LMFDB - Embedded newform 448.2.p.c.255.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(255,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("448.255");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.p (of order $6$, 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			255.2
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	448.255
Dual form			448.2.p.c.383.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32288 - 2.29129i) q^{3} +(1.50000 - 0.866025i) q^{5} -2.64575 q^{7} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})$	\(q+(1.32288 - 2.29129i) q^{3} +(1.50000 - 0.866025i) q^{5} -2.64575 q^{7} +(-2.00000 - 3.46410i) q^{9} +(-3.96863 - 2.29129i) q^{11} -3.46410i q^{13} -4.58258i q^{15} +(4.50000 + 2.59808i) q^{17} +(1.32288 + 2.29129i) q^{19} +(-3.50000 + 6.06218i) q^{21} +(3.96863 - 2.29129i) q^{23} +(-1.00000 + 1.73205i) q^{25} -2.64575 q^{27} +(1.32288 - 2.29129i) q^{31} +(-10.5000 + 6.06218i) q^{33} +(-3.96863 + 2.29129i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-7.93725 - 4.58258i) q^{39} -3.46410i q^{41} -9.16515i q^{43} +(-6.00000 - 3.46410i) q^{45} +(3.96863 + 6.87386i) q^{47} +7.00000 q^{49} +(11.9059 - 6.87386i) q^{51} +(1.50000 - 2.59808i) q^{53} -7.93725 q^{55} +7.00000 q^{57} +(-3.96863 + 6.87386i) q^{59} +(-1.50000 + 0.866025i) q^{61} +(5.29150 + 9.16515i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(3.96863 + 2.29129i) q^{67} -12.1244i q^{69} +9.16515i q^{71} +(-4.50000 - 2.59808i) q^{73} +(2.64575 + 4.58258i) q^{75} +(10.5000 + 6.06218i) q^{77} +(3.96863 - 2.29129i) q^{79} +(2.50000 - 4.33013i) q^{81} +9.00000 q^{85} +(1.50000 - 0.866025i) q^{89} +9.16515i q^{91} +(-3.50000 - 6.06218i) q^{93} +(3.96863 + 2.29129i) q^{95} -3.46410i q^{97} +18.3303i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{5} - 8 q^{9}+O(q^{10}) $ 4 * q + 6 * q^5 - 8 * q^9	$ 4 q + 6 q^{5} - 8 q^{9} + 18 q^{17} - 14 q^{21} - 4 q^{25} - 42 q^{33} + 14 q^{37} - 24 q^{45} + 28 q^{49} + 6 q^{53} + 28 q^{57} - 6 q^{61} - 12 q^{65} - 18 q^{73} + 42 q^{77} + 10 q^{81} + 36 q^{85} + 6 q^{89} - 14 q^{93}+O(q^{100}) $ 4 * q + 6 * q^5 - 8 * q^9 + 18 * q^17 - 14 * q^21 - 4 * q^25 - 42 * q^33 + 14 * q^37 - 24 * q^45 + 28 * q^49 + 6 * q^53 + 28 * q^57 - 6 * q^61 - 12 * q^65 - 18 * q^73 + 42 * q^77 + 10 * q^81 + 36 * q^85 + 6 * q^89 - 14 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.32288	−	2.29129i	0.763763	−	1.32288i	−0.177136	−	0.984186i	$-0.556683\pi$
$3$	1.32288	−	2.29129i	0.763763	−	1.32288i	0.940898	−	0.338689i	$-0.109984\pi$
$4$		0			0
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$		0			0
$7$	−2.64575			−1.00000
$7$	−2.64575			−1.00000
$8$		0			0
$9$	−2.00000	−	3.46410i	−0.666667	−	1.15470i
$10$		0			0
$11$	−3.96863	−	2.29129i	−1.19659	−	0.690849i	−0.236794	−	0.971560i	$-0.576097\pi$
$11$	−3.96863	−	2.29129i	−1.19659	−	0.690849i	−0.959792	+	0.280711i	$0.909430\pi$
$12$		0			0
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$		0			0
$15$		−	4.58258i		−	1.18322i
$16$		0			0
$17$	4.50000	+	2.59808i	1.09141	+	0.630126i	0.933952	−	0.357400i	$-0.116337\pi$
$17$	4.50000	+	2.59808i	1.09141	+	0.630126i	0.157459	+	0.987526i	$0.449670\pi$
$18$		0			0
$19$	1.32288	+	2.29129i	0.303488	+	0.525657i	0.976924	−	0.213589i	$-0.0685153\pi$
$19$	1.32288	+	2.29129i	0.303488	+	0.525657i	−0.673435	+	0.739246i	$0.735182\pi$
$20$		0			0
$21$	−3.50000	+	6.06218i	−0.763763	+	1.32288i
$22$		0			0
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	−0.0254855	−	0.999675i	$-0.508113\pi$
$23$	3.96863	−	2.29129i	0.827516	−	0.477767i	0.853001	+	0.521909i	$0.174780\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$		0			0
$27$	−2.64575			−0.509175
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	1.32288	−	2.29129i	0.237595	−	0.411527i	−0.722428	−	0.691446i	$-0.756974\pi$
$31$	1.32288	−	2.29129i	0.237595	−	0.411527i	0.960024	+	0.279918i	$0.0903074\pi$
$32$		0			0
$33$	−10.5000	+	6.06218i	−1.82782	+	1.05529i
$34$		0			0
$35$	−3.96863	+	2.29129i	−0.670820	+	0.387298i
$36$		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	$0.638181\pi$
$38$		0			0
$39$	−7.93725	−	4.58258i	−1.27098	−	0.733799i
$40$		0			0
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$		0			0
$43$		−	9.16515i		−	1.39767i	−0.715282	−	0.698836i	$-0.753702\pi$
$43$		−	9.16515i		−	1.39767i	0.715282	−	0.698836i	$-0.246298\pi$
$44$		0			0
$45$	−6.00000	−	3.46410i	−0.894427	−	0.516398i
$46$		0			0
$47$	3.96863	+	6.87386i	0.578884	+	1.00266i	0.995608	+	0.0936230i	$0.0298448\pi$
$47$	3.96863	+	6.87386i	0.578884	+	1.00266i	−0.416724	+	0.909033i	$0.636822\pi$
$48$		0			0
$49$	7.00000			1.00000
$50$		0			0
$51$	11.9059	−	6.87386i	1.66716	−	0.962533i
$52$		0			0
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$		0			0
$55$	−7.93725			−1.07026
$56$		0			0
$57$	7.00000			0.927173
$58$		0			0
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	0.483141	+	0.875542i	$0.339496\pi$
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	−0.999813	+	0.0193585i	$0.993838\pi$
$60$		0			0
$61$	−1.50000	+	0.866025i	−0.192055	+	0.110883i	−0.592944	−	0.805243i	$-0.702035\pi$
$61$	−1.50000	+	0.866025i	−0.192055	+	0.110883i	0.400889	+	0.916127i	$0.368701\pi$
$62$		0			0
$63$	5.29150	+	9.16515i	0.666667	+	1.15470i
$64$		0			0
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$		0			0
$67$	3.96863	+	2.29129i	0.484845	+	0.279925i	0.722433	−	0.691441i	$-0.243024\pi$
$67$	3.96863	+	2.29129i	0.484845	+	0.279925i	−0.237588	+	0.971366i	$0.576357\pi$
$68$		0			0
$69$		−	12.1244i		−	1.45960i
$70$		0			0
$71$			9.16515i			1.08770i	0.839181	+	0.543852i	$0.183035\pi$
$71$			9.16515i			1.08770i	−0.839181	+	0.543852i	$0.816965\pi$
$72$		0			0
$73$	−4.50000	−	2.59808i	−0.526685	−	0.304082i	0.212980	−	0.977056i	$-0.431683\pi$
$73$	−4.50000	−	2.59808i	−0.526685	−	0.304082i	−0.739666	+	0.672975i	$0.765016\pi$
$74$		0			0
$75$	2.64575	+	4.58258i	0.305505	+	0.529150i
$76$		0			0
$77$	10.5000	+	6.06218i	1.19659	+	0.690849i
$78$		0			0
$79$	3.96863	−	2.29129i	0.446505	−	0.257790i	−0.259848	−	0.965650i	$-0.583672\pi$
$79$	3.96863	−	2.29129i	0.446505	−	0.257790i	0.706353	+	0.707860i	$0.250339\pi$
$80$		0			0
