LMFDB - Embedded newform 378.2.h.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(289,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("378.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.h (of order $3$, degree $2$, not 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	378.289
Dual form			378.2.h.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +3.00000 q^{11} +(-2.50000 - 4.33013i) q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +3.00000 q^{23} +4.00000 q^{25} +(2.50000 - 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(-1.50000 + 7.79423i) q^{35} +(3.50000 - 6.06218i) q^{37} -5.00000 q^{38} -3.00000 q^{40} +(-4.50000 - 7.79423i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-6.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +5.00000 q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(0.500000 - 2.59808i) q^{56} -3.00000 q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-7.50000 - 12.9904i) q^{65} +(2.00000 - 3.46410i) q^{67} -3.00000 q^{68} +(-7.50000 + 2.59808i) q^{70} +(-5.50000 - 9.52628i) q^{73} +7.00000 q^{74} +(-2.50000 - 4.33013i) q^{76} +(-1.50000 + 7.79423i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{82} +(1.50000 - 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} -11.0000 q^{86} -3.00000 q^{88} +(7.50000 - 12.9904i) q^{89} +(12.5000 - 4.33013i) q^{91} +(-1.50000 + 2.59808i) q^{92} +(-7.50000 + 12.9904i) q^{95} +(0.500000 - 0.866025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 6 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + 6 * q^5 - q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + 6 q^{5} - q^{7} - 2 q^{8} + 3 q^{10} + 6 q^{11} - 5 q^{13} - 5 q^{14} - q^{16} + 3 q^{17} - 5 q^{19} - 3 q^{20} + 3 q^{22} + 6 q^{23} + 8 q^{25} + 5 q^{26} - 4 q^{28} - 3 q^{29} + 4 q^{31} + q^{32} - 3 q^{34} - 3 q^{35} + 7 q^{37} - 10 q^{38} - 6 q^{40} - 9 q^{41} - 11 q^{43} - 3 q^{44} + 3 q^{46} - 13 q^{49} + 4 q^{50} + 10 q^{52} - 3 q^{53} + 18 q^{55} + q^{56} - 6 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{62} + 2 q^{64} - 15 q^{65} + 4 q^{67} - 6 q^{68} - 15 q^{70} - 11 q^{73} + 14 q^{74} - 5 q^{76} - 3 q^{77} - 8 q^{79} - 3 q^{80} + 9 q^{82} + 3 q^{83} + 9 q^{85} - 22 q^{86} - 6 q^{88} + 15 q^{89} + 25 q^{91} - 3 q^{92} - 15 q^{95} + q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 6 * q^5 - q^7 - 2 * q^8 + 3 * q^10 + 6 * q^11 - 5 * q^13 - 5 * q^14 - q^16 + 3 * q^17 - 5 * q^19 - 3 * q^20 + 3 * q^22 + 6 * q^23 + 8 * q^25 + 5 * q^26 - 4 * q^28 - 3 * q^29 + 4 * q^31 + q^32 - 3 * q^34 - 3 * q^35 + 7 * q^37 - 10 * q^38 - 6 * q^40 - 9 * q^41 - 11 * q^43 - 3 * q^44 + 3 * q^46 - 13 * q^49 + 4 * q^50 + 10 * q^52 - 3 * q^53 + 18 * q^55 + q^56 - 6 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 15 * q^65 + 4 * q^67 - 6 * q^68 - 15 * q^70 - 11 * q^73 + 14 * q^74 - 5 * q^76 - 3 * q^77 - 8 * q^79 - 3 * q^80 + 9 * q^82 + 3 * q^83 + 9 * q^85 - 22 * q^86 - 6 * q^88 + 15 * q^89 + 25 * q^91 - 3 * q^92 - 15 * q^95 + q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−2.50000	+	0.866025i	−0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$		0			0
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	−1.50000	+	7.79423i	−0.253546	+	1.31747i
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−5.00000			−0.811107
$39$		0			0
$40$	−3.00000			−0.474342
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	5.00000			0.693375
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$		0			0
$58$	−3.00000			−0.393919
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.50000	−	12.9904i	−0.930261	−	1.61126i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−3.00000			−0.363803
$69$		0			0
$70$	−7.50000	+	2.59808i	−0.896421	+	0.310530i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	7.00000			0.813733
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$		0			0
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	1.50000	−	2.59808i	0.164646	−	0.285176i	−0.771883	−	0.635764i	$-0.780685\pi$
$83$	1.50000	−	2.59808i	0.164646	−	0.285176i	0.936530	+	0.350588i	$0.114018\pi$
$84$		0			0
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$	−11.0000			−1.18616
$87$		0			0
$88$	−3.00000			−0.319801
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$		0			0
$91$	12.5000	−	4.33013i	1.31036	−	0.453921i
$92$	−1.50000	+	2.59808i	−0.156386	+	0.270868i
$93$		0			0
$94$		0			0
$95$	−7.50000	+	12.9904i	−0.769484	+	1.33278i
$96$		0			0
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$		0			0
$103$	5.00000			0.492665			0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000			0.492665			0.246332	+	0.969185i	$0.420775\pi$
$104$	2.50000	+	4.33013i	0.245145	+	0.424604i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	0.233900	+	0.972261i	$0.424851\pi$
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	−0.958952	+	0.283567i	$0.908482\pi$
$108$		0			0
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$	4.50000	+	7.79423i	0.429058	+	0.743151i
$111$		0			0
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	9.00000			0.839254
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$		0			0
$118$	12.0000			1.10469
$119$	−7.50000	+	2.59808i	−0.687524	+	0.238165i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	1.00000	−	1.73205i	0.0905357	−	0.156813i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	7.50000	−	12.9904i	0.657794	−	1.13933i
