LMFDB - Embedded newform 240.2.v.c.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(17,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

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

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

chi := DirichletCharacter("240.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.v (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	240.113
Dual form			240.2.v.c.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.414214 + 0.414214i) q^{7} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.414214 + 0.414214i) q^{7} +(1.00000 + 2.82843i) q^{9} +4.82843i q^{11} +(-1.82843 - 1.82843i) q^{13} +(3.41421 - 1.82843i) q^{15} +(3.82843 + 3.82843i) q^{17} +4.82843i q^{19} +(1.00000 - 0.171573i) q^{21} +(-1.58579 + 1.58579i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(1.41421 - 5.00000i) q^{27} -7.65685 q^{29} +5.65685 q^{31} +(4.82843 - 6.82843i) q^{33} +(-0.414214 - 1.24264i) q^{35} +(-0.171573 + 0.171573i) q^{37} +(0.757359 + 4.41421i) q^{39} -5.65685i q^{41} +(-2.41421 - 2.41421i) q^{43} +(-6.65685 - 0.828427i) q^{45} +(-6.41421 - 6.41421i) q^{47} +6.65685i q^{49} +(-1.58579 - 9.24264i) q^{51} +(-3.00000 + 3.00000i) q^{53} +(-9.65685 - 4.82843i) q^{55} +(4.82843 - 6.82843i) q^{57} +4.00000 q^{59} +11.6569 q^{61} +(-1.58579 - 0.757359i) q^{63} +(5.48528 - 1.82843i) q^{65} +(4.07107 - 4.07107i) q^{67} +(3.82843 - 0.656854i) q^{69} +6.48528i q^{71} +(6.65685 + 6.65685i) q^{73} +(0.242641 + 8.65685i) q^{75} +(-2.00000 - 2.00000i) q^{77} -4.82843i q^{79} +(-7.00000 + 5.65685i) q^{81} +(5.24264 - 5.24264i) q^{83} +(-11.4853 + 3.82843i) q^{85} +(10.8284 + 7.65685i) q^{87} +4.34315 q^{89} +1.51472 q^{91} +(-8.00000 - 5.65685i) q^{93} +(-9.65685 - 4.82843i) q^{95} +(1.00000 - 1.00000i) q^{97} +(-13.6569 + 4.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^5 + 4 * q^7 + 4 * q^9	$ 4 q - 4 q^{5} + 4 q^{7} + 4 q^{9} + 4 q^{13} + 8 q^{15} + 4 q^{17} + 4 q^{21} - 12 q^{23} - 12 q^{25} - 8 q^{29} + 8 q^{33} + 4 q^{35} - 12 q^{37} + 20 q^{39} - 4 q^{43} - 4 q^{45} - 20 q^{47} - 12 q^{51} - 12 q^{53} - 16 q^{55} + 8 q^{57} + 16 q^{59} + 24 q^{61} - 12 q^{63} - 12 q^{65} - 12 q^{67} + 4 q^{69} + 4 q^{73} - 16 q^{75} - 8 q^{77} - 28 q^{81} + 4 q^{83} - 12 q^{85} + 32 q^{87} + 40 q^{89} + 40 q^{91} - 32 q^{93} - 16 q^{95} + 4 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 + 4 * q^7 + 4 * q^9 + 4 * q^13 + 8 * q^15 + 4 * q^17 + 4 * q^21 - 12 * q^23 - 12 * q^25 - 8 * q^29 + 8 * q^33 + 4 * q^35 - 12 * q^37 + 20 * q^39 - 4 * q^43 - 4 * q^45 - 20 * q^47 - 12 * q^51 - 12 * q^53 - 16 * q^55 + 8 * q^57 + 16 * q^59 + 24 * q^61 - 12 * q^63 - 12 * q^65 - 12 * q^67 + 4 * q^69 + 4 * q^73 - 16 * q^75 - 8 * q^77 - 28 * q^81 + 4 * q^83 - 12 * q^85 + 32 * q^87 + 40 * q^89 + 40 * q^91 - 32 * q^93 - 16 * q^95 + 4 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$4$		0			0