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	9.00000			0.976187
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	−0.418389	−	0.908268i	$-0.637405\pi$
$89$	1.50000	−	0.866025i	0.159000	−	0.0917985i	0.577389	+	0.816469i	$0.304072\pi$
$90$		0			0
$91$			9.16515i			0.960769i
$92$		0			0
$93$	−3.50000	−	6.06218i	−0.362933	−	0.628619i
$94$		0			0
$95$	3.96863	+	2.29129i	0.407173	+	0.235081i
$96$		0			0
$97$		−	3.46410i		−	0.351726i	−0.984415	−	0.175863i	$-0.943728\pi$
$97$		−	3.46410i		−	0.351726i	0.984415	−	0.175863i	$-0.0562716\pi$
$98$		0			0
$99$			18.3303i			1.84226i
$100$		0			0
$101$	−4.50000	−	2.59808i	−0.447767	−	0.258518i	0.259120	−	0.965845i	$-0.416568\pi$
$101$	−4.50000	−	2.59808i	−0.447767	−	0.258518i	−0.706887	+	0.707327i	$0.749901\pi$
$102$		0			0
$103$	1.32288	+	2.29129i	0.130347	+	0.225767i	0.923810	−	0.382851i	$-0.125058\pi$
$103$	1.32288	+	2.29129i	0.130347	+	0.225767i	−0.793463	+	0.608618i	$0.791724\pi$
$104$		0			0
$105$			12.1244i			1.18322i
$106$		0			0
$107$	−11.9059	+	6.87386i	−1.15098	+	0.664521i	−0.949127	−	0.314893i	$-0.898031\pi$
$107$	−11.9059	+	6.87386i	−1.15098	+	0.664521i	−0.201858	+	0.979415i	$0.564698\pi$
$108$		0			0
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$		0			0
$111$	18.5203			1.75787
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	3.96863	−	6.87386i	0.370076	−	0.640991i
$116$		0			0
$117$	−12.0000	+	6.92820i	−1.10940	+	0.640513i
$118$		0			0
$119$	−11.9059	−	6.87386i	−1.09141	−	0.630126i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$	−7.93725	−	4.58258i	−0.715678	−	0.413197i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$		−	9.16515i		−	0.813276i	−0.913589	−	0.406638i	$-0.866701\pi$
$127$		−	9.16515i		−	0.813276i	0.913589	−	0.406638i	$-0.133299\pi$
$128$		0			0
$129$	−21.0000	−	12.1244i	−1.84895	−	1.06749i
$130$		0			0
$131$	3.96863	+	6.87386i	0.346741	+	0.600572i	0.985668	−	0.168694i	$-0.0539551\pi$
$131$	3.96863	+	6.87386i	0.346741	+	0.600572i	−0.638928	+	0.769267i	$0.720622\pi$
$132$		0			0
$133$	−3.50000	−	6.06218i	−0.303488	−	0.525657i
$134$		0			0
$135$	−3.96863	+	2.29129i	−0.341565	+	0.197203i
$136$		0			0
$137$	−10.5000	+	18.1865i	−0.897076	+	1.55378i	−0.0658609	+	0.997829i	$0.520979\pi$
$137$	−10.5000	+	18.1865i	−0.897076	+	1.55378i	−0.831215	+	0.555952i	$0.812354\pi$
$138$		0			0
$139$	10.5830			0.897639			0.448819	−	0.893622i	$-0.351845\pi$
$139$	10.5830			0.897639			0.448819	+	0.893622i	$0.351845\pi$
$140$		0			0
$141$	21.0000			1.76852
$142$		0			0
$143$	−7.93725	+	13.7477i	−0.663747	+	1.14964i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	9.26013	−	16.0390i	0.763763	−	1.32288i
$148$		0			0
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	−0.990485	−	0.137619i	$-0.956055\pi$
$149$	−7.50000	−	12.9904i	−0.614424	−	1.06421i	0.376061	−	0.926595i	$-0.377278\pi$
$150$		0			0
$151$	19.8431	+	11.4564i	1.61481	+	0.932312i	0.988233	+	0.152953i	$0.0488783\pi$
$151$	19.8431	+	11.4564i	1.61481	+	0.932312i	0.626578	+	0.779359i	$0.284455\pi$
$152$		0			0
$153$		−	20.7846i		−	1.68034i
$154$		0			0
$155$		−	4.58258i		−	0.368081i
$156$		0			0
$157$	4.50000	+	2.59808i	0.359139	+	0.207349i	0.668703	−	0.743530i	$-0.266850\pi$
$157$	4.50000	+	2.59808i	0.359139	+	0.207349i	−0.309564	+	0.950879i	$0.600183\pi$
$158$		0			0
$159$	−3.96863	−	6.87386i	−0.314733	−	0.545133i
$160$		0			0
$161$	−10.5000	+	6.06218i	−0.827516	+	0.477767i
$162$		0			0
$163$	−3.96863	+	2.29129i	−0.310847	+	0.179468i	−0.647305	−	0.762231i	$-0.724104\pi$
$163$	−3.96863	+	2.29129i	−0.310847	+	0.179468i	0.336459	+	0.941698i	$0.390771\pi$
$164$		0			0
$165$	−10.5000	+	18.1865i	−0.817424	+	1.41582i
$166$		0			0
$167$	−15.8745			−1.22841			−0.614203	−	0.789148i	$-0.710522\pi$
$167$	−15.8745			−1.22841			−0.614203	+	0.789148i	$0.710522\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	5.29150	−	9.16515i	0.404651	−	0.700877i
$172$		0			0
$173$	−19.5000	+	11.2583i	−1.48256	+	0.855955i	−0.999804	−	0.0198012i	$-0.993697\pi$
$173$	−19.5000	+	11.2583i	−1.48256	+	0.855955i	−0.482754	+	0.875756i	$0.660363\pi$
$174$		0			0
$175$	2.64575	−	4.58258i	0.200000	−	0.346410i
$176$		0			0
$177$	10.5000	+	18.1865i	0.789228	+	1.36698i
$178$		0			0
$179$	11.9059	+	6.87386i	0.889887	+	0.513777i	0.873906	−	0.486096i	$-0.161579\pi$
$179$	11.9059	+	6.87386i	0.889887	+	0.513777i	0.0159817	+	0.999872i	$0.494913\pi$
$180$		0			0
$181$		−	20.7846i		−	1.54491i	−0.635071	−	0.772454i	$-0.719029\pi$
$181$		−	20.7846i		−	1.54491i	0.635071	−	0.772454i	$-0.280971\pi$
$182$		0			0
$183$			4.58258i			0.338754i
$184$		0			0
$185$	10.5000	+	6.06218i	0.771975	+	0.445700i
$186$		0			0
$187$	−11.9059	−	20.6216i	−0.870644	−	1.50800i
$188$		0			0
$189$	7.00000			0.509175
$190$		0			0
$191$	−19.8431	+	11.4564i	−1.43580	+	0.828959i	−0.997554	−	0.0698969i	$-0.977733\pi$
$191$	−19.8431	+	11.4564i	−1.43580	+	0.828959i	−0.438245	+	0.898856i	$0.644400\pi$
$192$		0			0
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	−0.597317	−	0.802005i	$-0.703766\pi$
$193$	5.50000	−	9.52628i	0.395899	−	0.685717i	0.993215	+	0.116289i	$0.0370998\pi$
$194$		0			0
$195$	−15.8745			−1.13680
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	6.61438	−	11.4564i	0.468881	−	0.812125i	−0.530486	−	0.847693i	$-0.677991\pi$
$199$	6.61438	−	11.4564i	0.468881	−	0.812125i	0.999367	+	0.0355680i	$0.0113240\pi$
$200$		0			0
$201$	10.5000	−	6.06218i	0.740613	−	0.427593i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$		0			0
$207$	−15.8745	−	9.16515i	−1.10335	−	0.637022i
$208$		0			0
$209$		−	12.1244i		−	0.838659i
$210$		0			0
$211$		−	9.16515i		−	0.630955i	−0.948933	−	0.315478i	$-0.897835\pi$
$211$		−	9.16515i		−	0.630955i	0.948933	−	0.315478i	$-0.102165\pi$
$212$		0			0
$213$	21.0000	+	12.1244i	1.43890	+	0.830747i
$214$		0			0
$215$	−7.93725	−	13.7477i	−0.541316	−	0.937587i
$216$		0			0
$217$	−3.50000	+	6.06218i	−0.237595	+	0.411527i
$218$		0			0
$219$	−11.9059	+	6.87386i	−0.804525	+	0.464493i
$220$		0			0
$221$	9.00000	−	15.5885i	0.605406	−	1.04859i
$222$		0			0
$223$	10.5830			0.708690			0.354345	−	0.935115i	$-0.384704\pi$
$223$	10.5830			0.708690			0.354345	+	0.935115i	$0.384704\pi$
$224$		0			0
$225$	8.00000			0.533333