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$		0			0
$133$	−10.0000	−	8.66025i	−0.867110	−	0.750939i
$134$	4.00000			0.345547
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	−6.00000	−	5.19615i	−0.507093	−	0.439155i
$141$		0			0
$142$		0			0
$143$	−7.50000	−	12.9904i	−0.627182	−	1.08631i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$		0			0
$148$	3.50000	+	6.06218i	0.287698	+	0.498308i
$149$	3.00000			0.245770			0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000			0.245770			0.122885	+	0.992421i	$0.460785\pi$
$150$		0			0
$151$	11.0000			0.895167			0.447584	−	0.894242i	$-0.352285\pi$
$151$	11.0000			0.895167			0.447584	+	0.894242i	$0.352285\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$		0			0
$154$	−7.50000	+	2.59808i	−0.604367	+	0.209359i
$155$	6.00000	−	10.3923i	0.481932	−	0.834730i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$		0			0
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	−1.50000	+	7.79423i	−0.118217	+	0.614271i
$162$		0			0
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	0.313304	+	0.949653i	$0.398564\pi$
$163$	−8.50000	+	14.7224i	−0.665771	+	1.15315i	−0.979076	+	0.203497i	$0.934769\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$	3.00000			0.232845
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−4.50000	+	7.79423i	−0.345134	+	0.597790i
$171$		0			0
$172$	−5.50000	−	9.52628i	−0.419371	−	0.726372i
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	15.0000			1.12430
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	10.0000	+	8.66025i	0.741249	+	0.641941i
$183$		0			0
$184$	−3.00000			−0.221163
$185$	10.5000	−	18.1865i	0.771975	−	1.33710i
$186$		0			0
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$	−15.0000			−1.08821
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	1.00000			0.0717958
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$	−4.00000			−0.282843
$201$		0			0
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	−6.00000	−	5.19615i	−0.421117	−	0.364698i
$204$		0			0
$205$	−13.5000	−	23.3827i	−0.942881	−	1.63312i
$206$	2.50000	+	4.33013i	0.174183	+	0.301694i
$207$		0			0
$208$	−2.50000	+	4.33013i	−0.173344	+	0.300240i
$209$	−7.50000	+	12.9904i	−0.518786	+	0.898563i
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	3.00000			0.206041
$213$		0			0
$214$	−15.0000			−1.02538
$215$	−16.5000	+	28.5788i	−1.12529	+	1.94906i
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	−3.50000	+	6.06218i	−0.237050	+	0.410582i
$219$		0			0
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$	7.50000	−	12.9904i	0.504505	−	0.873828i
$222$		0			0
$223$	−8.50000	+	14.7224i	−0.569202	+	0.985887i	0.427443	+	0.904042i	$0.359414\pi$
$223$	−8.50000	+	14.7224i	−0.569202	+	0.985887i	−0.996645	+	0.0818447i	$0.973919\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	−7.50000	+	12.9904i	−0.498893	+	0.864107i
$227$	−9.00000			−0.597351			−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000			−0.597351			−0.298675	+	0.954355i	$0.596545\pi$
$228$		0			0
$229$	17.0000			1.12339			0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000			1.12339			0.561696	+	0.827344i	$0.310149\pi$
$230$	4.50000	+	7.79423i	0.296721	+	0.513936i
$231$		0			0
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.0380310	−	0.999277i	$-0.487891\pi$
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.846383	−	0.532574i	$-0.178775\pi$
$234$		0			0
$235$		0			0
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$		0			0
$238$	−6.00000	−	5.19615i	−0.388922	−	0.336817i
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.858623	+	0.512607i	$0.171320\pi$
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.0146191	+	0.999893i	$0.495346\pi$
$240$		0			0
$241$	23.0000			1.48156			0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000			1.48156			0.740780	+	0.671748i	$0.234456\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$		0			0
$244$	2.00000			0.128037
$245$	−19.5000	−	7.79423i	−1.24581	−	0.497955i
$246$		0			0
$247$	25.0000			1.59071
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.0000			−0.935674			−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000			−0.935674			−0.467837	+	0.883815i	$0.654967\pi$
$258$		0			0
$259$	14.0000	+	12.1244i	0.869918	+	0.753371i
$260$	15.0000			0.930261
$261$		0			0
$262$	−1.50000	−	2.59808i	−0.0926703	−	0.160510i
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$	2.50000	−	12.9904i	0.153285	−	0.796491i
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	−0.598235	−	0.801321i	$-0.704131\pi$
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	0.993082	+	0.117426i	$0.0374643\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$		0			0
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$	12.0000			0.723627
$276$		0			0
$277$	−7.00000			−0.420589			−0.210295	−	0.977638i	$-0.567442\pi$
$277$	−7.00000			−0.420589			−0.210295	+	0.977638i	$0.567442\pi$
$278$	2.50000	−	4.33013i	0.149940	−	0.259704i
$279$		0			0
$280$	1.50000	−	7.79423i	0.0896421	−	0.465794i
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	−4.00000	+	6.92820i	−0.237775	+	0.411839i	−0.960076	−	0.279741i	$-0.909752\pi$
$283$	−4.00000	+	6.92820i	−0.237775	+	0.411839i	0.722300	+	0.691580i	$0.243085\pi$
$284$		0			0