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	−0.414214	+	0.414214i	−0.156558	+	0.156558i	−0.781040	−	0.624482i	$-0.785310\pi$
$7$	−0.414214	+	0.414214i	−0.156558	+	0.156558i	0.624482	+	0.781040i	$0.285310\pi$
$8$		0			0
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$		0			0
$11$			4.82843i			1.45583i	0.685670	+	0.727913i	$0.259509\pi$
$11$			4.82843i			1.45583i	−0.685670	+	0.727913i	$0.740491\pi$
$12$		0			0
$13$	−1.82843	−	1.82843i	−0.507114	−	0.507114i	0.406525	−	0.913640i	$-0.366740\pi$
$13$	−1.82843	−	1.82843i	−0.507114	−	0.507114i	−0.913640	+	0.406525i	$0.866740\pi$
$14$		0			0
$15$	3.41421	−	1.82843i	0.881546	−	0.472098i
$16$		0			0
$17$	3.82843	+	3.82843i	0.928530	+	0.928530i	0.997611	−	0.0690811i	$-0.0220067\pi$
$17$	3.82843	+	3.82843i	0.928530	+	0.928530i	−0.0690811	+	0.997611i	$0.522007\pi$
$18$		0			0
$19$			4.82843i			1.10772i	0.832611	+	0.553859i	$0.186845\pi$
$19$			4.82843i			1.10772i	−0.832611	+	0.553859i	$0.813155\pi$
$20$		0			0
$21$	1.00000	−	0.171573i	0.218218	−	0.0374403i
$22$		0			0
$23$	−1.58579	+	1.58579i	−0.330659	+	0.330659i	−0.852837	−	0.522178i	$-0.825120\pi$
$23$	−1.58579	+	1.58579i	−0.330659	+	0.330659i	0.522178	+	0.852837i	$0.325120\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$		0			0
$29$	−7.65685			−1.42184			−0.710921	−	0.703272i	$-0.751722\pi$
$29$	−7.65685			−1.42184			−0.710921	+	0.703272i	$0.751722\pi$
$30$		0			0
$31$	5.65685			1.01600			0.508001	−	0.861357i	$-0.330385\pi$
$31$	5.65685			1.01600			0.508001	+	0.861357i	$0.330385\pi$
$32$		0			0
$33$	4.82843	−	6.82843i	0.840521	−	1.18868i
$34$		0			0
$35$	−0.414214	−	1.24264i	−0.0700149	−	0.210045i
$36$		0			0
$37$	−0.171573	+	0.171573i	−0.0282064	+	0.0282064i	−0.721069	−	0.692863i	$-0.756349\pi$
$37$	−0.171573	+	0.171573i	−0.0282064	+	0.0282064i	0.692863	+	0.721069i	$0.256349\pi$
$38$		0			0
$39$	0.757359	+	4.41421i	0.121275	+	0.706840i
$40$		0			0
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$	−2.41421	−	2.41421i	−0.368164	−	0.368164i	0.498643	−	0.866807i	$-0.333832\pi$
$43$	−2.41421	−	2.41421i	−0.368164	−	0.368164i	−0.866807	+	0.498643i	$0.833832\pi$
$44$		0			0
$45$	−6.65685	−	0.828427i	−0.992345	−	0.123495i
$46$		0			0
$47$	−6.41421	−	6.41421i	−0.935609	−	0.935609i	0.0624395	−	0.998049i	$-0.480112\pi$
$47$	−6.41421	−	6.41421i	−0.935609	−	0.935609i	−0.998049	+	0.0624395i	$0.980112\pi$
$48$		0			0
$49$			6.65685i			0.950979i
$50$		0			0
$51$	−1.58579	−	9.24264i	−0.222055	−	1.29423i
$52$		0			0
$53$	−3.00000	+	3.00000i	−0.412082	+	0.412082i	−0.882463	−	0.470381i	$-0.844116\pi$
$53$	−3.00000	+	3.00000i	−0.412082	+	0.412082i	0.470381	+	0.882463i	$0.344116\pi$
$54$		0			0
$55$	−9.65685	−	4.82843i	−1.30213	−	0.651065i