$226$		0			0
$227$	−11.9059	+	20.6216i	−0.790221	+	1.36870i	0.135609	+	0.990762i	$0.456701\pi$
$227$	−11.9059	+	20.6216i	−0.790221	+	1.36870i	−0.925830	+	0.377941i	$0.876632\pi$
$228$		0			0
$229$	1.50000	−	0.866025i	0.0991228	−	0.0572286i	−0.449619	−	0.893220i	$-0.648440\pi$
$229$	1.50000	−	0.866025i	0.0991228	−	0.0572286i	0.548742	+	0.835992i	$0.315107\pi$
$230$		0			0
$231$	27.7804	−	16.0390i	1.82782	−	1.05529i
$232$		0			0
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	−0.972523	−	0.232806i	$-0.925209\pi$
$233$	−10.5000	−	18.1865i	−0.687878	−	1.19144i	0.284645	−	0.958633i	$-0.408124\pi$
$234$		0			0
$235$	11.9059	+	6.87386i	0.776654	+	0.448401i
$236$		0			0
$237$		−	12.1244i		−	0.787562i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−16.5000	−	9.52628i	−1.06286	−	0.613642i	−0.136637	−	0.990621i	$-0.543629\pi$
$241$	−16.5000	−	9.52628i	−1.06286	−	0.613642i	−0.926222	+	0.376980i	$0.876963\pi$
$242$		0			0
$243$	−10.5830	−	18.3303i	−0.678900	−	1.17589i
$244$		0			0
$245$	10.5000	−	6.06218i	0.670820	−	0.387298i
$246$		0			0
$247$	7.93725	−	4.58258i	0.505035	−	0.291582i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.8745			1.00199			0.500995	−	0.865450i	$-0.332967\pi$
$251$	15.8745			1.00199			0.500995	+	0.865450i	$0.332967\pi$
$252$		0			0
$253$	−21.0000			−1.32026
$254$		0			0
$255$	11.9059	−	20.6216i	0.745575	−	1.29137i
$256$		0			0
$257$	−1.50000	+	0.866025i	−0.0935674	+	0.0540212i	−0.546054	−	0.837750i	$-0.683871\pi$
$257$	−1.50000	+	0.866025i	−0.0935674	+	0.0540212i	0.452486	+	0.891771i	$0.350537\pi$
$258$		0			0
$259$	−9.26013	−	16.0390i	−0.575396	−	0.996616i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.96863	−	2.29129i	−0.244716	−	0.141287i	0.372626	−	0.927981i	$-0.378457\pi$
$263$	−3.96863	−	2.29129i	−0.244716	−	0.141287i	−0.617342	+	0.786695i	$0.711791\pi$
$264$		0			0
$265$		−	5.19615i		−	0.319197i
$266$		0			0
$267$		−	4.58258i		−	0.280449i
$268$		0			0
$269$	−25.5000	−	14.7224i	−1.55476	−	0.897643i	−0.997743	−	0.0671428i	$-0.978612\pi$
$269$	−25.5000	−	14.7224i	−1.55476	−	0.897643i	−0.557019	−	0.830500i	$-0.688055\pi$
$270$		0			0
$271$	−14.5516	−	25.2042i	−0.883949	−	1.53104i	−0.846914	−	0.531730i	$-0.821542\pi$
$271$	−14.5516	−	25.2042i	−0.883949	−	1.53104i	−0.0370348	−	0.999314i	$-0.511791\pi$
$272$		0			0
$273$	21.0000	+	12.1244i	1.27098	+	0.733799i
$274$		0			0
$275$	7.93725	−	4.58258i	0.478634	−	0.276340i
$276$		0			0
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$		0			0
$279$	−10.5830			−0.633588
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$	−6.61438	+	11.4564i	−0.393184	+	0.681015i	−0.992868	−	0.119223i	$-0.961960\pi$
$283$	−6.61438	+	11.4564i	−0.393184	+	0.681015i	0.599684	+	0.800237i	$0.295293\pi$
$284$		0			0
$285$	10.5000	−	6.06218i	0.621966	−	0.359092i
$286$		0			0
$287$			9.16515i			0.541002i
$288$		0			0
$289$	5.00000	+	8.66025i	0.294118	+	0.509427i
$290$		0			0
$291$	−7.93725	−	4.58258i	−0.465290	−	0.268635i
$292$		0			0
$293$			20.7846i			1.21425i	0.794606	+	0.607125i	$0.207677\pi$
$293$			20.7846i			1.21425i	−0.794606	+	0.607125i	$0.792323\pi$
$294$		0			0
$295$			13.7477i			0.800424i
$296$		0			0
$297$	10.5000	+	6.06218i	0.609272	+	0.351763i
$298$		0			0
$299$	−7.93725	−	13.7477i	−0.459023	−	0.795052i
$300$		0			0
$301$			24.2487i			1.39767i
$302$		0			0
$303$	−11.9059	+	6.87386i	−0.683975	+	0.394893i
$304$		0			0
$305$	−1.50000	+	2.59808i	−0.0858898	+	0.148765i
$306$		0			0
$307$	−10.5830			−0.604004			−0.302002	−	0.953307i	$-0.597655\pi$
$307$	−10.5830			−0.604004			−0.302002	+	0.953307i	$0.597655\pi$
$308$		0			0
$309$	7.00000			0.398216
$310$		0			0
$311$	−11.9059	+	20.6216i	−0.675121	+	1.16934i	0.301313	+	0.953525i	$0.402575\pi$
$311$	−11.9059	+	20.6216i	−0.675121	+	1.16934i	−0.976434	+	0.215818i	$0.930758\pi$
$312$		0			0
$313$	−22.5000	+	12.9904i	−1.27178	+	0.734260i	−0.975322	−	0.220788i	$-0.929137\pi$
$313$	−22.5000	+	12.9904i	−1.27178	+	0.734260i	−0.296453	+	0.955047i	$0.595804\pi$
$314$		0			0
$315$	15.8745	+	9.16515i	0.894427	+	0.516398i
$316$		0			0
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	0.996061	−	0.0886679i	$-0.0282610\pi$
$317$	7.50000	+	12.9904i	0.421242	+	0.729612i	−0.574819	+	0.818280i	$0.694928\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$			36.3731i			2.03015i
$322$		0			0
$323$			13.7477i			0.764944i
$324$		0			0
$325$	6.00000	+	3.46410i	0.332820	+	0.192154i
$326$		0			0
$327$	9.26013	+	16.0390i	0.512086	+	0.886960i
$328$		0			0
$329$	−10.5000	−	18.1865i	−0.578884	−	1.00266i
$330$		0			0
$331$	11.9059	−	6.87386i	0.654406	−	0.377822i	−0.135736	−	0.990745i	$-0.543340\pi$
$331$	11.9059	−	6.87386i	0.654406	−	0.377822i	0.790142	+	0.612923i	$0.210007\pi$
$332$		0			0
$333$	14.0000	−	24.2487i	0.767195	−	1.32882i
$334$		0			0
$335$	7.93725			0.433659
$336$		0			0
$337$	−28.0000			−1.52526			−0.762629	−	0.646837i	$-0.776092\pi$
$337$	−28.0000			−1.52526			−0.762629	+	0.646837i	$0.776092\pi$
$338$		0			0
$339$	15.8745	−	27.4955i	0.862185	−	1.49335i
$340$		0			0
$341$	−10.5000	+	6.06218i	−0.568607	+	0.328285i
$342$		0			0
$343$	−18.5203			−1.00000
$344$		0			0
$345$	−10.5000	−	18.1865i	−0.565301	−	0.979130i
$346$		0			0
$347$	3.96863	+	2.29129i	0.213047	+	0.123003i	0.602727	−	0.797948i	$-0.294081\pi$
$347$	3.96863	+	2.29129i	0.213047	+	0.123003i	−0.389680	+	0.920950i	$0.627414\pi$
$348$		0			0
$349$			3.46410i			0.185429i	0.995693	+	0.0927146i	$0.0295544\pi$
$349$			3.46410i			0.185429i	−0.995693	+	0.0927146i	$0.970446\pi$
$350$		0			0
$351$			9.16515i			0.489200i
$352$		0			0
$353$	16.5000	+	9.52628i	0.878206	+	0.507033i	0.870067	−	0.492934i	$-0.164076\pi$
$353$	16.5000	+	9.52628i	0.878206	+	0.507033i	0.00813978	+	0.999967i	$0.497409\pi$
$354$		0			0
$355$	7.93725	+	13.7477i	0.421266	+	0.729654i
$356$		0			0
$357$	−31.5000	+	18.1865i	−1.66716	+	0.962533i
$358$		0			0
$359$	11.9059	−	6.87386i	0.628368	−	0.362789i	−0.151752	−	0.988419i	$-0.548491\pi$
$359$	11.9059	−	6.87386i	0.628368	−	0.362789i	0.780120	+	0.625630i	$0.215158\pi$
$360$		0			0
$361$	6.00000	−	10.3923i	0.315789	−	0.546963i
$362$		0			0
$363$	26.4575			1.38866
$364$		0			0
$365$	−9.00000			−0.471082
$366$		0			0
