LMFDB - Embedded newform 378.2.e.a.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(37,378)]

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([2, 2]))

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

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

chi := DirichletCharacter("378.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.e (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:	$1$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	378.235
Dual form			378.2.e.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} +(2.00000 - 1.73205i) q^{14} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} -4.00000 q^{31} -1.00000 q^{32} +(-1.50000 + 2.59808i) q^{34} +(-1.50000 - 7.79423i) q^{35} +(3.50000 + 6.06218i) q^{37} +(2.50000 + 4.33013i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(1.50000 - 2.59808i) q^{46} +(1.00000 - 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-2.50000 - 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +(1.50000 - 2.59808i) q^{58} -12.0000 q^{59} +2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +15.0000 q^{65} -4.00000 q^{67} +(1.50000 - 2.59808i) q^{68} +(1.50000 + 7.79423i) q^{70} +(-5.50000 + 9.52628i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.50000 - 4.33013i) q^{76} +(7.50000 + 2.59808i) q^{77} +8.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(4.50000 + 7.79423i) q^{82} +(1.50000 - 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} +(5.50000 - 9.52628i) q^{86} +(1.50000 + 2.59808i) q^{88} +(7.50000 + 12.9904i) q^{89} +(12.5000 + 4.33013i) q^{91} +(-1.50000 + 2.59808i) q^{92} +15.0000 q^{95} +(0.500000 - 0.866025i) q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8	$ 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} + 3 q^{10} - 3 q^{11} - 5 q^{13} + 4 q^{14} + 2 q^{16} + 3 q^{17} - 5 q^{19} - 3 q^{20} + 3 q^{22} - 3 q^{23} - 4 q^{25} + 5 q^{26} - 4 q^{28} - 3 q^{29} - 8 q^{31} - 2 q^{32} - 3 q^{34} - 3 q^{35} + 7 q^{37} + 5 q^{38} + 3 q^{40} - 9 q^{41} - 11 q^{43} - 3 q^{44} + 3 q^{46} + 2 q^{49} + 4 q^{50} - 5 q^{52} - 3 q^{53} + 18 q^{55} + 4 q^{56} + 3 q^{58} - 24 q^{59} + 4 q^{61} + 8 q^{62} + 2 q^{64} + 30 q^{65} - 8 q^{67} + 3 q^{68} + 3 q^{70} - 11 q^{73} - 7 q^{74} - 5 q^{76} + 15 q^{77} + 16 q^{79} - 3 q^{80} + 9 q^{82} + 3 q^{83} + 9 q^{85} + 11 q^{86} + 3 q^{88} + 15 q^{89} + 25 q^{91} - 3 q^{92} + 30 q^{95} + q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8 + 3 * q^10 - 3 * q^11 - 5 * q^13 + 4 * q^14 + 2 * q^16 + 3 * q^17 - 5 * q^19 - 3 * q^20 + 3 * q^22 - 3 * q^23 - 4 * q^25 + 5 * q^26 - 4 * q^28 - 3 * q^29 - 8 * q^31 - 2 * q^32 - 3 * q^34 - 3 * q^35 + 7 * q^37 + 5 * q^38 + 3 * q^40 - 9 * q^41 - 11 * q^43 - 3 * q^44 + 3 * q^46 + 2 * q^49 + 4 * q^50 - 5 * q^52 - 3 * q^53 + 18 * q^55 + 4 * q^56 + 3 * q^58 - 24 * q^59 + 4 * q^61 + 8 * q^62 + 2 * q^64 + 30 * q^65 - 8 * q^67 + 3 * q^68 + 3 * q^70 - 11 * q^73 - 7 * q^74 - 5 * q^76 + 15 * q^77 + 16 * q^79 - 3 * q^80 + 9 * q^82 + 3 * q^83 + 9 * q^85 + 11 * q^86 + 3 * q^88 + 15 * q^89 + 25 * q^91 - 3 * q^92 + 30 * q^95 + q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		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	$-0.410544\pi$
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$		0			0
$16$	1.00000			0.250000
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	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
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000			−0.176777
$33$		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	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	2.50000	+	4.33013i	0.405554	+	0.702439i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−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			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$		0			0
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	15.0000			1.86052
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	1.50000	+	7.79423i	0.179284	+	0.931589i
$71$		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	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$		0			0
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	7.50000	+	2.59808i	0.854704	+	0.296078i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−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
$86$	5.50000	−	9.52628i	0.593080	−	1.02725i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$		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