$285$		0			0
$286$	7.50000	−	12.9904i	0.443484	−	0.768137i
$287$	22.5000	−	7.79423i	1.32813	−	0.460079i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−9.00000			−0.528498
$291$		0			0
$292$	11.0000			0.643726
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	−0.926777	−	0.375613i	$-0.877432\pi$
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	0.138098	−	0.990419i	$-0.455901\pi$
$294$		0			0
$295$	18.0000	−	31.1769i	1.04800	−	1.81519i
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$		0			0
$298$	1.50000	+	2.59808i	0.0868927	+	0.150503i
$299$	−7.50000	−	12.9904i	−0.433736	−	0.751253i
$300$		0			0
$301$	−22.0000	−	19.0526i	−1.26806	−	1.09817i
$302$	5.50000	+	9.52628i	0.316489	+	0.548176i
$303$		0			0
$304$	5.00000			0.286770
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−6.00000	−	5.19615i	−0.341882	−	0.296078i
$309$		0			0
$310$	12.0000			0.681554
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$		0			0
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$	3.00000			0.167705
$321$		0			0
$322$	−7.50000	+	2.59808i	−0.417959	+	0.144785i
$323$	−15.0000			−0.834622
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	−17.0000			−0.941543
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	1.50000	+	2.59808i	0.0823232	+	0.142588i
$333$		0			0
$334$	−1.50000	+	2.59808i	−0.0820763	+	0.142160i
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$		0			0
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	0.974701	+	0.223513i	$0.0717525\pi$
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	−0.293783	+	0.955872i	$0.594914\pi$
$338$	−12.0000			−0.652714
$339$		0			0
$340$	−9.00000			−0.488094
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	5.50000	−	9.52628i	0.296540	−	0.513623i
$345$		0			0
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	−0.925147	−	0.379610i	$-0.876058\pi$
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	0.791325	+	0.611396i	$0.209392\pi$
$350$	−10.0000	+	3.46410i	−0.534522	+	0.185164i
$351$		0			0
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	9.00000			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	+	12.9904i	0.397499	+	0.688489i
$357$		0			0
$358$	−1.50000	+	2.59808i	−0.0792775	+	0.137313i
$359$	7.50000	−	12.9904i	0.395835	−	0.685606i	−0.597372	−	0.801964i	$-0.703789\pi$
$359$	7.50000	−	12.9904i	0.395835	−	0.685606i	0.993207	+	0.116358i	$0.0371219\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$		0			0
$364$	−2.50000	+	12.9904i	−0.131036	+	0.680881i
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$		0			0
$367$	−1.00000			−0.0521996			−0.0260998	−	0.999659i	$-0.508309\pi$
$367$	−1.00000			−0.0521996			−0.0260998	+	0.999659i	$0.508309\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$	21.0000			1.09174
$371$	7.50000	−	2.59808i	0.389381	−	0.134885i
$372$		0			0
$373$	17.0000			0.880227			0.440113	−	0.897942i	$-0.354938\pi$
$373$	17.0000			0.880227			0.440113	+	0.897942i	$0.354938\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	15.0000			0.772539
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−7.50000	−	12.9904i	−0.384742	−	0.666392i
$381$		0			0
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	15.0000			0.766464			0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000			0.766464			0.383232	+	0.923652i	$0.374811\pi$
$384$		0			0
$385$	−4.50000	+	23.3827i	−0.229341	+	1.19169i
$386$	−14.0000			−0.712581
$387$		0			0
$388$	0.500000	+	0.866025i	0.0253837	+	0.0439658i
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$		0			0
$391$	4.50000	+	7.79423i	0.227575	+	0.394171i
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	−12.0000	−	20.7846i	−0.603786	−	1.04579i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$	−3.50000	+	6.06218i	−0.175439	+	0.303870i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−27.0000			−1.34832			−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000			−1.34832			−0.674158	+	0.738587i	$0.735493\pi$
$402$		0			0
$403$	−20.0000			−0.996271
$404$	−1.50000	+	2.59808i	−0.0746278	+	0.129259i
$405$		0			0
$406$	1.50000	−	7.79423i	0.0744438	−	0.386821i
$407$	10.5000	−	18.1865i	0.520466	−	0.901473i
$408$		0			0
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$	13.5000	−	23.3827i	0.666717	−	1.15479i
$411$		0			0
$412$	−2.50000	+	4.33013i	−0.123166	+	0.213330i
$413$	24.0000	+	20.7846i	1.18096	+	1.02274i
$414$		0			0
$415$	4.50000	−	7.79423i	0.220896	−	0.382604i
$416$	−5.00000			−0.245145
$417$		0			0
$418$	−15.0000			−0.733674
$419$	−1.50000	−	2.59808i	−0.0732798	−	0.126924i	0.827057	−	0.562118i	$-0.190013\pi$
$419$	−1.50000	−	2.59808i	−0.0732798	−	0.126924i	−0.900337	+	0.435194i	$0.856680\pi$
$420$		0			0
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	−0.189740	−	0.981834i	$-0.560764\pi$
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	0.945163	−	0.326598i	$-0.105902\pi$
$422$	2.50000	−	4.33013i	0.121698	−	0.210787i
$423$		0			0
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	5.00000	−	1.73205i	0.241967	−	0.0838198i
$428$	−7.50000	−	12.9904i	−0.362526	−	0.627914i
$429$		0			0
$430$	−33.0000			−1.59140
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	0.827636	−	0.561266i	$-0.189685\pi$
$431$	−1.50000	−	2.59808i	−0.0722525	−	0.125145i	−0.899888	+	0.436121i	$0.856352\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−2.00000	+	10.3923i	−0.0960031	+	0.498847i