$367$	−17.1974	+	29.7867i	−0.897696	+	1.55486i	−0.0672642	+	0.997735i	$0.521427\pi$
$367$	−17.1974	+	29.7867i	−0.897696	+	1.55486i	−0.830432	+	0.557120i	$0.811906\pi$
$368$		0			0
$369$	−12.0000	+	6.92820i	−0.624695	+	0.360668i
$370$		0			0
$371$	−3.96863	+	6.87386i	−0.206041	+	0.356873i
$372$		0			0
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	0.852791	−	0.522253i	$-0.174908\pi$
$373$	−0.500000	−	0.866025i	−0.0258890	−	0.0448411i	−0.878680	+	0.477412i	$0.841575\pi$
$374$		0			0
$375$	27.7804	+	16.0390i	1.43457	+	0.828251i
$376$		0			0
$377$		0			0
$378$		0			0
$379$			18.3303i			0.941564i	0.882249	+	0.470782i	$0.156028\pi$
$379$			18.3303i			0.941564i	−0.882249	+	0.470782i	$0.843972\pi$
$380$		0			0
$381$	−21.0000	−	12.1244i	−1.07586	−	0.621150i
$382$		0			0
$383$	3.96863	+	6.87386i	0.202787	+	0.351238i	0.949425	−	0.313992i	$-0.101667\pi$
$383$	3.96863	+	6.87386i	0.202787	+	0.351238i	−0.746638	+	0.665230i	$0.768333\pi$
$384$		0			0
$385$	21.0000			1.07026
$386$		0			0
$387$	−31.7490	+	18.3303i	−1.61389	+	0.931782i
$388$		0			0
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	−0.466915	−	0.884302i	$-0.654634\pi$
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	0.999286	−	0.0377914i	$-0.0120322\pi$
$390$		0			0
$391$	23.8118			1.20421
$392$		0			0
$393$	21.0000			1.05931
$394$		0			0
$395$	3.96863	−	6.87386i	0.199683	−	0.345862i
$396$		0			0
$397$	19.5000	−	11.2583i	0.978677	−	0.565039i	0.0768065	−	0.997046i	$-0.475528\pi$
$397$	19.5000	−	11.2583i	0.978677	−	0.565039i	0.901870	+	0.432007i	$0.142194\pi$
$398$		0			0
$399$	−18.5203			−0.927173
$400$		0			0
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$		0			0
$403$	−7.93725	−	4.58258i	−0.395383	−	0.228274i
$404$		0			0
$405$		−	8.66025i		−	0.430331i
$406$		0			0
$407$		−	32.0780i		−	1.59005i
$408$		0			0
$409$	16.5000	+	9.52628i	0.815872	+	0.471044i	0.848991	−	0.528407i	$-0.177211\pi$
$409$	16.5000	+	9.52628i	0.815872	+	0.471044i	−0.0331186	+	0.999451i	$0.510544\pi$
$410$		0			0
$411$	27.7804	+	48.1170i	1.37031	+	2.37344i
$412$		0			0
$413$	10.5000	−	18.1865i	0.516671	−	0.894901i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	14.0000	−	24.2487i	0.685583	−	1.18746i
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$		0			0
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$		0			0
$423$	15.8745	−	27.4955i	0.771845	−	1.33687i
$424$		0			0
$425$	−9.00000	+	5.19615i	−0.436564	+	0.252050i
$426$		0			0
$427$	3.96863	−	2.29129i	0.192055	−	0.110883i
$428$		0			0
$429$	21.0000	+	36.3731i	1.01389	+	1.75611i
$430$		0			0
$431$	19.8431	+	11.4564i	0.955810	+	0.551837i	0.894881	−	0.446305i	$-0.147260\pi$
$431$	19.8431	+	11.4564i	0.955810	+	0.551837i	0.0609292	+	0.998142i	$0.480594\pi$
$432$		0			0
$433$			3.46410i			0.166474i	0.996530	+	0.0832370i	$0.0265259\pi$
$433$			3.46410i			0.166474i	−0.996530	+	0.0832370i	$0.973474\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.5000	+	6.06218i	0.502283	+	0.289993i
$438$		0			0
$439$	14.5516	+	25.2042i	0.694512	+	1.20293i	0.970345	+	0.241724i	$0.0777128\pi$
$439$	14.5516	+	25.2042i	0.694512	+	1.20293i	−0.275834	+	0.961205i	$0.588954\pi$
$440$		0			0
$441$	−14.0000	−	24.2487i	−0.666667	−	1.15470i
$442$		0			0
$443$	3.96863	−	2.29129i	0.188555	−	0.108862i	−0.402751	−	0.915310i	$-0.631946\pi$
$443$	3.96863	−	2.29129i	0.188555	−	0.108862i	0.591306	+	0.806447i	$0.298613\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$		0			0
$447$	−39.6863			−1.87710
$448$		0			0
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$	−7.93725	+	13.7477i	−0.373751	+	0.647355i
$452$		0			0
$453$	52.5000	−	30.3109i	2.46667	−	1.42413i
$454$		0			0
$455$	7.93725	+	13.7477i	0.372104	+	0.644503i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$		0			0
$459$	−11.9059	−	6.87386i	−0.555719	−	0.320844i
$460$		0			0
$461$			3.46410i			0.161339i	0.996741	+	0.0806696i	$0.0257059\pi$
$461$			3.46410i			0.161339i	−0.996741	+	0.0806696i	$0.974294\pi$
$462$		0			0
$463$		−	27.4955i		−	1.27782i	−0.769281	−	0.638911i	$-0.779385\pi$
$463$		−	27.4955i		−	1.27782i	0.769281	−	0.638911i	$-0.220615\pi$
$464$		0			0
$465$	−10.5000	−	6.06218i	−0.486926	−	0.281127i
$466$		0			0
$467$	3.96863	+	6.87386i	0.183646	+	0.318084i	0.943119	−	0.332454i	$-0.107877\pi$
$467$	3.96863	+	6.87386i	0.183646	+	0.318084i	−0.759473	+	0.650538i	$0.774543\pi$
$468$		0			0
$469$	−10.5000	−	6.06218i	−0.484845	−	0.279925i
$470$		0			0
$471$	11.9059	−	6.87386i	0.548594	−	0.316731i
$472$		0			0
$473$	−21.0000	+	36.3731i	−0.965581	+	1.67244i
$474$		0			0
$475$	−5.29150			−0.242791
$476$		0			0
$477$	−12.0000			−0.549442
$478$		0			0
$479$	3.96863	−	6.87386i	0.181331	−	0.314075i	−0.761003	−	0.648748i	$-0.775293\pi$
$479$	3.96863	−	6.87386i	0.181331	−	0.314075i	0.942334	+	0.334674i	$0.108626\pi$
$480$		0			0
$481$	21.0000	−	12.1244i	0.957518	−	0.552823i
$482$		0			0
$483$			32.0780i			1.45960i
$484$		0			0
$485$	−3.00000	−	5.19615i	−0.136223	−	0.235945i
$486$		0			0
$487$	−35.7176	−	20.6216i	−1.61852	−	0.934453i	−0.987303	−	0.158848i	$-0.949222\pi$
$487$	−35.7176	−	20.6216i	−1.61852	−	0.934453i	−0.631218	−	0.775606i	$-0.717445\pi$
$488$		0			0
$489$			12.1244i			0.548282i
$490$		0			0
$491$		−	18.3303i		−	0.827235i	−0.910451	−	0.413617i	$-0.864265\pi$
$491$		−	18.3303i		−	0.827235i	0.910451	−	0.413617i	$-0.135735\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	15.8745	+	27.4955i	0.713506	+	1.23583i
$496$		0			0
$497$		−	24.2487i		−	1.08770i
$498$		0			0
$499$	27.7804	−	16.0390i	1.24362	−	0.718005i	0.273791	−	0.961789i	$-0.411722\pi$
$499$	27.7804	−	16.0390i	1.24362	−	0.718005i	0.969830	+	0.243784i	$0.0783888\pi$
$500$		0			0
$501$	−21.0000	+	36.3731i	−0.938211	+	1.62503i
$502$		0			0
$503$	31.7490			1.41562			0.707809	−	0.706404i	$-0.249684\pi$
$503$	31.7490			1.41562			0.707809	+	0.706404i	$0.249684\pi$
$504$		0			0
$505$	−9.00000			−0.400495
$506$		0			0
$507$	1.32288	−	2.29129i	0.0587510	−	0.101760i
$508$		0			0
$509$	−22.5000	+	12.9904i	−0.997295	+	0.575789i	−0.907447	−	0.420167i	$-0.861972\pi$
$509$	−22.5000	+	12.9904i	−0.997295	+	0.575789i	−0.0898481	+	0.995955i	$0.528638\pi$
$510$		0			0
$511$	11.9059	+	6.87386i	0.526685	+	0.304082i