$95$	15.0000			1.53897
$96$		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
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$	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	−0.958952	−	0.283567i	$-0.908482\pi$
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	0.233900	−	0.972261i	$-0.424851\pi$
$108$		0			0
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$	−9.00000			−0.858116
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	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
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$		0			0
$118$	12.0000			1.10469
$119$	1.50000	+	7.79423i	0.137505	+	0.714496i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−2.00000			−0.181071
$123$		0			0
$124$	−4.00000			−0.359211
$125$	−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	$0.751253\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−15.0000			−1.31559
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	−0.793028	−	0.609185i	$-0.791497\pi$
$131$	1.50000	−	2.59808i	0.131056	−	0.226995i	0.924084	+	0.382190i	$0.124830\pi$
$132$		0			0
$133$	12.5000	+	4.33013i	1.08389	+	0.375470i
$134$	4.00000			0.345547
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		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	$0.901346\pi$
$140$	−1.50000	−	7.79423i	−0.126773	−	0.658733i
$141$		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
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	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
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−8.00000			−0.636446
$159$		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	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	0.313304	−	0.949653i	$-0.398564\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	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
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$		0			0
$175$	10.0000	+	3.46410i	0.755929	+	0.261861i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$		0			0
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	1.50000	−	2.59808i	0.112115	−	0.194189i	−0.804508	−	0.593942i	$-0.797571\pi$
$179$	1.50000	−	2.59808i	0.112115	−	0.194189i	0.916623	+	0.399753i	$0.130904\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−12.5000	−	4.33013i	−0.926562	−	0.320970i
$183$		0			0
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	−21.0000			−1.54395
$186$		0			0
$187$	−9.00000			−0.658145
$188$		0			0
$189$		0			0
$190$	−15.0000			−1.08821
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	−0.500000	+	0.866025i	−0.0358979	+	0.0621770i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	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	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		0			0
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	−1.50000	−	7.79423i	−0.105279	−	0.547048i
$204$		0			0
$205$	27.0000			1.88576
$206$	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	$0.888391\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		0			0
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	−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
$220$	9.00000			0.606780
$221$	−15.0000			−1.00901
$222$		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
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$		0			0
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	0.435653	+	0.900115i	$0.356518\pi$
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	−0.997349	+	0.0727709i	$0.976816\pi$
$230$	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	0.846383	+	0.532574i	$0.178775\pi$
$233$	13.5000	+	23.3827i	0.884414	+	1.53185i	0.0380310	+	0.999277i	$0.487891\pi$
$234$		0			0
$235$		0			0
$236$	−12.0000			−0.781133
$237$		0			0
$238$	−1.50000	−	7.79423i	−0.0972306	−	0.505225i
$239$	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
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$		0			0
$244$	2.00000			0.128037
$245$	16.5000	+	12.9904i	1.05415	+	0.829925i
$246$		0			0
$247$	−12.5000	+	21.6506i	−0.795356	+	1.37760i
$248$	4.00000			0.254000
$249$		0			0
$250$	3.00000			0.189737
$251$	−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
$254$	16.0000			1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$	−17.5000	−	6.06218i	−1.08740	−	0.376685i
$260$	15.0000			0.930261
$261$		0			0
$262$	−1.50000	+	2.59808i	−0.0926703	+	0.160510i
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$	−12.5000	−	4.33013i	−0.766424	−	0.265497i