$435$		0			0
$436$	−7.00000			−0.335239
$437$	−7.50000	+	12.9904i	−0.358774	+	0.621414i
$438$		0			0
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	15.0000			0.713477
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$	22.5000	−	38.9711i	1.06660	−	1.84741i
$446$	−17.0000			−0.804973
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−13.5000	−	23.3827i	−0.635690	−	1.10105i
$452$	−15.0000			−0.705541
$453$		0			0
$454$	−4.50000	−	7.79423i	−0.211195	−	0.365801i
$455$	37.5000	−	12.9904i	1.75803	−	0.608998i
$456$		0			0
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	0.922695	+	0.385530i	$0.125981\pi$
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	−0.127469	+	0.991843i	$0.540685\pi$
$458$	8.50000	+	14.7224i	0.397179	+	0.687934i
$459$		0			0
$460$	−4.50000	+	7.79423i	−0.209814	+	0.363408i
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	−0.910546	−	0.413407i	$-0.864339\pi$
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	0.0972525	−	0.995260i	$-0.468995\pi$
$464$	3.00000			0.139272
$465$		0			0
$466$	27.0000			1.25075
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	−0.898642	−	0.438682i	$-0.855446\pi$
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	0.829231	+	0.558906i	$0.188779\pi$
$468$		0			0
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−16.5000	+	28.5788i	−0.758671	+	1.31406i
$474$		0			0
$475$	−10.0000	+	17.3205i	−0.458831	+	0.794719i
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$		0			0
$478$	−13.5000	+	23.3827i	−0.617476	+	1.06950i
$479$	9.00000			0.411220			0.205610	−	0.978634i	$-0.434082\pi$
$479$	9.00000			0.411220			0.205610	+	0.978634i	$0.434082\pi$
$480$		0			0
$481$	−35.0000			−1.59586
$482$	11.5000	+	19.9186i	0.523811	+	0.907267i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$		0			0
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	0.967632	+	0.252367i	$0.0812090\pi$
$487$	15.5000	+	26.8468i	0.702372	+	1.21654i	−0.265260	+	0.964177i	$0.585458\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$		0			0
$490$	−3.00000	−	20.7846i	−0.135526	−	0.938953i
$491$	−19.5000	−	33.7750i	−0.880023	−	1.52424i	−0.851314	−	0.524656i	$-0.824194\pi$
$491$	−19.5000	−	33.7750i	−0.880023	−	1.52424i	−0.0287085	−	0.999588i	$-0.509139\pi$
$492$		0			0
$493$	−9.00000			−0.405340
$494$	12.5000	+	21.6506i	0.562402	+	0.974108i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	11.0000			0.492428			0.246214	−	0.969216i	$-0.420813\pi$
$499$	11.0000			0.492428			0.246214	+	0.969216i	$0.420813\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$		0			0
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	4.50000	+	7.79423i	0.200049	+	0.346496i
$507$		0			0
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	27.0000			1.19675			0.598377	−	0.801215i	$-0.295813\pi$
$509$	27.0000			1.19675			0.598377	+	0.801215i	$0.295813\pi$
$510$		0			0
$511$	27.5000	−	9.52628i	1.21653	−	0.421418i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$	15.0000			0.660979
$516$		0			0
$517$		0			0
$518$	−3.50000	+	18.1865i	−0.153781	+	0.799070i
$519$		0			0
$520$	7.50000	+	12.9904i	0.328897	+	0.569666i
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$		0			0
$523$	3.50000	−	6.06218i	0.153044	−	0.265081i	−0.779301	−	0.626650i	$-0.784426\pi$
$523$	3.50000	−	6.06218i	0.153044	−	0.265081i	0.932345	+	0.361569i	$0.117759\pi$
$524$	1.50000	−	2.59808i	0.0655278	−	0.113497i
$525$		0			0
$526$	4.50000	+	7.79423i	0.196209	+	0.339845i
$527$	12.0000			0.522728
$528$		0			0
$529$	−14.0000			−0.608696
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$		0			0
$532$	12.5000	−	4.33013i	0.541944	−	0.187735i
$533$	−22.5000	+	38.9711i	−0.974583	+	1.68803i
$534$		0			0
$535$	−22.5000	+	38.9711i	−0.972760	+	1.68487i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$		0			0
$538$	−10.5000	+	18.1865i	−0.452687	+	0.784077i
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$	13.0000			0.558398
$543$		0			0
$544$	3.00000			0.128624
$545$	10.5000	+	18.1865i	0.449771	+	0.779026i
$546$		0			0
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	−0.959320	−	0.282321i	$-0.908896\pi$
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	0.724157	+	0.689635i	$0.242229\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$		0			0
$550$	6.00000	+	10.3923i	0.255841	+	0.443129i
$551$	−7.50000	−	12.9904i	−0.319511	−	0.553409i
$552$		0			0
$553$	20.0000	−	6.92820i	0.850487	−	0.294617i
$554$	−3.50000	−	6.06218i	−0.148701	−	0.257557i
$555$		0			0
$556$	5.00000			0.212047
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	55.0000			2.32625
$560$	7.50000	−	2.59808i	0.316933	−	0.109789i
$561$		0			0
$562$	3.00000			0.126547
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	22.5000	+	38.9711i	0.946582	+	1.63953i
$566$	−8.00000			−0.336265
$567$		0			0
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	15.0000			0.627182
$573$		0			0
$574$	18.0000	+	15.5885i	0.751305	+	0.650650i
$575$	12.0000			0.500435
$576$		0			0
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	8.00000			0.332756
$579$		0			0
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$	6.00000	+	5.19615i	0.248922	+	0.215573i
$582$		0			0
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	5.50000	+	9.52628i	0.227592	+	0.394200i