$512$		0			0
$513$	−3.50000	−	6.06218i	−0.154529	−	0.267652i
$514$		0			0
$515$	3.96863	+	2.29129i	0.174879	+	0.100966i
$516$		0			0
$517$		−	36.3731i		−	1.59969i
$518$		0			0
$519$			59.5735i			2.61499i
$520$		0			0
$521$	37.5000	+	21.6506i	1.64290	+	0.948532i	0.979794	+	0.200011i	$0.0640976\pi$
$521$	37.5000	+	21.6506i	1.64290	+	0.948532i	0.663111	+	0.748521i	$0.269236\pi$
$522$		0			0
$523$	6.61438	+	11.4564i	0.289227	+	0.500955i	0.973625	−	0.228153i	$-0.0732686\pi$
$523$	6.61438	+	11.4564i	0.289227	+	0.500955i	−0.684399	+	0.729108i	$0.739935\pi$
$524$		0			0
$525$	−7.00000	−	12.1244i	−0.305505	−	0.529150i
$526$		0			0
$527$	11.9059	−	6.87386i	0.518628	−	0.299430i
$528$		0			0
$529$	−1.00000	+	1.73205i	−0.0434783	+	0.0753066i
$530$		0			0
$531$	31.7490			1.37779
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$	−11.9059	+	20.6216i	−0.514736	+	0.891549i
$536$		0			0
$537$	31.5000	−	18.1865i	1.35933	−	0.784807i
$538$		0			0
$539$	−27.7804	−	16.0390i	−1.19659	−	0.690849i
$540$		0			0
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	0.971250	−	0.238062i	$-0.0765123\pi$
$541$	6.50000	+	11.2583i	0.279457	+	0.484033i	−0.691793	+	0.722096i	$0.743179\pi$
$542$		0			0
$543$	−47.6235	−	27.4955i	−2.04372	−	1.17994i
$544$		0			0
$545$			12.1244i			0.519350i
$546$		0			0
$547$		−	18.3303i		−	0.783747i	−0.920019	−	0.391874i	$-0.871827\pi$
$547$		−	18.3303i		−	0.783747i	0.920019	−	0.391874i	$-0.128173\pi$
$548$		0			0
$549$	6.00000	+	3.46410i	0.256074	+	0.147844i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−10.5000	+	6.06218i	−0.446505	+	0.257790i
$554$		0			0
$555$	27.7804	−	16.0390i	1.17921	−	0.680818i
$556$		0			0
$557$	−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
$559$	−31.7490			−1.34284
$560$		0			0
$561$	−63.0000			−2.65986
$562$		0			0
$563$	−3.96863	+	6.87386i	−0.167258	+	0.289699i	−0.937455	−	0.348107i	$-0.886825\pi$
$563$	−3.96863	+	6.87386i	−0.167258	+	0.289699i	0.770197	+	0.637806i	$0.220158\pi$
$564$		0			0
$565$	18.0000	−	10.3923i	0.757266	−	0.437208i
$566$		0			0
$567$	−6.61438	+	11.4564i	−0.277778	+	0.481125i
$568$		0			0
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	0.997703	−	0.0677445i	$-0.0215803\pi$
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	−0.557520	+	0.830164i	$0.688247\pi$
$570$		0			0
$571$	11.9059	+	6.87386i	0.498246	+	0.287662i	0.727989	−	0.685589i	$-0.240455\pi$
$571$	11.9059	+	6.87386i	0.498246	+	0.287662i	−0.229743	+	0.973251i	$0.573789\pi$
$572$		0			0
$573$			60.6218i			2.53251i
$574$		0			0
$575$			9.16515i			0.382213i
$576$		0			0
$577$	−16.5000	−	9.52628i	−0.686904	−	0.396584i	0.115547	−	0.993302i	$-0.463138\pi$
$577$	−16.5000	−	9.52628i	−0.686904	−	0.396584i	−0.802451	+	0.596718i	$0.796471\pi$
$578$		0			0
$579$	−14.5516	−	25.2042i	−0.604745	−	1.04745i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−11.9059	+	6.87386i	−0.493091	+	0.284686i
$584$		0			0
$585$	−12.0000	+	20.7846i	−0.496139	+	0.859338i
$586$		0			0
$587$	−31.7490			−1.31042			−0.655211	−	0.755446i	$-0.727420\pi$
$587$	−31.7490			−1.31042			−0.655211	+	0.755446i	$0.727420\pi$
$588$		0			0
$589$	7.00000			0.288430
$590$		0			0
$591$	15.8745	−	27.4955i	0.652990	−	1.13101i
$592$		0			0
$593$	−19.5000	+	11.2583i	−0.800769	+	0.462324i	−0.843740	−	0.536752i	$-0.819651\pi$
$593$	−19.5000	+	11.2583i	−0.800769	+	0.462324i	0.0429710	+	0.999076i	$0.486318\pi$
$594$		0			0
$595$	−23.8118			−0.976187
$596$		0			0
$597$	−17.5000	−	30.3109i	−0.716227	−	1.24054i
$598$		0			0
$599$	−3.96863	−	2.29129i	−0.162154	−	0.0936195i	0.416727	−	0.909032i	$-0.363177\pi$
$599$	−3.96863	−	2.29129i	−0.162154	−	0.0936195i	−0.578881	+	0.815412i	$0.696510\pi$
$600$		0			0
$601$		−	3.46410i		−	0.141304i	−0.997501	−	0.0706518i	$-0.977492\pi$
$601$		−	3.46410i		−	0.141304i	0.997501	−	0.0706518i	$-0.0225079\pi$
$602$		0			0
$603$		−	18.3303i		−	0.746468i
$604$		0			0
$605$	15.0000	+	8.66025i	0.609837	+	0.352089i
$606$		0			0
$607$	−1.32288	−	2.29129i	−0.0536939	−	0.0930005i	0.837929	−	0.545779i	$-0.183766\pi$
$607$	−1.32288	−	2.29129i	−0.0536939	−	0.0930005i	−0.891623	+	0.452778i	$0.850433\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	23.8118	−	13.7477i	0.963321	−	0.556174i
$612$		0			0
$613$	−3.50000	+	6.06218i	−0.141364	+	0.244849i	−0.928010	−	0.372554i	$-0.878482\pi$
$613$	−3.50000	+	6.06218i	−0.141364	+	0.244849i	0.786647	+	0.617403i	$0.211815\pi$
$614$		0			0
$615$	−15.8745			−0.640122
$616$		0			0
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$		0			0
$619$	−9.26013	+	16.0390i	−0.372196	+	0.644662i	−0.989903	−	0.141746i	$-0.954728\pi$
$619$	−9.26013	+	16.0390i	−0.372196	+	0.644662i	0.617707	+	0.786408i	$0.288062\pi$
$620$		0			0
$621$	−10.5000	+	6.06218i	−0.421350	+	0.243267i
$622$		0			0
$623$	−3.96863	+	2.29129i	−0.159000	+	0.0917985i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$	−27.7804	−	16.0390i	−1.10944	−	0.640537i
$628$		0			0
$629$			36.3731i			1.45029i
$630$		0			0
$631$		−	45.8258i		−	1.82429i	−0.409863	−	0.912147i	$-0.634423\pi$
$631$		−	45.8258i		−	1.82429i	0.409863	−	0.912147i	$-0.365577\pi$
$632$		0			0
$633$	−21.0000	−	12.1244i	−0.834675	−	0.481900i
$634$		0			0
$635$	−7.93725	−	13.7477i	−0.314980	−	0.545562i
$636$		0			0
$637$		−	24.2487i		−	0.960769i
$638$		0			0
$639$	31.7490	−	18.3303i	1.25597	−	0.725136i
$640$		0			0
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	−0.580674	−	0.814136i	$-0.697211\pi$
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	0.995400	+	0.0958109i	$0.0305444\pi$
$642$		0			0
$643$	21.1660			0.834706			0.417353	−	0.908744i	$-0.362958\pi$
$643$	21.1660			0.834706			0.417353	+	0.908744i	$0.362958\pi$
$644$		0			0
$645$	−42.0000			−1.65375
$646$		0			0
$647$	19.8431	−	34.3693i	0.780114	−	1.35120i	−0.151761	−	0.988417i	$-0.548494\pi$
$647$	19.8431	−	34.3693i	0.780114	−	1.35120i	0.931875	−	0.362780i	$-0.118172\pi$
$648$		0			0
$649$	31.5000	−	18.1865i	1.23648	−	0.713884i
$650$		0			0
$651$	9.26013	+	16.0390i	0.362933	+	0.628619i
$652$		0			0
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	0.584091	−	0.811688i	$-0.301451\pi$
$653$	−10.5000	−	18.1865i	−0.410897	−	0.711694i	−0.994988	+	0.0999939i	$0.968118\pi$