$56$		0			0
$57$	4.82843	−	6.82843i	0.639541	−	0.904447i
$58$		0			0
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$	11.6569			1.49251			0.746254	−	0.665662i	$-0.231851\pi$
$61$	11.6569			1.49251			0.746254	+	0.665662i	$0.231851\pi$
$62$		0			0
$63$	−1.58579	−	0.757359i	−0.199790	−	0.0954183i
$64$		0			0
$65$	5.48528	−	1.82843i	0.680365	−	0.226788i
$66$		0			0
$67$	4.07107	−	4.07107i	0.497360	−	0.497360i	−0.413255	−	0.910615i	$-0.635608\pi$
$67$	4.07107	−	4.07107i	0.497360	−	0.497360i	0.910615	+	0.413255i	$0.135608\pi$
$68$		0			0
$69$	3.82843	−	0.656854i	0.460888	−	0.0790760i
$70$		0			0
$71$			6.48528i			0.769661i	0.922987	+	0.384831i	$0.125740\pi$
$71$			6.48528i			0.769661i	−0.922987	+	0.384831i	$0.874260\pi$
$72$		0			0
$73$	6.65685	+	6.65685i	0.779126	+	0.779126i	0.979682	−	0.200556i	$-0.0642750\pi$
$73$	6.65685	+	6.65685i	0.779126	+	0.779126i	−0.200556	+	0.979682i	$0.564275\pi$
$74$		0			0
$75$	0.242641	+	8.65685i	0.0280177	+	0.999607i
$76$		0			0
$77$	−2.00000	−	2.00000i	−0.227921	−	0.227921i
$78$		0			0
$79$		−	4.82843i		−	0.543240i	−0.962405	−	0.271620i	$-0.912441\pi$
$79$		−	4.82843i		−	0.543240i	0.962405	−	0.271620i	$-0.0875595\pi$
$80$		0			0
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$		0			0
$83$	5.24264	−	5.24264i	0.575455	−	0.575455i	−0.358193	−	0.933648i	$-0.616607\pi$
$83$	5.24264	−	5.24264i	0.575455	−	0.575455i	0.933648	+	0.358193i	$0.116607\pi$
$84$		0			0
$85$	−11.4853	+	3.82843i	−1.24575	+	0.415251i
$86$		0			0
$87$	10.8284	+	7.65685i	1.16093	+	0.820901i
$88$		0			0
$89$	4.34315			0.460373			0.230186	−	0.973147i	$-0.426066\pi$
$89$	4.34315			0.460373			0.230186	+	0.973147i	$0.426066\pi$
$90$		0			0
$91$	1.51472			0.158786
$92$		0			0
$93$	−8.00000	−	5.65685i	−0.829561	−	0.586588i
$94$		0			0
$95$	−9.65685	−	4.82843i	−0.990772	−	0.495386i
$96$		0			0
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	−0.654515	−	0.756049i	$-0.727127\pi$
$97$	1.00000	−	1.00000i	0.101535	−	0.101535i	0.756049	+	0.654515i	$0.227127\pi$
$98$		0			0
$99$	−13.6569	+	4.82843i	−1.37257	+	0.485275i
$100$		0			0
$101$			1.65685i			0.164863i	0.996597	+	0.0824316i	$0.0262686\pi$
$101$			1.65685i			0.164863i	−0.996597	+	0.0824316i	$0.973731\pi$
$102$		0			0
$103$	8.41421	+	8.41421i	0.829077	+	0.829077i	0.987389	−	0.158312i	$-0.0506052\pi$
$103$	8.41421	+	8.41421i	0.829077	+	0.829077i	−0.158312	+	0.987389i	$0.550605\pi$
$104$		0			0
$105$	−0.656854	+	2.17157i	−0.0641024	+	0.211924i
$106$		0			0
$107$	12.4142	+	12.4142i	1.20013	+	1.20013i	0.974127	+	0.226000i	$0.0725649\pi$
$107$	12.4142	+	12.4142i	1.20013	+	1.20013i	0.226000	+	0.974127i	$0.427435\pi$
$108$		0			0
$109$		−	4.00000i		−	0.383131i	−0.981480	−	0.191565i	$-0.938644\pi$
$109$		−	4.00000i		−	0.383131i	0.981480	−	0.191565i	$-0.0613564\pi$