$585$		0			0
$586$	13.5000	−	23.3827i	0.557680	−	0.965930i
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	0.293640	+	0.955916i	$0.405133\pi$
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	−0.974668	+	0.223659i	$0.928200\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$	36.0000			1.48210
$591$		0			0
$592$	−7.00000			−0.287698
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$		0			0
$595$	−22.5000	+	7.79423i	−0.922410	+	0.319532i
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$		0			0
$598$	7.50000	−	12.9904i	0.306698	−	0.531216i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$	5.50000	−	28.5788i	0.224163	−	1.16479i
$603$		0			0
$604$	−5.50000	+	9.52628i	−0.223792	+	0.387619i
$605$	−6.00000			−0.243935
$606$		0			0
$607$	−43.0000			−1.74532			−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000			−1.74532			−0.872658	+	0.488332i	$0.837606\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$		0			0
$610$	3.00000	−	5.19615i	0.121466	−	0.210386i
$611$		0			0
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$	1.50000	−	7.79423i	0.0604367	−	0.314038i
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	−19.0000			−0.763674			−0.381837	−	0.924230i	$-0.624709\pi$
$619$	−19.0000			−0.763674			−0.381837	+	0.924230i	$0.624709\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$		0			0
$622$	−24.0000			−0.962312
$623$	30.0000	+	25.9808i	1.20192	+	1.04090i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	21.0000			0.837325
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$		0			0
$634$	−15.0000	+	25.9808i	−0.595726	+	1.03183i
$635$	−48.0000			−1.90482
$636$		0			0
$637$	5.00000	+	34.6410i	0.198107	+	1.37253i
$638$	−9.00000			−0.356313
$639$		0			0
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	45.0000			1.77739			0.888697	−	0.458496i	$-0.151612\pi$
$641$	45.0000			1.77739			0.888697	+	0.458496i	$0.151612\pi$
$642$		0			0
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	−0.996379	−	0.0850262i	$-0.972903\pi$
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	0.424555	−	0.905402i	$-0.360431\pi$
$644$	−6.00000	−	5.19615i	−0.236433	−	0.204757i
$645$		0			0
$646$	−7.50000	−	12.9904i	−0.295084	−	0.511100i
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	0.835033	−	0.550200i	$-0.185449\pi$
$647$	−1.50000	−	2.59808i	−0.0589711	−	0.102141i	−0.894004	+	0.448059i	$0.852115\pi$
$648$		0			0
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$	10.0000	−	17.3205i	0.392232	−	0.679366i
$651$		0			0
$652$	−8.50000	−	14.7224i	−0.332886	−	0.576575i
$653$	−9.00000			−0.352197			−0.176099	−	0.984373i	$-0.556348\pi$
$653$	−9.00000			−0.352197			−0.176099	+	0.984373i	$0.556348\pi$
$654$		0			0
$655$	−9.00000			−0.351659
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$		0			0
$658$		0			0
$659$	19.5000	−	33.7750i	0.759612	−	1.31569i	−0.183436	−	0.983032i	$-0.558722\pi$
$659$	19.5000	−	33.7750i	0.759612	−	1.31569i	0.943049	−	0.332655i	$-0.107945\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	10.0000	−	17.3205i	0.388661	−	0.673181i
$663$		0			0
$664$	−1.50000	+	2.59808i	−0.0582113	+	0.100825i
$665$	−30.0000	−	25.9808i	−1.16335	−	1.00749i
$666$		0			0
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$	−3.00000			−0.116073
$669$		0			0
$670$	12.0000			0.463600
$671$	−3.00000	−	5.19615i	−0.115814	−	0.200595i
$672$		0			0
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$	−12.5000	+	21.6506i	−0.481482	+	0.833951i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	2.00000	+	1.73205i	0.0767530	+	0.0664700i
$680$	−4.50000	−	7.79423i	−0.172567	−	0.298895i
$681$		0			0
$682$	12.0000			0.459504
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	−0.987275	−	0.159022i	$-0.949166\pi$
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	0.355920	−	0.934516i	$-0.384168\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	11.0000			0.419371
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$		0			0
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−7.50000	−	12.9904i	−0.284491	−	0.492753i
$696$		0			0
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$	−5.00000			−0.189253
$699$		0			0
$700$	−8.00000	−	6.92820i	−0.302372	−	0.261861i
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	17.5000	+	30.3109i	0.660025	+	1.14320i
$704$	3.00000			0.113067
$705$		0			0
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$	−1.50000	+	7.79423i	−0.0564133	+	0.293132i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$	−7.50000	+	12.9904i	−0.281074	+	0.486835i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$	−22.5000	−	38.9711i	−0.841452	−	1.45744i
$716$	−3.00000			−0.112115
$717$		0			0
$718$	15.0000			0.559795
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	−0.230823	−	0.972996i	$-0.574142\pi$
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	0.958051	−	0.286599i	$-0.0925247\pi$
$720$		0			0
$721$	−2.50000	+	12.9904i	−0.0931049	+	0.483787i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	−2.50000	+	4.33013i	−0.0927199	+	0.160596i	−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−2.50000	+	4.33013i	−0.0927199	+	0.160596i	0.815935	+	0.578144i	$0.196223\pi$
$728$	−12.5000	+	4.33013i	−0.463281	+	0.160485i
$729$		0			0
$730$	16.5000	−	28.5788i	0.610692	−	1.05775i
$731$	−33.0000			−1.22055