$267$		0			0
$268$	−4.00000			−0.244339
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$		0			0
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	0.993082	−	0.117426i	$-0.0374643\pi$
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	−0.598235	+	0.801321i	$0.704131\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$		0			0
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$	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
$283$	8.00000			0.475551			0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000			0.475551			0.237775	+	0.971320i	$0.423582\pi$
$284$		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
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$		0			0
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	−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
$299$	15.0000			0.867472
$300$		0			0
$301$	−5.50000	−	28.5788i	−0.317015	−	1.64726i
$302$	5.50000	+	9.52628i	0.316489	+	0.548176i
$303$		0			0
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	−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	$0.794649\pi$
$308$	7.50000	+	2.59808i	0.427352	+	0.148039i
$309$		0			0
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	8.00000			0.450035
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$		0			0
$319$	9.00000			0.503903
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		0			0
$322$	1.50000	+	7.79423i	0.0835917	+	0.434355i
$323$	−15.0000			−0.834622
$324$		0			0
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$	8.50000	+	14.7224i	0.470771	+	0.815400i
$327$		0			0
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	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	$0.594914\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	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
$346$	6.00000			0.322562
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$		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
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$		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	0.993207	−	0.116358i	$-0.0371219\pi$
$359$	7.50000	+	12.9904i	0.395835	+	0.685606i	−0.597372	+	0.801964i	$0.703789\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	10.0000			0.525588
$363$		0			0
$364$	12.5000	+	4.33013i	0.655178	+	0.226960i
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$		0			0
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	0.878780	−	0.477227i	$-0.158358\pi$
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	−0.852680	+	0.522433i	$0.825025\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$		0			0
$370$	21.0000			1.09174
$371$	−1.50000	−	7.79423i	−0.0778761	−	0.404656i
$372$		0			0
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	−0.997697	−	0.0678218i	$-0.978395\pi$
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	0.557584	+	0.830120i	$0.311728\pi$
$374$	9.00000			0.465379
$375$		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	$0.634797\pi$
$380$	15.0000			0.769484
$381$		0			0
$382$	12.0000			0.613973
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$		0			0
$385$	−18.0000	+	15.5885i	−0.917365	+	0.794461i
$386$	−14.0000			−0.712581
$387$		0			0
$388$	0.500000	−	0.866025i	0.0253837	−	0.0439658i
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$		0			0
$391$	4.50000	+	7.79423i	0.227575	+	0.394171i
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$		0			0
$394$	−6.00000			−0.302276
$395$	−12.0000	+	20.7846i	−0.603786	+	1.04579i
$396$		0			0
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	−0.957839	−	0.287307i	$-0.907240\pi$
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	0.230105	−	0.973166i	$-0.426093\pi$
$398$	−3.50000	+	6.06218i	−0.175439	+	0.303870i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	−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
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$	−27.0000			−1.33343
$411$		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
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$		0			0
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$	−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
$425$	−12.0000			−0.582086
$426$		0			0
$427$	−4.00000	+	3.46410i	−0.193574	+	0.167640i
$428$	−7.50000	−	12.9904i	−0.362526	−	0.627914i
$429$		0			0
$430$	16.5000	+	28.5788i	0.795701	+	1.37819i
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	−0.899888	−	0.436121i	$-0.856352\pi$
