LMFDB - Embedded newform 2646.2.e.e.2125.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1549,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, 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("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.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:	$21.1284163748$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2125.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.2125
Dual form			2646.2.e.e.1549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−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	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	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
$28$		0			0
$29$	−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	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$		0			0
$36$		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	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		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
$49$		0			0
$50$	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
$56$		0			0
$57$		0			0
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	12.0000			1.56227			0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000			1.56227			0.781133	+	0.624364i	$0.214642\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	−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
$70$		0			0
$71$		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	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$		0			0
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$		0			0
$78$		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	−0.936530	−	0.350588i	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$		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	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$		0			0
$91$		0			0
$92$	−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	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	−0.716173	−	0.697923i	$-0.754108\pi$
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	0.962505	+	0.271263i	$0.0874412\pi$
$104$	−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
$112$		0			0
$113$	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
$119$		0			0
$120$		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	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		0			0
$133$		0			0
$134$	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	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		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
$154$		0			0
$155$	6.00000	−	10.3923i	0.481932	−	0.834730i
$156$		0			0
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	−8.00000			−0.636446
$159$		0			0
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$		0			0
$162$		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	0.802135	−	0.597143i	$-0.203697\pi$
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$168$		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	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		0			0
$175$		0			0
$176$	−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	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$		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
$196$		0			0
$197$	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	$-0.913142\pi$
$199$	−3.50000	+	6.06218i	−0.248108	+	0.429736i	0.714893	+	0.699234i	$0.246476\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		0			0
$202$	−1.50000	−	2.59808i	−0.105540	−	0.182800i
$203$		0			0
$204$		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
$217$		0			0
$218$	−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	$-0.640586\pi$
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	0.996645	−	0.0818447i	$-0.0260811\pi$
$224$		0			0
$225$		0			0
$226$	−7.50000	−	12.9904i	−0.498893	−	0.864107i
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$		0			0
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	−0.435653	−	0.900115i	$-0.643482\pi$
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	0.997349	−	0.0727709i	$-0.0231842\pi$
$230$	−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
$238$		0			0
$239$	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	$0.0988773\pi$
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	−0.211360	+	0.977408i	$0.567789\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$		0			0
$244$	−2.00000			−0.128037
$245$		0			0
$246$		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	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		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	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$		0			0
$259$		0			0
$260$	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
$266$		0			0
$267$		0			0
$268$	−4.00000			−0.244339
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$		0			0
$271$	−6.50000	−	11.2583i	−0.394847	−	0.683895i	0.598235	−	0.801321i	$-0.295869\pi$
$271$	−6.50000	−	11.2583i	−0.394847	−	0.683895i	−0.993082	+	0.117426i	$0.962536\pi$
$272$	−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