$732$		0			0
$733$	41.0000			1.51437			0.757185	−	0.653201i	$-0.226574\pi$
$733$	41.0000			1.51437			0.757185	+	0.653201i	$0.226574\pi$
$734$	−0.500000	−	0.866025i	−0.0184553	−	0.0319656i
$735$		0			0
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$	10.5000	+	18.1865i	0.385988	+	0.668550i
$741$		0			0
$742$	6.00000	+	5.19615i	0.220267	+	0.190757i
$743$	1.50000	+	2.59808i	0.0550297	+	0.0953142i	0.892228	−	0.451585i	$-0.149141\pi$
$743$	1.50000	+	2.59808i	0.0550297	+	0.0953142i	−0.837198	+	0.546899i	$0.815808\pi$
$744$		0			0
$745$	9.00000			0.329734
$746$	8.50000	+	14.7224i	0.311207	+	0.539027i
$747$		0			0
$748$	−9.00000			−0.329073
$749$	−30.0000	−	25.9808i	−1.09618	−	0.949316i
$750$		0			0
$751$	29.0000			1.05823			0.529113	−	0.848552i	$-0.322525\pi$
$751$	29.0000			1.05823			0.529113	+	0.848552i	$0.322525\pi$
$752$		0			0
$753$		0			0
$754$	7.50000	+	12.9904i	0.273134	+	0.473082i
$755$	33.0000			1.20099
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−8.00000	−	13.8564i	−0.290573	−	0.503287i
$759$		0			0
$760$	7.50000	−	12.9904i	0.272054	−	0.471211i
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$		0			0
$763$	−17.5000	+	6.06218i	−0.633543	+	0.219466i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	7.50000	+	12.9904i	0.270986	+	0.469362i
$767$	−60.0000			−2.16647
$768$		0			0
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	0.874900	−	0.484304i	$-0.160927\pi$
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	−0.856869	+	0.515534i	$0.827594\pi$
$770$	−22.5000	+	7.79423i	−0.810844	+	0.280885i
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$		0			0
$775$	8.00000	−	13.8564i	0.287368	−	0.497737i
$776$	−0.500000	+	0.866025i	−0.0179490	+	0.0310885i
$777$		0			0
$778$	−4.50000	−	7.79423i	−0.161333	−	0.279437i
$779$	45.0000			1.61229
$780$		0			0
$781$		0			0
$782$	−4.50000	+	7.79423i	−0.160920	+	0.278721i
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	−21.0000	+	36.3731i	−0.749522	+	1.29821i
$786$		0			0
$787$	−22.0000	+	38.1051i	−0.784215	+	1.35830i	0.145251	+	0.989395i	$0.453601\pi$
$787$	−22.0000	+	38.1051i	−0.784215	+	1.35830i	−0.929467	+	0.368906i	$0.879732\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		0			0
$790$	12.0000	−	20.7846i	0.426941	−	0.739483i
$791$	−37.5000	+	12.9904i	−1.33335	+	0.461885i
$792$		0			0
$793$	−5.00000	+	8.66025i	−0.177555	+	0.307535i
$794$	−29.0000			−1.02917
$795$		0			0
$796$	−7.00000			−0.248108
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$		0			0
$799$		0			0
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$		0			0
$802$	−13.5000	−	23.3827i	−0.476702	−	0.825671i
$803$	−16.5000	−	28.5788i	−0.582272	−	1.00853i
$804$		0			0
$805$	−4.50000	+	23.3827i	−0.158604	+	0.824131i
$806$	−10.0000	−	17.3205i	−0.352235	−	0.610089i
$807$		0			0
$808$	−3.00000			−0.105540
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	7.50000	−	2.59808i	0.263198	−	0.0911746i
$813$		0			0
$814$	21.0000			0.736050
$815$	−25.5000	+	44.1673i	−0.893226	+	1.54711i
$816$		0			0
$817$	−27.5000	−	47.6314i	−0.962103	−	1.66641i
$818$	22.0000			0.769212
$819$		0			0
$820$	27.0000			0.942881
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.761056	−	0.648686i	$-0.775319\pi$
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.181250	−	0.983437i	$-0.558014\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	−5.00000			−0.174183
$825$		0			0
$826$	−6.00000	+	31.1769i	−0.208767	+	1.08478i
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$		0			0
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	−0.964107	−	0.265513i	$-0.914459\pi$
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	0.252113	−	0.967698i	$-0.418875\pi$
$830$	9.00000			0.312395
$831$		0			0
$832$	−2.50000	−	4.33013i	−0.0866719	−	0.150120i
$833$	−3.00000	−	20.7846i	−0.103944	−	0.720144i
$834$		0			0
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	−7.50000	−	12.9904i	−0.259393	−	0.449282i
$837$		0			0
$838$	1.50000	−	2.59808i	0.0518166	−	0.0897491i
$839$	−19.5000	+	33.7750i	−0.673215	+	1.16604i	0.303773	+	0.952745i	$0.401754\pi$
$839$	−19.5000	+	33.7750i	−0.673215	+	1.16604i	−0.976987	+	0.213298i	$0.931580\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	31.0000			1.06833
$843$		0			0
$844$	5.00000			0.172107
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$	1.00000	−	5.19615i	0.0343604	−	0.178542i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$		0			0
$850$	−6.00000	+	10.3923i	−0.205798	+	0.356453i
$851$	10.5000	−	18.1865i	0.359935	−	0.623426i
$852$		0			0
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	−0.974055	−	0.226313i	$-0.927333\pi$
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	0.683020	+	0.730400i	$0.260666\pi$
$854$	4.00000	+	3.46410i	0.136877	+	0.118539i
$855$		0			0
$856$	7.50000	−	12.9904i	0.256345	−	0.444002i
$857$	33.0000			1.12726			0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000			1.12726			0.563629	+	0.826028i	$0.309405\pi$
$858$		0			0
$859$	11.0000			0.375315			0.187658	−	0.982235i	$-0.439910\pi$
$859$	11.0000			0.375315			0.187658	+	0.982235i	$0.439910\pi$
$860$	−16.5000	−	28.5788i	−0.562645	−	0.974530i
$861$		0			0
$862$	1.50000	−	2.59808i	0.0510902	−	0.0884908i
$863$	7.50000	−	12.9904i	0.255303	−	0.442198i	−0.709675	−	0.704529i	$-0.751158\pi$