$110$		0			0
$111$	0.414214	−	0.0710678i	0.0393154	−	0.00674546i
$112$		0			0
$113$	−7.48528	+	7.48528i	−0.704156	+	0.704156i	−0.965300	−	0.261144i	$-0.915900\pi$
$113$	−7.48528	+	7.48528i	−0.704156	+	0.704156i	0.261144	+	0.965300i	$0.415900\pi$
$114$		0			0
$115$	−1.58579	−	4.75736i	−0.147875	−	0.443626i
$116$		0			0
$117$	3.34315	−	7.00000i	0.309074	−	0.647150i
$118$		0			0
$119$	−3.17157			−0.290738
$120$		0			0
$121$	−12.3137			−1.11943
$122$		0			0
$123$	−5.65685	+	8.00000i	−0.510061	+	0.721336i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−8.41421	+	8.41421i	−0.746641	+	0.746641i	−0.973847	−	0.227206i	$-0.927041\pi$
$127$	−8.41421	+	8.41421i	−0.746641	+	0.746641i	0.227206	+	0.973847i	$0.427041\pi$
$128$		0			0
$129$	1.00000	+	5.82843i	0.0880451	+	0.513164i
$130$		0			0
$131$		−	3.17157i		−	0.277102i	−0.990355	−	0.138551i	$-0.955756\pi$
$131$		−	3.17157i		−	0.277102i	0.990355	−	0.138551i	$-0.0442444\pi$
$132$		0			0
$133$	−2.00000	−	2.00000i	−0.173422	−	0.173422i
$134$		0			0
$135$	8.58579	+	7.82843i	0.738947	+	0.673764i
$136$		0			0
$137$	−4.17157	−	4.17157i	−0.356402	−	0.356402i	0.506083	−	0.862485i	$-0.331093\pi$
$137$	−4.17157	−	4.17157i	−0.356402	−	0.356402i	−0.862485	+	0.506083i	$0.831093\pi$
$138$		0			0
$139$		−	3.17157i		−	0.269009i	−0.990913	−	0.134505i	$-0.957056\pi$
$139$		−	3.17157i		−	0.269009i	0.990913	−	0.134505i	$-0.0429443\pi$
$140$		0			0
$141$	2.65685	+	15.4853i	0.223747	+	1.30410i
$142$		0			0
$143$	8.82843	−	8.82843i	0.738270	−	0.738270i
$144$		0			0
$145$	7.65685	−	15.3137i	0.635867	−	1.27173i
$146$		0			0
$147$	6.65685	−	9.41421i	0.549048	−	0.776471i
$148$		0			0
$149$	9.31371			0.763009			0.381504	−	0.924367i	$-0.375406\pi$
$149$	9.31371			0.763009			0.381504	+	0.924367i	$0.375406\pi$
$150$		0			0
$151$	2.34315			0.190682			0.0953412	−	0.995445i	$-0.469606\pi$
$151$	2.34315			0.190682			0.0953412	+	0.995445i	$0.469606\pi$
$152$		0			0
$153$	−7.00000	+	14.6569i	−0.565916	+	1.18494i
$154$		0			0
$155$	−5.65685	+	11.3137i	−0.454369	+	0.908739i
$156$		0			0
$157$	−11.4853	+	11.4853i	−0.916625	+	0.916625i	−0.996782	−	0.0801570i	$-0.974458\pi$
$157$	−11.4853	+	11.4853i	−0.916625	+	0.916625i	0.0801570	+	0.996782i	$0.474458\pi$
$158$		0			0
$159$	7.24264	−	1.24264i	0.574379	−	0.0985478i
$160$		0			0
$161$		−	1.31371i		−	0.103535i
$162$		0			0
$163$	−2.41421	−	2.41421i	−0.189096	−	0.189096i	0.606209	−	0.795305i	$-0.292689\pi$
$163$	−2.41421	−	2.41421i	−0.189096	−	0.189096i	−0.795305	+	0.606209i	$0.792689\pi$
$164$		0			0
$165$	8.82843	+	16.4853i	0.687292	+	1.28338i
$166$		0			0
$167$	−0.757359	−	0.757359i	−0.0586062	−	0.0586062i	0.677196	−	0.735802i	$-0.263195\pi$
$167$	−0.757359	−	0.757359i	−0.0586062	−	0.0586062i	−0.735802	+	0.677196i	$0.763195\pi$
$168$		0			0
$169$		−	6.31371i		−	0.485670i