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	0.827636	+	0.561266i	$0.189685\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−8.00000	+	6.92820i	−0.384012	+	0.332564i
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	15.0000			0.717547
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	15.0000			0.713477
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$	−45.0000			−2.13320
$446$	8.50000	−	14.7224i	0.402487	−	0.697127i
$447$		0			0
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	−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
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$		0			0
$454$	−4.50000	−	7.79423i	−0.211195	−	0.365801i
$455$	−30.0000	+	25.9808i	−1.40642	+	1.21800i
$456$		0			0
$457$	−34.0000			−1.59045			−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000			−1.59045			−0.795226	+	0.606313i	$0.792648\pi$
$458$	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	$-0.468995\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	−13.5000	−	23.3827i	−0.625375	−	1.08318i
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	0.829231	−	0.558906i	$-0.188779\pi$
$467$	−1.50000	−	2.59808i	−0.0694117	−	0.120225i	−0.898642	+	0.438682i	$0.855446\pi$
$468$		0			0
$469$	8.00000	−	6.92820i	0.369406	−	0.319915i
$470$		0			0
$471$		0			0
$472$	12.0000			0.552345
$473$	33.0000			1.51734
$474$		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
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	0.744717	−	0.667381i	$-0.232585\pi$
$479$	−4.50000	−	7.79423i	−0.205610	−	0.356127i	−0.950327	+	0.311253i	$0.899251\pi$
$480$		0			0
$481$	17.5000	−	30.3109i	0.797931	−	1.38206i
$482$	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	−0.265260	−	0.964177i	$-0.585458\pi$
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	0.967632	−	0.252367i	$-0.0812090\pi$
$488$	−2.00000			−0.0905357
$489$		0			0
$490$	−16.5000	−	12.9904i	−0.745394	−	0.586846i
$491$	−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
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$	12.5000	−	21.6506i	0.562402	−	0.974108i
$495$		0			0
$496$	−4.00000			−0.179605
$497$		0			0
$498$		0			0
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	0.716258	+	0.697835i	$0.245853\pi$
$500$	−3.00000			−0.134164
$501$		0			0
$502$	12.0000			0.535586
$503$	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
$506$	−9.00000			−0.400099
$507$		0			0
$508$	−16.0000			−0.709885
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	0.394684	+	0.918817i	$0.370854\pi$
$509$	−13.5000	+	23.3827i	−0.598377	+	1.03642i	−0.993061	+	0.117602i	$0.962479\pi$
$510$		0			0
$511$	−5.50000	−	28.5788i	−0.243306	−	1.26425i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$	−7.50000	−	12.9904i	−0.330489	−	0.572425i
$516$		0			0
$517$		0			0
$518$	17.5000	+	6.06218i	0.768906	+	0.266357i
$519$		0			0
$520$	−15.0000			−0.657794
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	−0.831295	−	0.555831i	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$		0			0
$523$	3.50000	+	6.06218i	0.153044	+	0.265081i	0.932345	−	0.361569i	$-0.117759\pi$
$523$	3.50000	+	6.06218i	0.153044	+	0.265081i	−0.779301	+	0.626650i	$0.784426\pi$
$524$	1.50000	−	2.59808i	0.0655278	−	0.113497i
$525$		0			0
$526$	4.50000	+	7.79423i	0.196209	+	0.339845i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	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
$535$	45.0000			1.94552
$536$	4.00000			0.172774
$537$		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	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	−6.50000	−	11.2583i	−0.279199	−	0.483587i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	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
$551$	15.0000			0.639021
$552$		0			0
$553$	−16.0000	+	13.8564i	−0.680389	+	0.589234i
$554$	−3.50000	−	6.06218i	−0.148701	−	0.257557i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	−0.896053	−	0.443947i	$-0.853578\pi$
$557$	−1.50000	+	2.59808i	−0.0635570	+	0.110084i	0.832496	+	0.554031i	$0.186911\pi$
$558$		0			0
$559$	55.0000			2.32625
$560$	−1.50000	−	7.79423i	−0.0633866	−	0.329366i
$561$		0			0
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	12.0000			0.505740			0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000			0.505740			0.252870	+	0.967500i	$0.418626\pi$
$564$		0			0
$565$	−45.0000			−1.89316
$566$	−8.00000			−0.336265
$567$		0			0
$568$		0			0
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	−7.50000	+	12.9904i	−0.313591	+	0.543155i