$863$	7.50000	−	12.9904i	0.255303	−	0.442198i	0.964978	+	0.262332i	$0.0844915\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$		0			0
$868$	−10.0000	+	3.46410i	−0.339422	+	0.117579i
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	−20.0000			−0.677674
$872$	−3.50000	−	6.06218i	−0.118525	−	0.205291i
$873$		0			0
$874$	−15.0000			−0.507383
$875$	1.50000	−	7.79423i	0.0507093	−	0.263493i
$876$		0			0
$877$	−43.0000			−1.45201			−0.726003	−	0.687691i	$-0.758624\pi$
$877$	−43.0000			−1.45201			−0.726003	+	0.687691i	$0.758624\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$		0			0
$880$	−4.50000	−	7.79423i	−0.151695	−	0.262743i
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	7.50000	+	12.9904i	0.252252	+	0.436914i
$885$		0			0
$886$		0			0
$887$	39.0000			1.30949			0.654746	−	0.755849i	$-0.272776\pi$
$887$	39.0000			1.30949			0.654746	+	0.755849i	$0.272776\pi$
$888$		0			0
$889$	8.00000	−	41.5692i	0.268311	−	1.39419i
$890$	45.0000			1.50840
$891$		0			0
$892$	−8.50000	−	14.7224i	−0.284601	−	0.492943i
$893$		0			0
$894$		0			0
$895$	4.50000	+	7.79423i	0.150418	+	0.260532i
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$		0			0
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$		0			0
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$	13.5000	−	23.3827i	0.449501	−	0.778558i
$903$		0			0
$904$	−7.50000	−	12.9904i	−0.249446	−	0.432054i
$905$	−30.0000			−0.997234
$906$		0			0
$907$	17.0000			0.564476			0.282238	−	0.959344i	$-0.408923\pi$
$907$	17.0000			0.564476			0.282238	+	0.959344i	$0.408923\pi$
$908$	4.50000	−	7.79423i	0.149338	−	0.258661i
$909$		0			0
$910$	30.0000	+	25.9808i	0.994490	+	0.861254i
$911$	4.50000	−	7.79423i	0.149092	−	0.258234i	−0.781800	−	0.623529i	$-0.785698\pi$
$911$	4.50000	−	7.79423i	0.149092	−	0.258234i	0.930892	+	0.365295i	$0.119032\pi$
$912$		0			0
$913$	4.50000	−	7.79423i	0.148928	−	0.257951i
$914$	−17.0000	+	29.4449i	−0.562310	+	0.973950i
$915$		0			0
$916$	−8.50000	+	14.7224i	−0.280848	+	0.486443i
$917$	1.50000	−	7.79423i	0.0495344	−	0.257388i
$918$		0			0
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	0.500000	−	0.866025i	0.0164935	−	0.0285675i	0.874154	+	0.485648i	$0.161416\pi$
$920$	−9.00000			−0.296721
$921$		0			0
$922$	9.00000			0.296399
$923$		0			0
$924$		0			0
$925$	14.0000	−	24.2487i	0.460317	−	0.797293i
$926$	17.5000	−	30.3109i	0.575086	−	0.996078i
$927$		0			0
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$	27.5000	−	21.6506i	0.901276	−	0.709571i
$932$	13.5000	+	23.3827i	0.442207	+	0.765925i
$933$		0			0
$934$	−3.00000			−0.0981630
$935$	13.5000	+	23.3827i	0.441497	+	0.764696i
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	−2.00000	+	10.3923i	−0.0653023	+	0.339321i
$939$		0			0
$940$		0			0
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.0290288	−	0.999579i	$-0.490759\pi$
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.851146	−	0.524929i	$-0.175908\pi$
$942$		0			0
$943$	−13.5000	−	23.3827i	−0.439620	−	0.761445i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−33.0000			−1.07292
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$	−27.5000	+	47.6314i	−0.892688	+	1.54618i
$950$	−20.0000			−0.648886
$951$		0			0
$952$	7.50000	−	2.59808i	0.243076	−	0.0842041i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	18.0000	+	31.1769i	0.582466	+	1.00886i
$956$	−27.0000			−0.873242
$957$		0			0
$958$	4.50000	+	7.79423i	0.145388	+	0.251820i
$959$	1.50000	−	7.79423i	0.0484375	−	0.251689i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−17.5000	−	30.3109i	−0.564223	−	0.977262i
$963$		0			0
$964$	−11.5000	+	19.9186i	−0.370390	+	0.641534i
$965$	−21.0000	+	36.3731i	−0.676014	+	1.17089i
$966$		0			0
$967$	24.5000	+	42.4352i	0.787867	+	1.36463i	0.927271	+	0.374390i	$0.122148\pi$
$967$	24.5000	+	42.4352i	0.787867	+	1.36463i	−0.139404	+	0.990236i	$0.544519\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$	3.00000			0.0963242
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	−0.997150	−	0.0754473i	$-0.975962\pi$
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	0.563914	+	0.825833i	$0.309295\pi$
$972$		0			0
$973$	12.5000	−	4.33013i	0.400732	−	0.138817i
$974$	−15.5000	+	26.8468i	−0.496652	+	0.860227i
$975$		0			0
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$		0			0
$979$	22.5000	−	38.9711i	0.719103	−	1.24552i
$980$	16.5000	−	12.9904i	0.527073	−	0.414963i
$981$		0			0
$982$	19.5000	−	33.7750i	0.622270	−	1.07780i
$983$	21.0000			0.669796			0.334898	−	0.942254i	$-0.391298\pi$
$983$	21.0000			0.669796			0.334898	+	0.942254i	$0.391298\pi$
$984$		0			0
$985$	18.0000			0.573528
$986$	−4.50000	−	7.79423i	−0.143309	−	0.248219i
$987$		0			0
$988$	−12.5000	+	21.6506i	−0.397678	+	0.688798i
$989$	−16.5000	+	28.5788i	−0.524669	+	0.908754i
$990$		0			0
$991$	−14.5000	−	25.1147i	−0.460608	−	0.797796i	0.538384	−	0.842700i	$-0.319035\pi$
$991$	−14.5000	−	25.1147i	−0.460608	−	0.797796i	−0.998991	+	0.0449040i	$0.985702\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$		0			0
$995$	10.5000	+	18.1865i	0.332872	+	0.576552i
$996$		0			0
$997$	41.0000			1.29848			0.649242	−	0.760582i	$-0.275086\pi$
$997$	41.0000			1.29848			0.649242	+	0.760582i	$0.275086\pi$
$998$	5.50000	+	9.52628i	0.174099	+	0.301549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.h.b.289.1		2
3.2	odd	2		126.2.h.a.79.1	yes	2