$654$		0			0
$655$	11.9059	+	6.87386i	0.465201	+	0.268584i
$656$		0			0
$657$			20.7846i			0.810885i
$658$		0			0
$659$		−	9.16515i		−	0.357024i	−0.983938	−	0.178512i	$-0.942872\pi$
$659$		−	9.16515i		−	0.357024i	0.983938	−	0.178512i	$-0.0571283\pi$
$660$		0			0
$661$	4.50000	+	2.59808i	0.175030	+	0.101053i	0.584955	−	0.811065i	$-0.301112\pi$
$661$	4.50000	+	2.59808i	0.175030	+	0.101053i	−0.409926	+	0.912119i	$0.634445\pi$
$662$		0			0
$663$	−23.8118	−	41.2432i	−0.924772	−	1.60175i
$664$		0			0
$665$	−10.5000	−	6.06218i	−0.407173	−	0.235081i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	14.0000	−	24.2487i	0.541271	−	0.937509i
$670$		0			0
$671$	7.93725			0.306414
$672$		0			0
$673$	28.0000			1.07932			0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000			1.07932			0.539660	+	0.841883i	$0.318553\pi$
$674$		0			0
$675$	2.64575	−	4.58258i	0.101835	−	0.176383i
$676$		0			0
$677$	1.50000	−	0.866025i	0.0576497	−	0.0332841i	−0.470898	−	0.882188i	$-0.656070\pi$
$677$	1.50000	−	0.866025i	0.0576497	−	0.0332841i	0.528548	+	0.848904i	$0.322737\pi$
$678$		0			0
$679$			9.16515i			0.351726i
$680$		0			0
$681$	31.5000	+	54.5596i	1.20708	+	2.09073i
$682$		0			0
$683$	−3.96863	−	2.29129i	−0.151855	−	0.0876737i	0.422147	−	0.906527i	$-0.361277\pi$
$683$	−3.96863	−	2.29129i	−0.151855	−	0.0876737i	−0.574002	+	0.818854i	$0.694610\pi$
$684$		0			0
$685$			36.3731i			1.38974i
$686$		0			0
$687$		−	4.58258i		−	0.174836i
$688$		0			0
$689$	−9.00000	−	5.19615i	−0.342873	−	0.197958i
$690$		0			0
$691$	−1.32288	−	2.29129i	−0.0503246	−	0.0871647i	0.839766	−	0.542949i	$-0.182692\pi$
$691$	−1.32288	−	2.29129i	−0.0503246	−	0.0871647i	−0.890090	+	0.455784i	$0.849359\pi$
$692$		0			0
$693$		−	48.4974i		−	1.84226i
$694$		0			0
$695$	15.8745	−	9.16515i	0.602154	−	0.347654i
$696$		0			0
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$		0			0
$699$	−55.5608			−2.10150
$700$		0			0
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	−9.26013	+	16.0390i	−0.349252	+	0.604923i
$704$		0			0
$705$	31.5000	−	18.1865i	1.18636	−	0.684944i
$706$		0			0
$707$	11.9059	+	6.87386i	0.447767	+	0.258518i
$708$		0			0
$709$	17.5000	+	30.3109i	0.657226	+	1.13835i	0.981331	+	0.192328i	$0.0616038\pi$
$709$	17.5000	+	30.3109i	0.657226	+	1.13835i	−0.324104	+	0.946021i	$0.605063\pi$
$710$		0			0
$711$	−15.8745	−	9.16515i	−0.595341	−	0.343720i
$712$		0			0
$713$		−	12.1244i		−	0.454061i
$714$		0			0
$715$			27.4955i			1.02827i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.96863	−	6.87386i	−0.148005	−	0.256352i	0.782485	−	0.622669i	$-0.213952\pi$
$719$	−3.96863	−	6.87386i	−0.148005	−	0.256352i	−0.930490	+	0.366317i	$0.880618\pi$
$720$		0			0
$721$	−3.50000	−	6.06218i	−0.130347	−	0.225767i
$722$		0			0
$723$	−43.6549	+	25.2042i	−1.62354	+	0.937353i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	21.1660			0.785004			0.392502	−	0.919751i	$-0.371610\pi$
$727$	21.1660			0.785004			0.392502	+	0.919751i	$0.371610\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$		0			0
$731$	23.8118	−	41.2432i	0.880710	−	1.52543i
$732$		0			0
$733$	−19.5000	+	11.2583i	−0.720249	+	0.415836i	−0.814844	−	0.579680i	$-0.803178\pi$
$733$	−19.5000	+	11.2583i	−0.720249	+	0.415836i	0.0945954	+	0.995516i	$0.469844\pi$
$734$		0			0
$735$		−	32.0780i		−	1.18322i
$736$		0			0
$737$	−10.5000	−	18.1865i	−0.386772	−	0.669910i
$738$		0			0
$739$	−19.8431	−	11.4564i	−0.729942	−	0.421432i	0.0884593	−	0.996080i	$-0.471806\pi$
$739$	−19.8431	−	11.4564i	−0.729942	−	0.421432i	−0.818401	+	0.574648i	$0.805139\pi$
$740$		0			0
$741$		−	24.2487i		−	0.890799i
$742$		0			0
$743$		−	45.8258i		−	1.68118i	−0.541669	−	0.840592i	$-0.682207\pi$
$743$		−	45.8258i		−	1.68118i	0.541669	−	0.840592i	$-0.317793\pi$
$744$		0			0
$745$	−22.5000	−	12.9904i	−0.824336	−	0.475931i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	31.5000	−	18.1865i	1.15098	−	0.664521i
$750$		0			0
$751$	11.9059	−	6.87386i	0.434452	−	0.250831i	−0.266790	−	0.963755i	$-0.585963\pi$
$751$	11.9059	−	6.87386i	0.434452	−	0.250831i	0.701241	+	0.712924i	$0.252630\pi$
$752$		0			0
$753$	21.0000	−	36.3731i	0.765283	−	1.32551i
$754$		0			0
$755$	39.6863			1.44433
$756$		0			0
$757$	28.0000			1.01768			0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000			1.01768			0.508839	+	0.860862i	$0.330075\pi$
$758$		0			0
$759$	−27.7804	+	48.1170i	−1.00836	+	1.74654i
$760$		0			0
$761$	22.5000	−	12.9904i	0.815624	−	0.470901i	−0.0332809	−	0.999446i	$-0.510596\pi$
$761$	22.5000	−	12.9904i	0.815624	−	0.470901i	0.848905	+	0.528545i	$0.177262\pi$
$762$		0			0
$763$	9.26013	−	16.0390i	0.335239	−	0.580651i
$764$		0			0
$765$	−18.0000	−	31.1769i	−0.650791	−	1.12720i
$766$		0			0
$767$	23.8118	+	13.7477i	0.859793	+	0.496402i
$768$		0			0
$769$			51.9615i			1.87378i	0.349624	+	0.936890i	$0.386309\pi$
$769$			51.9615i			1.87378i	−0.349624	+	0.936890i	$0.613691\pi$
$770$		0			0
$771$			4.58258i			0.165037i
$772$		0			0
$773$	25.5000	+	14.7224i	0.917171	+	0.529529i	0.882732	−	0.469878i	$-0.155702\pi$
$773$	25.5000	+	14.7224i	0.917171	+	0.529529i	0.0344397	+	0.999407i	$0.489035\pi$
$774$		0			0
$775$	2.64575	+	4.58258i	0.0950382	+	0.164611i
$776$		0			0
$777$	−49.0000			−1.75787
$778$		0			0
$779$	7.93725	−	4.58258i	0.284382	−	0.164188i
$780$		0			0
$781$	21.0000	−	36.3731i	0.751439	−	1.30153i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	9.00000			0.321224
$786$		0			0
$787$	6.61438	−	11.4564i	0.235777	−	0.408378i	−0.723721	−	0.690093i	$-0.757570\pi$
$787$	6.61438	−	11.4564i	0.235777	−	0.408378i	0.959498	+	0.281715i	$0.0909031\pi$
$788$		0			0
$789$	−10.5000	+	6.06218i	−0.373810	+	0.215819i
$790$		0			0
$791$	−31.7490			−1.12887
$792$		0			0
$793$	3.00000	+	5.19615i	0.106533	+	0.184521i
$794$		0			0
$795$	−11.9059	−	6.87386i	−0.422258	−	0.243791i
$796$		0			0
$797$		−	3.46410i		−	0.122705i	−0.998116	−	0.0613524i	$-0.980459\pi$
$797$		−	3.46410i		−	0.122705i	0.998116	−	0.0613524i	$-0.0195413\pi$
$798$		0			0
$799$			41.2432i			1.45908i
$800$		0			0
$801$	−6.00000	−	3.46410i	−0.212000	−	0.122398i
$802$		0			0
$803$	11.9059	+	20.6216i	0.420149	+	0.727720i
$804$		0			0