$280$		0			0
$281$	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	$-0.576418\pi$
$283$	−8.00000			−0.475551			−0.237775	+	0.971320i	$0.576418\pi$
$284$		0			0
$285$		0			0
$286$	−7.50000	+	12.9904i	−0.443484	+	0.768137i
$287$		0			0
$288$		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	$0.122568\pi$
$293$	13.5000	+	23.3827i	0.788678	+	1.36603i	−0.138098	+	0.990419i	$0.544099\pi$
$294$		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
$301$		0			0
$302$	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	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	−14.0000			−0.791327			−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000			−0.791327			−0.395663	+	0.918396i	$0.629485\pi$
$314$	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
$322$		0			0
$323$	−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
$343$		0			0
$344$	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	−0.791325	−	0.611396i	$-0.790608\pi$
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	0.925147	+	0.379610i	$0.123942\pi$
$350$		0			0
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	0.960574	−	0.278024i	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$		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
$364$		0			0
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$		0			0
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	0.852680	−	0.522433i	$-0.174975\pi$
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	−0.878780	+	0.477227i	$0.841642\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$		0			0
$370$	−21.0000			−1.09174
$371$		0			0
$372$		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	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$		0			0
$386$	−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
$392$		0			0
$393$		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	$0.0927599\pi$
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	−0.230105	+	0.973166i	$0.573907\pi$
$398$	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
$406$		0			0
$407$	10.5000	−	18.1865i	0.520466	−	0.901473i
$408$		0			0
$409$	22.0000			1.08783			0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000			1.08783			0.543915	+	0.839140i	$0.316941\pi$
$410$	−27.0000			−1.33343
$411$		0			0
$412$	2.50000	−	4.33013i	0.123166	−	0.213330i
$413$		0			0
$414$		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	0.900337	−	0.435194i	$-0.143320\pi$
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	−0.827057	+	0.562118i	$0.809987\pi$
$420$		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
$427$		0			0
$428$	−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	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		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	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	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
$448$		0			0
$449$	−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
$455$		0			0
$456$		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	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		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	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$		0			0
$469$		0			0
$470$		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
$476$		0			0
$477$		0			0
$478$	−13.5000	−	23.3827i	−0.617476	−	1.06950i
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	0.950327	−	0.311253i	$-0.100749\pi$
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	−0.744717	+	0.667381i	$0.767415\pi$
$480$		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
$490$		0			0
$491$	−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	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		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	$-0.629146\pi$
$509$	13.5000	−	23.3827i	0.598377	−	1.03642i	0.993061	−	0.117602i	$-0.0375208\pi$
$510$		0			0
$511$		0			0
$512$	−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
$518$		0			0
$519$		0			0
$520$	−15.0000			−0.657794
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	−0.897011	−	0.442007i	$-0.854267\pi$
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	0.831295	+	0.555831i	$0.187600\pi$
$522$		0			0
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	0.779301	−	0.626650i	$-0.215574\pi$
$523$	−3.50000	−	6.06218i	−0.153044	−	0.265081i	−0.932345	+	0.361569i	$0.882241\pi$
$524$	−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
$532$		0			0
$533$	−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
$539$		0			0
$540$		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
$553$		0			0
$554$	−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
$560$		0			0
$561$		0			0
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		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
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	5.50000	−	9.52628i	0.228968	−	0.396584i	−0.728535	−	0.685009i	$-0.759798\pi$
$577$	5.50000	−	9.52628i	0.228968	−	0.396584i	0.957503	+	0.288425i	$0.0931316\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	4.50000	+	7.79423i	0.186852	+	0.323638i