4.3	odd	2		3024.2.t.f.289.1		2
7.2	even	3		2646.2.f.e.883.1		2
7.3	odd	6		2646.2.e.e.2125.1		2
7.4	even	3		378.2.e.a.235.1		2
7.5	odd	6		2646.2.f.i.883.1		2
7.6	odd	2		2646.2.h.f.667.1		2
9.2	odd	6		1134.2.g.d.163.1		2
9.4	even	3		378.2.e.a.37.1		2
9.5	odd	6		126.2.e.b.121.1	yes	2
9.7	even	3		1134.2.g.f.163.1		2
12.11	even	2		1008.2.t.c.961.1		2
21.2	odd	6		882.2.f.e.295.1		2
21.5	even	6		882.2.f.a.295.1		2
21.11	odd	6		126.2.e.b.25.1	✓	2
21.17	even	6		882.2.e.h.655.1		2
21.20	even	2		882.2.h.e.79.1		2
28.11	odd	6		3024.2.q.a.2881.1		2
36.23	even	6		1008.2.q.e.625.1		2
36.31	odd	6		3024.2.q.a.2305.1		2
63.2	odd	6		7938.2.a.r.1.1		1
63.4	even	3	inner	378.2.h.b.361.1		2
63.5	even	6		882.2.f.a.589.1		2
63.11	odd	6		1134.2.g.d.487.1		2
63.13	odd	6		2646.2.e.e.1549.1		2
63.16	even	3		7938.2.a.o.1.1		1
63.23	odd	6		882.2.f.e.589.1		2
63.25	even	3		1134.2.g.f.487.1		2
63.31	odd	6		2646.2.h.f.361.1		2
63.32	odd	6		126.2.h.a.67.1	yes	2
63.40	odd	6		2646.2.f.i.1765.1		2
63.41	even	6		882.2.e.h.373.1		2
63.47	even	6		7938.2.a.bd.1.1		1
63.58	even	3		2646.2.f.e.1765.1		2
63.59	even	6		882.2.h.e.67.1		2
63.61	odd	6		7938.2.a.c.1.1		1
84.11	even	6		1008.2.q.e.529.1		2
252.67	odd	6		3024.2.t.f.1873.1		2
252.95	even	6		1008.2.t.c.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	21.11	odd	6
126.2.e.b.121.1	yes	2	9.5	odd	6
126.2.h.a.67.1	yes	2	63.32	odd	6
126.2.h.a.79.1	yes	2	3.2	odd	2
378.2.e.a.37.1		2	9.4	even	3
378.2.e.a.235.1		2	7.4	even	3
378.2.h.b.289.1		2	1.1	even	1	trivial
378.2.h.b.361.1		2	63.4	even	3	inner
882.2.e.h.373.1		2	63.41	even	6
882.2.e.h.655.1		2	21.17	even	6
882.2.f.a.295.1		2	21.5	even	6
882.2.f.a.589.1		2	63.5	even	6
882.2.f.e.295.1		2	21.2	odd	6
882.2.f.e.589.1		2	63.23	odd	6
882.2.h.e.67.1		2	63.59	even	6
882.2.h.e.79.1		2	21.20	even	2
1008.2.q.e.529.1		2	84.11	even	6
1008.2.q.e.625.1		2	36.23	even	6
1008.2.t.c.193.1		2	252.95	even	6
1008.2.t.c.961.1		2	12.11	even	2
1134.2.g.d.163.1		2	9.2	odd	6
1134.2.g.d.487.1		2	63.11	odd	6
1134.2.g.f.163.1		2	9.7	even	3
1134.2.g.f.487.1		2	63.25	even	3
2646.2.e.e.1549.1		2	63.13	odd	6
2646.2.e.e.2125.1		2	7.3	odd	6
2646.2.f.e.883.1		2	7.2	even	3
2646.2.f.e.1765.1		2	63.58	even	3
2646.2.f.i.883.1		2	7.5	odd	6
2646.2.f.i.1765.1		2	63.40	odd	6
2646.2.h.f.361.1		2	63.31	odd	6
2646.2.h.f.667.1		2	7.6	odd	2
3024.2.q.a.2305.1		2	36.31	odd	6
3024.2.q.a.2881.1		2	28.11	odd	6
3024.2.t.f.289.1		2	4.3	odd	2
3024.2.t.f.1873.1		2	252.67	odd	6
7938.2.a.c.1.1		1	63.61	odd	6
7938.2.a.o.1.1		1	63.16	even	3
7938.2.a.r.1.1		1	63.2	odd	6
7938.2.a.bd.1.1		1	63.47	even	6

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +3.00000 q^{11} +(-2.50000 - 4.33013i) q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +3.00000 q^{23} +4.00000 q^{25} +(2.50000 - 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(-1.50000 + 7.79423i) q^{35} +(3.50000 - 6.06218i) q^{37} -5.00000 q^{38} -3.00000 q^{40} +(-4.50000 - 7.79423i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-6.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +5.00000 q^{52} +(-1.50000 - 2.59808i) q^{53} +9.00000 q^{55} +(0.500000 - 2.59808i) q^{56} -3.00000 q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-7.50000 - 12.9904i) q^{65} +(2.00000 - 3.46410i) q^{67} -3.00000 q^{68} +(-7.50000 + 2.59808i) q^{70} +(-5.50000 - 9.52628i) q^{73} +7.00000 q^{74} +(-2.50000 - 4.33013i) q^{76} +(-1.50000 + 7.79423i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(4.50000 - 7.79423i) q^{82} +(1.50000 - 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} -11.0000 q^{86} -3.00000 q^{88} +(7.50000 - 12.9904i) q^{89} +(12.5000 - 4.33013i) q^{91} +(-1.50000 + 2.59808i) q^{92} +(-7.50000 + 12.9904i) q^{95} +(0.500000 - 0.866025i) q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 6 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + 6 * q^5 - q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + 6 q^{5} - q^{7} - 2 q^{8} + 3 q^{10} + 6 q^{11} - 5 q^{13} - 5 q^{14} - q^{16} + 3 q^{17} - 5 q^{19} - 3 q^{20} + 3 q^{22} + 6 q^{23} + 8 q^{25} + 5 q^{26} - 4 q^{28} - 3 q^{29} + 4 q^{31} + q^{32} - 3 q^{34} - 3 q^{35} + 7 q^{37} - 10 q^{38} - 6 q^{40} - 9 q^{41} - 11 q^{43} - 3 q^{44} + 3 q^{46} - 13 q^{49} + 4 q^{50} + 10 q^{52} - 3 q^{53} + 18 q^{55} + q^{56} - 6 q^{58} + 12 q^{59} - 2 q^{61} + 8 q^{62} + 2 q^{64} - 15 q^{65} + 4 q^{67} - 6 q^{68} - 15 q^{70} - 11 q^{73} + 14 q^{74} - 5 q^{76} - 3 q^{77} - 8 q^{79} - 3 q^{80} + 9 q^{82} + 3 q^{83} + 9 q^{85} - 22 q^{86} - 6 q^{88} + 15 q^{89} + 25 q^{91} - 3 q^{92} - 15 q^{95} + q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 6 * q^5 - q^7 - 2 * q^8 + 3 * q^10 + 6 * q^11 - 5 * q^13 - 5 * q^14 - q^16 + 3 * q^17 - 5 * q^19 - 3 * q^20 + 3 * q^22 + 6 * q^23 + 8 * q^25 + 5 * q^26 - 4 * q^28 - 3 * q^29 + 4 * q^31 + q^32 - 3 * q^34 - 3 * q^35 + 7 * q^37 - 10 * q^38 - 6 * q^40 - 9 * q^41 - 11 * q^43 - 3 * q^44 + 3 * q^46 - 13 * q^49 + 4 * q^50 + 10 * q^52 - 3 * q^53 + 18 * q^55 + q^56 - 6 * q^58 + 12 * q^59 - 2 * q^61 + 8 * q^62 + 2 * q^64 - 15 * q^65 + 4 * q^67 - 6 * q^68 - 15 * q^70 - 11 * q^73 + 14 * q^74 - 5 * q^76 - 3 * q^77 - 8 * q^79 - 3 * q^80 + 9 * q^82 + 3 * q^83 + 9 * q^85 - 22 * q^86 - 6 * q^88 + 15 * q^89 + 25 * q^91 - 3 * q^92 - 15 * q^95 + q^97 - 2 * q^98

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