$573$		0			0
$574$	−22.5000	−	7.79423i	−0.939132	−	0.325325i
$575$	12.0000			0.500435
$576$		0			0
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$	1.50000	+	7.79423i	0.0622305	+	0.323359i
$582$		0			0
$583$	9.00000			0.372742
$584$	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
$590$	−18.0000	+	31.1769i	−0.741048	+	1.28353i
$591$		0			0
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	0.565792	−	0.824548i	$-0.308570\pi$
$593$	−10.5000	−	18.1865i	−0.431183	−	0.746831i	−0.996976	+	0.0777165i	$0.975237\pi$
$594$		0			0
$595$	−22.5000	−	7.79423i	−0.922410	−	0.319532i
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$		0			0
$598$	−15.0000			−0.613396
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		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
$605$	3.00000	+	5.19615i	0.121967	+	0.211254i
$606$		0			0
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	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	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$	28.0000			1.12999
$615$		0			0
$616$	−7.50000	−	2.59808i	−0.302184	−	0.104679i
$617$	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
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$		0			0
$622$	−24.0000			−0.962312
$623$	−37.5000	−	12.9904i	−1.50241	−	0.520449i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−14.0000			−0.559553
$627$		0			0
$628$	14.0000			0.558661
$629$	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	$0.449096\pi$
$632$	−8.00000			−0.318223
$633$		0			0
$634$	30.0000			1.19145
$635$	24.0000	−	41.5692i	0.952411	−	1.64962i
$636$		0			0
$637$	−32.5000	+	12.9904i	−1.28770	+	0.514698i
$638$	−9.00000			−0.356313
$639$		0			0
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.0472793	−	0.998882i	$-0.515055\pi$
$642$		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	$-0.360431\pi$
$644$	−1.50000	−	7.79423i	−0.0591083	−	0.307136i
$645$		0			0
$646$	15.0000			0.590167
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	−0.894004	−	0.448059i	$-0.852115\pi$
$647$	−1.50000	+	2.59808i	−0.0589711	+	0.102141i	0.835033	+	0.550200i	$0.185449\pi$
$648$		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
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	0.940541	+	0.339680i	$0.110319\pi$
$654$		0			0
$655$	4.50000	+	7.79423i	0.175830	+	0.304546i
$656$	−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
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	−20.0000			−0.777322
$663$		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
$668$	1.50000	+	2.59808i	0.0580367	+	0.100523i
$669$		0			0
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	−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
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$		0			0
$679$	0.500000	+	2.59808i	0.0191882	+	0.0997050i
$680$	−4.50000	−	7.79423i	−0.172567	−	0.298895i
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−16.5000	+	28.5788i	−0.631355	+	1.09354i	0.355920	+	0.934516i	$0.384168\pi$
$683$	−16.5000	+	28.5788i	−0.631355	+	1.09354i	−0.987275	+	0.159022i	$0.949166\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$	−10.0000	−	15.5885i	−0.381802	−	0.595170i
$687$		0			0
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$	15.0000			0.571454
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	15.0000			0.568982
$696$		0			0
$697$	−27.0000			−1.02270
$698$	2.50000	−	4.33013i	0.0946264	−	0.163898i
$699$		0			0
$700$	10.0000	+	3.46410i	0.377964	+	0.130931i
$701$	−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
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$	7.50000	+	2.59808i	0.282067	+	0.0977107i
$708$		0			0
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		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
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$		0			0
$718$	−7.50000	−	12.9904i	−0.279898	−	0.484797i
$719$	19.5000	+	33.7750i	0.727227	+	1.25959i	0.958051	+	0.286599i	$0.0925247\pi$
$719$	19.5000	+	33.7750i	0.727227	+	1.25959i	−0.230823	+	0.972996i	$0.574142\pi$
$720$		0			0
$721$	−2.50000	−	12.9904i	−0.0931049	−	0.483787i
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$		0			0
$724$	−10.0000			−0.371647
$725$	12.0000			0.445669
$726$		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
$731$	16.5000	+	28.5788i	0.610275	+	1.05703i
$732$		0			0
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	0.187096	+	0.982342i	$0.440092\pi$