$581$		0			0
$582$		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	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$		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	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$		0			0
$595$		0			0
$596$	−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	−0.876043	−	0.482233i	$-0.839826\pi$
$601$	−0.500000	+	0.866025i	−0.0203954	+	0.0353259i	0.855648	+	0.517559i	$0.173159\pi$
$602$		0			0
$603$		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	$0.504272\pi$
$607$	−21.5000	+	37.2391i	−0.872658	+	1.51149i	−0.859237	+	0.511578i	$0.829061\pi$
$608$	−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
$616$		0			0
$617$	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	0.609488	−	0.792796i	$-0.291375\pi$
$619$	−9.50000	−	16.4545i	−0.381837	−	0.661361i	−0.991325	+	0.131434i	$0.958042\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$		0			0
$622$	24.0000			0.962312
$623$		0			0
$624$		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
$637$		0			0
$638$	−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	$0.0270974\pi$
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	−0.424555	+	0.905402i	$0.639569\pi$
$644$		0			0
$645$		0			0
$646$	15.0000			0.590167
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$		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	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	−20.0000			−0.777322
$663$		0			0
$664$	1.50000	−	2.59808i	0.0582113	−	0.100825i
$665$		0			0
$666$		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	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$		0			0
$680$	−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
$686$		0			0
$687$		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	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$	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
$700$		0			0
$701$	−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
$707$		0			0
$708$		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	$-0.907475\pi$
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	0.230823	−	0.972996i	$-0.425858\pi$
$720$		0			0
$721$		0			0
$722$	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	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	0.908655	+	0.417548i	$0.137111\pi$
$728$		0			0
$729$		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	$-0.559908\pi$
$733$	20.5000	−	35.5070i	0.757185	−	1.31148i	0.944281	−	0.329141i	$-0.106759\pi$
$734$	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
$742$		0			0
$743$	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
$749$		0			0
$750$		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	−0.891932	−	0.452170i	$-0.850650\pi$
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	0.837557	+	0.546350i	$0.183983\pi$
$762$		0			0
$763$		0			0
$764$	−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	0.856869	−	0.515534i	$-0.172406\pi$
$769$	−0.500000	−	0.866025i	−0.0180305	−	0.0312297i	−0.874900	+	0.484304i	$0.839073\pi$
$770$		0			0
$771$		0			0
$772$	14.0000			0.503871
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	−0.990721	−	0.135910i	$-0.956604\pi$
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	0.613062	+	0.790034i	$0.289937\pi$
$774$		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
$784$		0			0
$785$	−21.0000	+	36.3731i	−0.749522	+	1.29821i
$786$		0			0
$787$	−44.0000			−1.56843			−0.784215	−	0.620489i	$-0.786934\pi$
$787$	−44.0000			−1.56843			−0.784215	+	0.620489i	$0.786934\pi$
$788$	6.00000			0.213741
$789$		0			0
$790$	−12.0000	+	20.7846i	−0.426941	+	0.739483i
$791$		0			0
$792$		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	0.999687	−	0.0249984i	$-0.00795805\pi$
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	−0.521493	+	0.853256i	$0.674625\pi$
$798$		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
$805$		0			0
$806$	−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	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		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
$826$		0			0
$827$	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	$-0.581125\pi$
$829$	20.5000	−	35.5070i	0.711994	−	1.23321i	0.964107	−	0.265513i	$-0.0855412\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$		0			0
$832$	2.50000	+	4.33013i	0.0866719	+	0.150120i
$833$		0			0
$834$		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	$-0.598246\pi$
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	0.976987	−	0.213298i	$-0.0684204\pi$
$840$		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
$847$		0			0
$848$	−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	−0.683020	−	0.730400i	$-0.739334\pi$
$853$	8.50000	−	14.7224i	0.291034	−	0.504086i	0.974055	+	0.226313i	$0.0726672\pi$
$854$		0			0
$855$		0			0
$856$	7.50000	+	12.9904i	0.256345	+	0.444002i
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	0.997176	+	0.0751033i	$0.0239287\pi$