$805$	−10.5000	+	18.1865i	−0.370076	+	0.640991i
$806$		0			0
$807$	−67.4667	+	38.9519i	−2.37494	+	1.37117i
$808$		0			0
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	−0.134255	−	0.990947i	$-0.542864\pi$
$809$	22.5000	−	38.9711i	0.791058	−	1.37015i	0.925312	−	0.379206i	$-0.123803\pi$
$810$		0			0
$811$	−21.1660			−0.743239			−0.371620	−	0.928385i	$-0.621197\pi$
$811$	−21.1660			−0.743239			−0.371620	+	0.928385i	$0.621197\pi$
$812$		0			0
$813$	−77.0000			−2.70051
$814$		0			0
$815$	−3.96863	+	6.87386i	−0.139015	+	0.240781i
$816$		0			0
$817$	21.0000	−	12.1244i	0.734697	−	0.424178i
$818$		0			0
$819$	31.7490	−	18.3303i	1.10940	−	0.640513i
$820$		0			0
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	0.528302	−	0.849056i	$-0.322829\pi$
$821$	−13.5000	−	23.3827i	−0.471153	−	0.816061i	−0.999456	+	0.0329950i	$0.989495\pi$
$822$		0			0
$823$	27.7804	+	16.0390i	0.968363	+	0.559085i	0.898737	−	0.438488i	$-0.144486\pi$
$823$	27.7804	+	16.0390i	0.968363	+	0.559085i	0.0696265	+	0.997573i	$0.477819\pi$
$824$		0			0
$825$		−	24.2487i		−	0.844232i
$826$		0			0
$827$			9.16515i			0.318704i	0.987222	+	0.159352i	$0.0509404\pi$
$827$			9.16515i			0.318704i	−0.987222	+	0.159352i	$0.949060\pi$
$828$		0			0
$829$	−4.50000	−	2.59808i	−0.156291	−	0.0902349i	0.419815	−	0.907610i	$-0.362095\pi$
$829$	−4.50000	−	2.59808i	−0.156291	−	0.0902349i	−0.576106	+	0.817375i	$0.695428\pi$
$830$		0			0
$831$	22.4889	+	38.9519i	0.780131	+	1.35123i
$832$		0			0
$833$	31.5000	+	18.1865i	1.09141	+	0.630126i
$834$		0			0
$835$	−23.8118	+	13.7477i	−0.824040	+	0.475760i
$836$		0			0
$837$	−3.50000	+	6.06218i	−0.120978	+	0.209540i
$838$		0			0
$839$	−31.7490			−1.09610			−0.548049	−	0.836446i	$-0.684629\pi$
$839$	−31.7490			−1.09610			−0.548049	+	0.836446i	$0.684629\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.50000	−	0.866025i	0.0516016	−	0.0297922i
$846$		0			0
$847$	−13.2288	−	22.9129i	−0.454545	−	0.787296i
$848$		0			0
$849$	17.5000	+	30.3109i	0.600598	+	1.04027i
$850$		0			0
$851$	27.7804	+	16.0390i	0.952299	+	0.549810i
$852$		0			0
$853$			51.9615i			1.77913i	0.456810	+	0.889564i	$0.348992\pi$
$853$			51.9615i			1.77913i	−0.456810	+	0.889564i	$0.651008\pi$
$854$		0			0
$855$		−	18.3303i		−	0.626883i
$856$		0			0
$857$	25.5000	+	14.7224i	0.871063	+	0.502909i	0.867701	−	0.497086i	$-0.165597\pi$
$857$	25.5000	+	14.7224i	0.871063	+	0.502909i	0.00336193	+	0.999994i	$0.498930\pi$
$858$		0			0
$859$	1.32288	+	2.29129i	0.0451359	+	0.0781777i	0.887711	−	0.460402i	$-0.152295\pi$
$859$	1.32288	+	2.29129i	0.0451359	+	0.0781777i	−0.842575	+	0.538579i	$0.818961\pi$
$860$		0			0
$861$	21.0000	+	12.1244i	0.715678	+	0.413197i
$862$		0			0
$863$	−11.9059	+	6.87386i	−0.405281	+	0.233989i	−0.688760	−	0.724989i	$-0.741845\pi$
$863$	−11.9059	+	6.87386i	−0.405281	+	0.233989i	0.283479	+	0.958978i	$0.408511\pi$
$864$		0			0
$865$	−19.5000	+	33.7750i	−0.663020	+	1.14838i
$866$		0			0
$867$	26.4575			0.898544
$868$		0			0
$869$	−21.0000			−0.712376
$870$		0			0
$871$	7.93725	−	13.7477i	0.268944	−	0.465824i
$872$		0			0
$873$	−12.0000	+	6.92820i	−0.406138	+	0.234484i
$874$		0			0
$875$		−	32.0780i		−	1.08444i
$876$		0			0
$877$	−3.50000	−	6.06218i	−0.118187	−	0.204705i	0.800862	−	0.598848i	$-0.204375\pi$
$877$	−3.50000	−	6.06218i	−0.118187	−	0.204705i	−0.919049	+	0.394143i	$0.871041\pi$
$878$		0			0
$879$	47.6235	+	27.4955i	1.60630	+	0.927399i
$880$		0			0
$881$			27.7128i			0.933668i	0.884345	+	0.466834i	$0.154606\pi$
$881$			27.7128i			0.933668i	−0.884345	+	0.466834i	$0.845394\pi$
$882$		0			0
$883$		−	27.4955i		−	0.925296i	−0.886542	−	0.462648i	$-0.846899\pi$
$883$		−	27.4955i		−	0.925296i	0.886542	−	0.462648i	$-0.153101\pi$
$884$		0			0
$885$	31.5000	+	18.1865i	1.05886	+	0.611334i
$886$		0			0
$887$	−11.9059	−	20.6216i	−0.399760	−	0.692405i	0.593936	−	0.804512i	$-0.297573\pi$
$887$	−11.9059	−	20.6216i	−0.399760	−	0.692405i	−0.993696	+	0.112107i	$0.964240\pi$
$888$		0			0
$889$			24.2487i			0.813276i
$890$		0			0
$891$	−19.8431	+	11.4564i	−0.664770	+	0.383805i
$892$		0			0
$893$	−10.5000	+	18.1865i	−0.351369	+	0.608589i
$894$		0			0
$895$	23.8118			0.795939
$896$		0			0
$897$	−42.0000			−1.40234
$898$		0			0
$899$		0			0
$900$		0			0
$901$	13.5000	−	7.79423i	0.449750	−	0.259663i
$902$		0			0
$903$	55.5608	+	32.0780i	1.84895	+	1.06749i
$904$		0			0
$905$	−18.0000	−	31.1769i	−0.598340	−	1.03636i
$906$		0			0
$907$	19.8431	+	11.4564i	0.658880	+	0.380405i	0.791850	−	0.610715i	$-0.209118\pi$
$907$	19.8431	+	11.4564i	0.658880	+	0.380405i	−0.132970	+	0.991120i	$0.542451\pi$
$908$		0			0
$909$			20.7846i			0.689382i
$910$		0			0
$911$			27.4955i			0.910965i	0.890245	+	0.455483i	$0.150533\pi$
$911$			27.4955i			0.910965i	−0.890245	+	0.455483i	$0.849467\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	3.96863	+	6.87386i	0.131199	+	0.227243i
$916$		0			0
$917$	−10.5000	−	18.1865i	−0.346741	−	0.600572i
$918$		0			0
$919$	−19.8431	+	11.4564i	−0.654565	+	0.377913i	−0.790203	−	0.612845i	$-0.790025\pi$
$919$	−19.8431	+	11.4564i	−0.654565	+	0.377913i	0.135638	+	0.990758i	$0.456692\pi$
$920$		0			0
$921$	−14.0000	+	24.2487i	−0.461316	+	0.799022i
$922$		0			0
$923$	31.7490			1.04503
$924$		0			0
$925$	−14.0000			−0.460317
$926$		0			0
$927$	5.29150	−	9.16515i	0.173796	−	0.301023i
$928$		0			0
$929$	−40.5000	+	23.3827i	−1.32876	+	0.767161i	−0.985108	−	0.171935i	$-0.944998\pi$
$929$	−40.5000	+	23.3827i	−1.32876	+	0.767161i	−0.343654	+	0.939096i	$0.611665\pi$
$930$		0			0
$931$	9.26013	+	16.0390i	0.303488	+	0.525657i
$932$		0			0
$933$	31.5000	+	54.5596i	1.03126	+	1.78620i
$934$		0			0
$935$	−35.7176	−	20.6216i	−1.16809	−	0.674398i
$936$		0			0
$937$		−	27.7128i		−	0.905338i	−0.891679	−	0.452669i	$-0.850472\pi$
$937$		−	27.7128i		−	0.905338i	0.891679	−	0.452669i	$-0.149528\pi$
$938$		0			0
$939$			68.7386i			2.24320i
$940$		0			0
$941$	16.5000	+	9.52628i	0.537885	+	0.310548i	0.744221	−	0.667933i	$-0.232821\pi$
$941$	16.5000	+	9.52628i	0.537885	+	0.310548i	−0.206337	+	0.978481i	$0.566154\pi$
$942$		0			0
$943$	−7.93725	−	13.7477i	−0.258473	−	0.447688i
$944$		0			0
$945$	10.5000	−	6.06218i	0.341565	−	0.197203i
$946$		0			0