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	−0.944281	+	0.329141i	$0.893241\pi$
$734$	−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	0.00311943	+	0.999995i	$0.499007\pi$
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	−0.867581	+	0.497296i	$0.834326\pi$
$740$	−21.0000			−0.771975
$741$		0			0
$742$	1.50000	+	7.79423i	0.0550667	+	0.286135i
$743$	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
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$	8.50000	−	14.7224i	0.311207	−	0.539027i
$747$		0			0
$748$	−9.00000			−0.329073
$749$	37.5000	+	12.9904i	1.37022	+	0.474658i
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$		0			0
$753$		0			0
$754$	−15.0000			−0.546268
$755$	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	$0.418116\pi$
$758$	16.0000			0.581146
$759$		0			0
$760$	−15.0000			−0.544107
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$		0			0
$763$	3.50000	+	18.1865i	0.126709	+	0.658397i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$		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	$0.827594\pi$
$770$	18.0000	−	15.5885i	0.648675	−	0.561769i
$771$		0			0
$772$	14.0000			0.503871
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$		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
$779$	−22.5000	+	38.9711i	−0.806146	+	1.39629i
$780$		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
$787$	44.0000			1.56843			0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000			1.56843			0.784215	+	0.620489i	$0.213066\pi$
$788$	6.00000			0.213741
$789$		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
$794$	14.5000	+	25.1147i	0.514586	+	0.891289i
$795$		0			0
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$	−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
$803$	33.0000			1.16454
$804$		0			0
$805$	22.5000	+	7.79423i	0.793021	+	0.274710i
$806$	−10.0000	−	17.3205i	−0.352235	−	0.610089i
$807$		0			0
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	−0.287670	−	0.957730i	$-0.592880\pi$
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	0.973253	−	0.229736i	$-0.0737862\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−1.50000	−	7.79423i	−0.0526397	−	0.273524i
$813$		0			0
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	51.0000			1.78645
$816$		0			0
$817$	55.0000			1.92421
$818$	22.0000			0.769212
$819$		0			0
$820$	27.0000			0.942881
$821$	54.0000			1.88461			0.942306	−	0.334751i	$-0.108652\pi$
$821$	54.0000			1.88461			0.942306	+	0.334751i	$0.108652\pi$
$822$		0			0
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$	2.50000	−	4.33013i	0.0870916	−	0.150847i
$825$		0			0
$826$	−24.0000	+	20.7846i	−0.835067	+	0.723189i
$827$	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	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$		0			0
$832$	−2.50000	−	4.33013i	−0.0866719	−	0.150120i
$833$	−16.5000	−	12.9904i	−0.571691	−	0.450090i
$834$		0			0
$835$	−9.00000			−0.311458
$836$	−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
$842$	−15.5000	+	26.8468i	−0.534165	+	0.925201i
$843$		0			0
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	−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
$850$	12.0000			0.411597
$851$	−21.0000			−0.719871
$852$		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
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$		0			0
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	−0.944469	−	0.328601i	$-0.893423\pi$
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	0.756811	+	0.653633i	$0.226756\pi$
$860$	−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	0.964978	−	0.262332i	$-0.0844915\pi$
$863$	7.50000	+	12.9904i	0.255303	+	0.442198i	−0.709675	+	0.704529i	$0.751158\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	−14.0000			−0.475739
$867$		0			0
$868$	8.00000	−	6.92820i	0.271538	−	0.235159i
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	−3.50000	+	6.06218i	−0.118525	+	0.205291i
$873$		0			0
$874$	−15.0000			−0.507383
$875$	6.00000	−	5.19615i	0.202837	−	0.175662i
$876$		0			0
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	−0.232556	−	0.972583i	$-0.574709\pi$
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	0.958560	−	0.284892i	$-0.0919577\pi$
$878$	−8.00000			−0.269987
$879$		0			0
$880$	9.00000			0.303390
$881$	−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	$0.521440\pi$
$884$	−15.0000			−0.504505
$885$		0			0
$886$		0			0