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	−0.433546	+	0.901131i	$0.642738\pi$
$858$		0			0
$859$	5.50000	−	9.52628i	0.187658	−	0.325032i	−0.756811	−	0.653633i	$-0.773244\pi$
$859$	5.50000	−	9.52628i	0.187658	−	0.325032i	0.944469	+	0.328601i	$0.106577\pi$
$860$	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
$868$		0			0
$869$	−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
$875$		0			0
$876$		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	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		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	$-0.606109\pi$
$887$	19.5000	−	33.7750i	0.654746	−	1.13405i	0.981957	−	0.189102i	$-0.0605577\pi$
$888$		0			0
$889$		0			0
$890$	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
$896$		0			0
$897$		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
$910$		0			0
$911$	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
$917$		0			0
$918$		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	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$		0			0
$931$		0			0
$932$	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	$-0.312578\pi$
$937$	34.0000			1.11073			0.555366	+	0.831606i	$0.312578\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	54.0000			1.76035			0.880175	−	0.474650i	$-0.157425\pi$
$941$	54.0000			1.76035			0.880175	+	0.474650i	$0.157425\pi$
$942$		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
$952$		0			0
$953$	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
$959$		0			0
$960$		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	0.997150	−	0.0754473i	$-0.0240385\pi$
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	−0.563914	+	0.825833i	$0.690705\pi$
$972$		0			0
$973$		0			0
$974$	−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
$980$		0			0
$981$		0			0
$982$	19.5000	+	33.7750i	0.622270	+	1.07780i
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	0.983465	−	0.181097i	$-0.0579648\pi$
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	−0.648567	+	0.761157i	$0.724631\pi$
$984$		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	$0.0582469\pi$
$997$	20.5000	+	35.5070i	0.649242	+	1.12452i	−0.334063	+	0.942551i	$0.608420\pi$
$998$	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	2646.2.e.e.2125.1		2
3.2	odd	2		882.2.e.h.655.1		2
7.2	even	3		2646.2.h.f.667.1		2
7.3	odd	6		2646.2.f.e.883.1		2
7.4	even	3		2646.2.f.i.883.1		2
7.5	odd	6		378.2.h.b.289.1		2
7.6	odd	2		378.2.e.a.235.1		2
9.4	even	3		2646.2.h.f.361.1		2
9.5	odd	6		882.2.h.e.67.1		2
21.2	odd	6		882.2.h.e.79.1		2
21.5	even	6		126.2.h.a.79.1	yes	2
21.11	odd	6		882.2.f.a.295.1		2
21.17	even	6		882.2.f.e.295.1		2
21.20	even	2		126.2.e.b.25.1	✓	2
28.19	even	6		3024.2.t.f.289.1		2
28.27	even	2		3024.2.q.a.2881.1		2
63.4	even	3		2646.2.f.i.1765.1		2
63.5	even	6		126.2.e.b.121.1	yes	2
63.11	odd	6		7938.2.a.bd.1.1		1
63.13	odd	6		378.2.h.b.361.1		2
63.20	even	6		1134.2.g.d.487.1		2
63.23	odd	6		882.2.e.h.373.1		2
63.25	even	3		7938.2.a.c.1.1		1
63.31	odd	6		2646.2.f.e.1765.1		2
63.32	odd	6		882.2.f.a.589.1		2
63.34	odd	6		1134.2.g.f.487.1		2
63.38	even	6		7938.2.a.r.1.1		1
63.40	odd	6		378.2.e.a.37.1		2
63.41	even	6		126.2.h.a.67.1	yes	2
63.47	even	6		1134.2.g.d.163.1		2
63.52	odd	6		7938.2.a.o.1.1		1
63.58	even	3	inner	2646.2.e.e.1549.1		2
63.59	even	6		882.2.f.e.589.1		2
63.61	odd	6		1134.2.g.f.163.1		2
84.47	odd	6		1008.2.t.c.961.1		2
84.83	odd	2		1008.2.q.e.529.1		2
252.103	even	6		3024.2.q.a.2305.1		2
252.131	odd	6		1008.2.q.e.625.1		2
252.139	even	6		3024.2.t.f.1873.1		2
252.167	odd	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	21.20	even	2
126.2.e.b.121.1	yes	2	63.5	even	6
126.2.h.a.67.1	yes	2	63.41	even	6
126.2.h.a.79.1	yes	2	21.5	even	6
378.2.e.a.37.1		2	63.40	odd	6
378.2.e.a.235.1		2	7.6	odd	2
378.2.h.b.289.1		2	7.5	odd	6
378.2.h.b.361.1		2	63.13	odd	6
882.2.e.h.373.1		2	63.23	odd	6
882.2.e.h.655.1		2	3.2	odd	2
882.2.f.a.295.1		2	21.11	odd	6
882.2.f.a.589.1		2	63.32	odd	6
882.2.f.e.295.1		2	21.17	even	6
882.2.f.e.589.1		2	63.59	even	6
882.2.h.e.67.1		2	9.5	odd	6
882.2.h.e.79.1		2	21.2	odd	6
1008.2.q.e.529.1		2	84.83	odd	2
1008.2.q.e.625.1		2	252.131	odd	6
1008.2.t.c.193.1		2	252.167	odd	6
1008.2.t.c.961.1		2	84.47	odd	6
1134.2.g.d.163.1		2	63.47	even	6
1134.2.g.d.487.1		2	63.20	even	6
1134.2.g.f.163.1		2	63.61	odd	6
1134.2.g.f.487.1		2	63.34	odd	6
2646.2.e.e.1549.1		2	63.58	even	3	inner
2646.2.e.e.2125.1		2	1.1	even	1	trivial
2646.2.f.e.883.1		2	7.3	odd	6
2646.2.f.e.1765.1		2	63.31	odd	6
2646.2.f.i.883.1		2	7.4	even	3
2646.2.f.i.1765.1		2	63.4	even	3
2646.2.h.f.361.1		2	9.4	even	3
2646.2.h.f.667.1		2	7.2	even	3
3024.2.q.a.2305.1		2	252.103	even	6
3024.2.q.a.2881.1		2	28.27	even	2
3024.2.t.f.289.1		2	28.19	even	6
3024.2.t.f.1873.1		2	252.139	even	6
7938.2.a.c.1.1		1	63.25	even	3
7938.2.a.o.1.1		1	63.52	odd	6
7938.2.a.r.1.1		1	63.38	even	6
7938.2.a.bd.1.1		1	63.11	odd	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.e (of order \(3\), degree \(2\), not minimal)

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

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