$947$	−3.96863	+	2.29129i	−0.128963	+	0.0744569i	−0.563094	−	0.826393i	$-0.690389\pi$
$947$	−3.96863	+	2.29129i	−0.128963	+	0.0744569i	0.434131	+	0.900850i	$0.357056\pi$
$948$		0			0
$949$	−9.00000	+	15.5885i	−0.292152	+	0.506023i
$950$		0			0
$951$	39.6863			1.28692
$952$		0			0
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$		0			0
$955$	−19.8431	+	34.3693i	−0.642109	+	1.11217i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	27.7804	−	48.1170i	0.897076	−	1.55378i
$960$		0			0
$961$	12.0000	+	20.7846i	0.387097	+	0.670471i
$962$		0			0
$963$	47.6235	+	27.4955i	1.53465	+	0.886029i
$964$		0			0
$965$		−	19.0526i		−	0.613324i
$966$		0			0
$967$			45.8258i			1.47366i	0.676080	+	0.736828i	$0.263677\pi$
$967$			45.8258i			1.47366i	−0.676080	+	0.736828i	$0.736323\pi$
$968$		0			0
$969$	31.5000	+	18.1865i	1.01193	+	0.584236i
$970$		0			0
$971$	−27.7804	−	48.1170i	−0.891515	−	1.54415i	−0.838059	−	0.545579i	$-0.816310\pi$
$971$	−27.7804	−	48.1170i	−0.891515	−	1.54415i	−0.0534559	−	0.998570i	$-0.517024\pi$
$972$		0			0
$973$	−28.0000			−0.897639
$974$		0			0
$975$	15.8745	−	9.16515i	0.508391	−	0.293520i
$976$		0			0
$977$	−10.5000	+	18.1865i	−0.335925	+	0.581839i	−0.983662	−	0.180025i	$-0.942382\pi$
$977$	−10.5000	+	18.1865i	−0.335925	+	0.581839i	0.647737	+	0.761864i	$0.275715\pi$
$978$		0			0
$979$	−7.93725			−0.253676
$980$		0			0
$981$	28.0000			0.893971
$982$		0			0
$983$	−3.96863	+	6.87386i	−0.126580	+	0.219242i	−0.922349	−	0.386357i	$-0.873733\pi$
$983$	−3.96863	+	6.87386i	−0.126580	+	0.219242i	0.795770	+	0.605599i	$0.207067\pi$
$984$		0			0
$985$	18.0000	−	10.3923i	0.573528	−	0.331126i
$986$		0			0
$987$	−55.5608			−1.76852
$988$		0			0
$989$	−21.0000	−	36.3731i	−0.667761	−	1.15660i
$990$		0			0
$991$	−3.96863	−	2.29129i	−0.126068	−	0.0727852i	0.435640	−	0.900121i	$-0.356522\pi$
$991$	−3.96863	−	2.29129i	−0.126068	−	0.0727852i	−0.561708	+	0.827336i	$0.689855\pi$
$992$		0			0
$993$		−	36.3731i		−	1.15426i
$994$		0			0
$995$		−	22.9129i		−	0.726387i
$996$		0			0
$997$	−37.5000	−	21.6506i	−1.18764	−	0.685682i	−0.229868	−	0.973222i	$-0.573829\pi$
$997$	−37.5000	−	21.6506i	−1.18764	−	0.685682i	−0.957769	+	0.287539i	$0.907163\pi$
$998$		0			0
$999$	−9.26013	−	16.0390i	−0.292978	−	0.507452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.p.c.255.2		4
4.3	odd	2	inner	448.2.p.c.255.1		4
7.3	odd	6		3136.2.f.f.3135.3		4
7.4	even	3		3136.2.f.f.3135.2		4
7.5	odd	6	inner	448.2.p.c.383.1		4
8.3	odd	2		112.2.p.c.31.2	yes	4
8.5	even	2		112.2.p.c.31.1	✓	4
24.5	odd	2		1008.2.cs.q.703.1		4
24.11	even	2		1008.2.cs.q.703.2		4
28.3	even	6		3136.2.f.f.3135.1		4
28.11	odd	6		3136.2.f.f.3135.4		4
28.19	even	6	inner	448.2.p.c.383.2		4
56.3	even	6		784.2.f.d.783.4		4
56.5	odd	6		112.2.p.c.47.2	yes	4
56.11	odd	6		784.2.f.d.783.1		4
56.13	odd	2		784.2.p.g.31.2		4
56.19	even	6		112.2.p.c.47.1	yes	4
56.27	even	2		784.2.p.g.31.1		4
56.37	even	6		784.2.p.g.607.1		4
56.45	odd	6		784.2.f.d.783.2		4
56.51	odd	6		784.2.p.g.607.2		4
56.53	even	6		784.2.f.d.783.3		4
168.5	even	6		1008.2.cs.q.271.2		4
168.11	even	6		7056.2.b.s.1567.3		4
168.53	odd	6		7056.2.b.s.1567.4		4
168.59	odd	6		7056.2.b.s.1567.1		4
168.101	even	6		7056.2.b.s.1567.2		4
168.131	odd	6		1008.2.cs.q.271.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.p.c.31.1	✓	4	8.5	even	2
112.2.p.c.31.2	yes	4	8.3	odd	2
112.2.p.c.47.1	yes	4	56.19	even	6
112.2.p.c.47.2	yes	4	56.5	odd	6
448.2.p.c.255.1		4	4.3	odd	2	inner
448.2.p.c.255.2		4	1.1	even	1	trivial
448.2.p.c.383.1		4	7.5	odd	6	inner
448.2.p.c.383.2		4	28.19	even	6	inner
784.2.f.d.783.1		4	56.11	odd	6
784.2.f.d.783.2		4	56.45	odd	6
784.2.f.d.783.3		4	56.53	even	6
784.2.f.d.783.4		4	56.3	even	6
784.2.p.g.31.1		4	56.27	even	2
784.2.p.g.31.2		4	56.13	odd	2
784.2.p.g.607.1		4	56.37	even	6
784.2.p.g.607.2		4	56.51	odd	6
1008.2.cs.q.271.1		4	168.131	odd	6
1008.2.cs.q.271.2		4	168.5	even	6
1008.2.cs.q.703.1		4	24.5	odd	2
1008.2.cs.q.703.2		4	24.11	even	2
3136.2.f.f.3135.1		4	28.3	even	6
3136.2.f.f.3135.2		4	7.4	even	3
3136.2.f.f.3135.3		4	7.3	odd	6
3136.2.f.f.3135.4		4	28.11	odd	6
7056.2.b.s.1567.1		4	168.59	odd	6
7056.2.b.s.1567.2		4	168.101	even	6
7056.2.b.s.1567.3		4	168.11	even	6
7056.2.b.s.1567.4		4	168.53	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32288 - 2.29129i) q^{3} +(1.50000 - 0.866025i) q^{5} -2.64575 q^{7} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\)	\(q+(1.32288 - 2.29129i) q^{3} +(1.50000 - 0.866025i) q^{5} -2.64575 q^{7} +(-2.00000 - 3.46410i) q^{9} +(-3.96863 - 2.29129i) q^{11} -3.46410i q^{13} -4.58258i q^{15} +(4.50000 + 2.59808i) q^{17} +(1.32288 + 2.29129i) q^{19} +(-3.50000 + 6.06218i) q^{21} +(3.96863 - 2.29129i) q^{23} +(-1.00000 + 1.73205i) q^{25} -2.64575 q^{27} +(1.32288 - 2.29129i) q^{31} +(-10.5000 + 6.06218i) q^{33} +(-3.96863 + 2.29129i) q^{35} +(3.50000 + 6.06218i) q^{37} +(-7.93725 - 4.58258i) q^{39} -3.46410i q^{41} -9.16515i q^{43} +(-6.00000 - 3.46410i) q^{45} +(3.96863 + 6.87386i) q^{47} +7.00000 q^{49} +(11.9059 - 6.87386i) q^{51} +(1.50000 - 2.59808i) q^{53} -7.93725 q^{55} +7.00000 q^{57} +(-3.96863 + 6.87386i) q^{59} +(-1.50000 + 0.866025i) q^{61} +(5.29150 + 9.16515i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(3.96863 + 2.29129i) q^{67} -12.1244i q^{69} +9.16515i q^{71} +(-4.50000 - 2.59808i) q^{73} +(2.64575 + 4.58258i) q^{75} +(10.5000 + 6.06218i) q^{77} +(3.96863 - 2.29129i) q^{79} +(2.50000 - 4.33013i) q^{81} +9.00000 q^{85} +(1.50000 - 0.866025i) q^{89} +9.16515i q^{91} +(-3.50000 - 6.06218i) q^{93} +(3.96863 + 2.29129i) q^{95} -3.46410i q^{97} +18.3303i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5} - 8 q^{9}+O(q^{10}) \) 4 * q + 6 * q^5 - 8 * q^9	\( 4 q + 6 q^{5} - 8 q^{9} + 18 q^{17} - 14 q^{21} - 4 q^{25} - 42 q^{33} + 14 q^{37} - 24 q^{45} + 28 q^{49} + 6 q^{53} + 28 q^{57} - 6 q^{61} - 12 q^{65} - 18 q^{73} + 42 q^{77} + 10 q^{81} + 36 q^{85} + 6 q^{89} - 14 q^{93}+O(q^{100}) \) 4 * q + 6 * q^5 - 8 * q^9 + 18 * q^17 - 14 * q^21 - 4 * q^25 - 42 * q^33 + 14 * q^37 - 24 * q^45 + 28 * q^49 + 6 * q^53 + 28 * q^57 - 6 * q^61 - 12 * q^65 - 18 * q^73 + 42 * q^77 + 10 * q^81 + 36 * q^85 + 6 * q^89 - 14 * q^93

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