$887$	−19.5000	+	33.7750i	−0.654746	+	1.13405i	0.327212	+	0.944951i	$0.393891\pi$
$887$	−19.5000	+	33.7750i	−0.654746	+	1.13405i	−0.981957	+	0.189102i	$0.939442\pi$
$888$		0			0
$889$	32.0000	−	27.7128i	1.07325	−	0.929458i
$890$	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
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$		0			0
$898$	30.0000			1.00111
$899$	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
$905$	15.0000	−	25.9808i	0.498617	−	0.863630i
$906$		0			0
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$	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
$913$	−9.00000			−0.297857
$914$	34.0000			1.12462
$915$		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	0.874154	−	0.485648i	$-0.161416\pi$
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	−0.857661	+	0.514216i	$0.828083\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$		0			0
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$		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
$929$	18.0000			0.590561			0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000			0.590561			0.295280	+	0.955411i	$0.404587\pi$
$930$		0			0
$931$	−32.5000	+	12.9904i	−1.06514	+	0.425743i
$932$	13.5000	+	23.3827i	0.442207	+	0.765925i
$933$		0			0
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$	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	$0.687422\pi$
$938$	−8.00000	+	6.92820i	−0.261209	+	0.226214i
$939$		0			0
$940$		0			0
$941$	−54.0000			−1.76035			−0.880175	−	0.474650i	$-0.842575\pi$
$941$	−54.0000			−1.76035			−0.880175	+	0.474650i	$0.842575\pi$
$942$		0			0
$943$	27.0000			0.879241
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−33.0000			−1.07292
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	55.0000			1.78538
$950$	10.0000	−	17.3205i	0.324443	−	0.561951i
$951$		0			0
$952$	−1.50000	−	7.79423i	−0.0486153	−	0.252612i
$953$	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
$956$	13.5000	+	23.3827i	0.436621	+	0.756250i
$957$		0			0
$958$	4.50000	+	7.79423i	0.145388	+	0.251820i
$959$	−7.50000	−	2.59808i	−0.242188	−	0.0838963i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−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	$0.544519\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		0			0
$970$	−1.50000	−	2.59808i	−0.0481621	−	0.0834192i
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	0.563914	−	0.825833i	$-0.309295\pi$
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	−0.997150	+	0.0754473i	$0.975962\pi$
$972$		0			0
$973$	12.5000	+	4.33013i	0.400732	+	0.138817i
$974$	−15.5000	+	26.8468i	−0.496652	+	0.860227i
$975$		0			0
$976$	2.00000			0.0640184
$977$	−6.00000			−0.191957			−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000			−0.191957			−0.0959785	+	0.995383i	$0.530598\pi$
$978$		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
$983$	−10.5000	−	18.1865i	−0.334898	−	0.580060i	0.648567	−	0.761157i	$-0.275369\pi$
$983$	−10.5000	−	18.1865i	−0.334898	−	0.580060i	−0.983465	+	0.181097i	$0.942035\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−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	−0.998991	−	0.0449040i	$-0.985702\pi$
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	0.538384	+	0.842700i	$0.319035\pi$
$992$	4.00000			0.127000
$993$		0			0
$994$		0			0
$995$	10.5000	+	18.1865i	0.332872	+	0.576552i
$996$		0			0
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$	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.e.a.235.1		2
3.2	odd	2		126.2.e.b.25.1	✓	2
4.3	odd	2		3024.2.q.a.2881.1		2
7.2	even	3		378.2.h.b.289.1		2
7.3	odd	6		2646.2.f.i.883.1		2
7.4	even	3		2646.2.f.e.883.1		2
7.5	odd	6		2646.2.h.f.667.1		2
7.6	odd	2		2646.2.e.e.2125.1		2
9.2	odd	6		1134.2.g.d.487.1		2
9.4	even	3		378.2.h.b.361.1		2
9.5	odd	6		126.2.h.a.67.1	yes	2
9.7	even	3		1134.2.g.f.487.1		2
12.11	even	2		1008.2.q.e.529.1		2
21.2	odd	6		126.2.h.a.79.1	yes	2
21.5	even	6		882.2.h.e.79.1		2
21.11	odd	6		882.2.f.e.295.1		2
21.17	even	6		882.2.f.a.295.1		2
21.20	even	2		882.2.e.h.655.1		2
28.23	odd	6		3024.2.t.f.289.1		2
36.23	even	6		1008.2.t.c.193.1		2
36.31	odd	6		3024.2.t.f.1873.1		2
63.2	odd	6		1134.2.g.d.163.1		2
63.4	even	3		2646.2.f.e.1765.1		2
63.5	even	6		882.2.e.h.373.1		2
63.11	odd	6		7938.2.a.r.1.1		1
63.13	odd	6		2646.2.h.f.361.1		2
63.16	even	3		1134.2.g.f.163.1		2
63.23	odd	6		126.2.e.b.121.1	yes	2
63.25	even	3		7938.2.a.o.1.1		1
63.31	odd	6		2646.2.f.i.1765.1		2
63.32	odd	6		882.2.f.e.589.1		2
