0.502011 - 0.182717i) q^{50} +(-1.82791 + 0.543303i) q^{51} +(4.19214 + 1.52582i) q^{52} +(2.35202 - 4.07382i) q^{53} +(0.0308378 - 5.19606i) q^{54} +4.80571 q^{55} +(0.717892 - 2.54649i) q^{56} +(-8.24290 - 7.80766i) q^{57} +(-3.90857 - 3.27968i) q^{58} +(-3.22478 + 1.17372i) q^{59} +(-2.01738 + 3.05410i) q^{60} +(-0.248045 - 1.40673i) q^{61} +(-3.54216 - 6.13519i) q^{62} +(-2.36864 - 7.57559i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-8.85899 - 3.22441i) q^{65} +(3.16409 - 2.34586i) q^{66} +(-5.47003 - 4.58990i) q^{67} +(1.03458 - 0.376555i) q^{68} +(-7.86055 + 5.82783i) q^{69} +(-1.51708 + 5.38135i) q^{70} +(-2.73928 + 4.74457i) q^{71} +(0.162584 + 2.99559i) q^{72} +13.0625 q^{73} +(8.43070 - 7.07419i) q^{74} +(-0.509995 + 0.772079i) q^{75} +(5.02144 + 4.21349i) q^{76} +(3.51473 - 4.88337i) q^{77} +(-7.40675 + 2.20148i) q^{78} +(4.38906 - 3.68286i) q^{79} +(1.05662 - 1.83012i) q^{80} +(5.31713 + 7.26141i) q^{81} +(-3.70686 - 6.42047i) q^{82} +(-0.173835 - 0.985869i) q^{83} +(1.62801 + 4.28364i) q^{84} +(-2.18631 + 0.795751i) q^{85} +(-1.11176 + 6.30513i) q^{86} +(8.82141 + 0.531301i) q^{87} +(-1.74206 + 1.46176i) q^{88} +(4.05995 - 7.03203i) q^{89} +(-0.343578 - 6.33039i) q^{90} +(-9.75568 + 6.64393i) q^{91} +(4.32780 - 3.63145i) q^{92} +(11.2572 + 4.88233i) q^{93} +(-5.53120 - 4.64123i) q^{94} +(-10.6115 - 8.90410i) q^{95} +(-0.197675 - 1.72073i) q^{96} +(0.607697 - 0.509919i) q^{97} +(4.35877 + 5.47733i) q^{98} +(-1.98250 + 6.52789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9	\( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 6 * q^7 - 36 * q^8 + 24 * q^9 - 6 * q^10 + 12 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 - 18 * q^19 - 30 * q^21 - 6 * q^22 + 30 * q^23 + 6 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 - 18 * q^35 + 9 * q^36 - 24 * q^39 - 6 * q^41 + 12 * q^42 + 24 * q^43 + 51 * q^45 + 45 * q^47 - 6 * q^48 - 12 * q^49 + 6 * q^50 - 51 * q^51 + 6 * q^52 - 15 * q^53 + 27 * q^54 + 72 * q^55 - 3 * q^56 - 63 * q^57 + 3 * q^58 - 30 * q^59 - 3 * q^60 + 9 * q^61 - 24 * q^62 - 39 * q^63 - 36 * q^64 + 9 * q^65 - 6 * q^67 + 9 * q^68 - 21 * q^69 - 33 * q^70 + 12 * q^71 - 12 * q^72 + 132 * q^73 - 18 * q^74 - 30 * q^75 - 33 * q^77 + 30 * q^78 - 9 * q^79 - 6 * q^80 + 36 * q^81 - 33 * q^82 - 18 * q^83 + 15 * q^84 + 21 * q^85 - 12 * q^86 - 39 * q^87 - 6 * q^88 - 36 * q^89 + 69 * q^90 + 39 * q^91 + 30 * q^92 - 66 * q^93 - 9 * q^94 - 33 * q^95 - 48 * q^97 - 12 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more