63.38	even	6		7938.2.a.bd.1.1		1
63.40	odd	6		2646.2.e.e.1549.1		2
63.41	even	6		882.2.h.e.67.1		2
63.52	odd	6		7938.2.a.c.1.1		1
63.58	even	3	inner	378.2.e.a.37.1		2
63.59	even	6		882.2.f.a.589.1		2
84.23	even	6		1008.2.t.c.961.1		2
252.23	even	6		1008.2.q.e.625.1		2
252.247	odd	6		3024.2.q.a.2305.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	3.2	odd	2
126.2.e.b.121.1	yes	2	63.23	odd	6
126.2.h.a.67.1	yes	2	9.5	odd	6
126.2.h.a.79.1	yes	2	21.2	odd	6
378.2.e.a.37.1		2	63.58	even	3	inner
378.2.e.a.235.1		2	1.1	even	1	trivial
378.2.h.b.289.1		2	7.2	even	3
378.2.h.b.361.1		2	9.4	even	3
882.2.e.h.373.1		2	63.5	even	6
882.2.e.h.655.1		2	21.20	even	2
882.2.f.a.295.1		2	21.17	even	6
882.2.f.a.589.1		2	63.59	even	6
882.2.f.e.295.1		2	21.11	odd	6
882.2.f.e.589.1		2	63.32	odd	6
882.2.h.e.67.1		2	63.41	even	6
882.2.h.e.79.1		2	21.5	even	6
1008.2.q.e.529.1		2	12.11	even	2
1008.2.q.e.625.1		2	252.23	even	6
1008.2.t.c.193.1		2	36.23	even	6
1008.2.t.c.961.1		2	84.23	even	6
1134.2.g.d.163.1		2	63.2	odd	6
1134.2.g.d.487.1		2	9.2	odd	6
1134.2.g.f.163.1		2	63.16	even	3
1134.2.g.f.487.1		2	9.7	even	3
2646.2.e.e.1549.1		2	63.40	odd	6
2646.2.e.e.2125.1		2	7.6	odd	2
2646.2.f.e.883.1		2	7.4	even	3
2646.2.f.e.1765.1		2	63.4	even	3
2646.2.f.i.883.1		2	7.3	odd	6
2646.2.f.i.1765.1		2	63.31	odd	6
2646.2.h.f.361.1		2	63.13	odd	6
2646.2.h.f.667.1		2	7.5	odd	6
3024.2.q.a.2305.1		2	252.247	odd	6
3024.2.q.a.2881.1		2	4.3	odd	2
3024.2.t.f.289.1		2	28.23	odd	6
3024.2.t.f.1873.1		2	36.31	odd	6
7938.2.a.c.1.1		1	63.52	odd	6
7938.2.a.o.1.1		1	63.25	even	3
7938.2.a.r.1.1		1	63.11	odd	6
7938.2.a.bd.1.1		1	63.38	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-2.50000 - 4.33013i) q^{13} +(2.00000 - 1.73205i) q^{14} +1.00000 q^{16} +(1.50000 - 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.00000 + 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} -4.00000 q^{31} -1.00000 q^{32} +(-1.50000 + 2.59808i) q^{34} +(-1.50000 - 7.79423i) q^{35} +(3.50000 + 6.06218i) q^{37} +(2.50000 + 4.33013i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(-1.50000 - 2.59808i) q^{44} +(1.50000 - 2.59808i) q^{46} +(1.00000 - 6.92820i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-2.50000 - 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +(1.50000 - 2.59808i) q^{58} -12.0000 q^{59} +2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +15.0000 q^{65} -4.00000 q^{67} +(1.50000 - 2.59808i) q^{68} +(1.50000 + 7.79423i) q^{70} +(-5.50000 + 9.52628i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.50000 - 4.33013i) q^{76} +(7.50000 + 2.59808i) q^{77} +8.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(4.50000 + 7.79423i) q^{82} +(1.50000 - 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} +(5.50000 - 9.52628i) q^{86} +(1.50000 + 2.59808i) q^{88} +(7.50000 + 12.9904i) q^{89} +(12.5000 + 4.33013i) q^{91} +(-1.50000 + 2.59808i) q^{92} +15.0000 q^{95} +(0.500000 - 0.866025i) q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8	\( 2 q - 2 q^{2} + 2 q^{4} - 3 q^{5} - 4 q^{7} - 2 q^{8} + 3 q^{10} - 3 q^{11} - 5 q^{13} + 4 q^{14} + 2 q^{16} + 3 q^{17} - 5 q^{19} - 3 q^{20} + 3 q^{22} - 3 q^{23} - 4 q^{25} + 5 q^{26} - 4 q^{28} - 3 q^{29} - 8 q^{31} - 2 q^{32} - 3 q^{34} - 3 q^{35} + 7 q^{37} + 5 q^{38} + 3 q^{40} - 9 q^{41} - 11 q^{43} - 3 q^{44} + 3 q^{46} + 2 q^{49} + 4 q^{50} - 5 q^{52} - 3 q^{53} + 18 q^{55} + 4 q^{56} + 3 q^{58} - 24 q^{59} + 4 q^{61} + 8 q^{62} + 2 q^{64} + 30 q^{65} - 8 q^{67} + 3 q^{68} + 3 q^{70} - 11 q^{73} - 7 q^{74} - 5 q^{76} + 15 q^{77} + 16 q^{79} - 3 q^{80} + 9 q^{82} + 3 q^{83} + 9 q^{85} + 11 q^{86} + 3 q^{88} + 15 q^{89} + 25 q^{91} - 3 q^{92} + 30 q^{95} + q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - 3 * q^5 - 4 * q^7 - 2 * q^8 + 3 * q^10 - 3 * q^11 - 5 * q^13 + 4 * q^14 + 2 * q^16 + 3 * q^17 - 5 * q^19 - 3 * q^20 + 3 * q^22 - 3 * q^23 - 4 * q^25 + 5 * q^26 - 4 * q^28 - 3 * q^29 - 8 * q^31 - 2 * q^32 - 3 * q^34 - 3 * q^35 + 7 * q^37 + 5 * q^38 + 3 * q^40 - 9 * q^41 - 11 * q^43 - 3 * q^44 + 3 * q^46 + 2 * q^49 + 4 * q^50 - 5 * q^52 - 3 * q^53 + 18 * q^55 + 4 * q^56 + 3 * q^58 - 24 * q^59 + 4 * q^61 + 8 * q^62 + 2 * q^64 + 30 * q^65 - 8 * q^67 + 3 * q^68 + 3 * q^70 - 11 * q^73 - 7 * q^74 - 5 * q^76 + 15 * q^77 + 16 * q^79 - 3 * q^80 + 9 * q^82 + 3 * q^83 + 9 * q^85 + 11 * q^86 + 3 * q^88 + 15 * q^89 + 25 * q^91 - 3 * q^92 + 30 * q^95 + q^97 - 2 * q^98

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