$170$		0			0
$171$	−13.6569	+	4.82843i	−1.04437	+	0.369239i
$172$		0			0
$173$	10.6569	−	10.6569i	0.810226	−	0.810226i	−0.174442	−	0.984667i	$-0.555812\pi$
$173$	10.6569	−	10.6569i	0.810226	−	0.810226i	0.984667	+	0.174442i	$0.0558121\pi$
$174$		0			0
$175$	2.89949	+	0.414214i	0.219181	+	0.0313116i
$176$		0			0
$177$	−5.65685	−	4.00000i	−0.425195	−	0.300658i
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	17.3137			1.28692			0.643459	−	0.765481i	$-0.277499\pi$
$181$	17.3137			1.28692			0.643459	+	0.765481i	$0.277499\pi$
$182$		0			0
$183$	−16.4853	−	11.6569i	−1.21863	−	0.861699i
$184$		0			0
$185$	−0.171573	−	0.514719i	−0.0126143	−	0.0378429i
$186$		0			0
$187$	−18.4853	+	18.4853i	−1.35178	+	1.35178i
$188$		0			0
$189$	1.48528	+	2.65685i	0.108038	+	0.193258i
$190$		0			0
$191$		−	24.1421i		−	1.74686i	−0.486946	−	0.873432i	$-0.661889\pi$
$191$		−	24.1421i		−	1.74686i	0.486946	−	0.873432i	$-0.338111\pi$
$192$		0			0
$193$	3.34315	+	3.34315i	0.240645	+	0.240645i	0.817117	−	0.576472i	$-0.195571\pi$
$193$	3.34315	+	3.34315i	0.240645	+	0.240645i	−0.576472	+	0.817117i	$0.695571\pi$
$194$		0			0
$195$	−9.58579	−	2.89949i	−0.686452	−	0.207637i
$196$		0			0
$197$	3.34315	+	3.34315i	0.238189	+	0.238189i	0.816100	−	0.577911i	$-0.196132\pi$
$197$	3.34315	+	3.34315i	0.238189	+	0.238189i	−0.577911	+	0.816100i	$0.696132\pi$
$198$		0			0
$199$		−	1.51472i		−	0.107376i	−0.998558	−	0.0536878i	$-0.982902\pi$
$199$		−	1.51472i		−	0.107376i	0.998558	−	0.0536878i	$-0.0170976\pi$
$200$		0			0
$201$	−9.82843	+	1.68629i	−0.693244	+	0.118942i
$202$		0			0
$203$	3.17157	−	3.17157i	0.222601	−	0.222601i
$204$		0			0
$205$	11.3137	+	5.65685i	0.790184	+	0.395092i
$206$		0			0
$207$	−6.07107	−	2.89949i	−0.421968	−	0.201529i
$208$		0			0
$209$	−23.3137			−1.61264
$210$		0			0
$211$	12.9706			0.892930			0.446465	−	0.894801i	$-0.352683\pi$
$211$	12.9706			0.892930			0.446465	+	0.894801i	$0.352683\pi$
$212$		0			0
$213$	6.48528	−	9.17157i	0.444364	−	0.628426i
$214$		0			0
$215$	7.24264	−	2.41421i	0.493944	−	0.164648i
$216$		0			0
$217$	−2.34315	+	2.34315i	−0.159063	+	0.159063i
$218$		0			0
$219$	−2.75736	−	16.0711i	−0.186325	−	1.08598i
$220$		0			0
$221$		−	14.0000i		−	0.941742i
$222$		0			0
$223$	8.41421	+	8.41421i	0.563457	+	0.563457i	0.930288	−	0.366830i	$-0.119557\pi$
$223$	8.41421	+	8.41421i	0.563457	+	0.563457i	−0.366830	+	0.930288i	$0.619557\pi$
$224$		0			0
$225$	8.31371	−	12.4853i	0.554247	−	0.832352i
$226$		0			0
$227$	−14.8995	−	14.8995i	−0.988914	−	0.988914i	0.0110250	−	0.999939i	$-0.496491\pi$
$227$	−14.8995	−	14.8995i	−0.988914	−	0.988914i	−0.999939	+	0.0110250i	$0.996491\pi$
$228$		0			0
$229$		−	25.6569i		−	1.69545i	−0.530434	−	0.847726i	$-0.677971\pi$
$229$		−	25.6569i		−	1.69545i	0.530434	−	0.847726i	$-0.322029\pi$
$230$		0			0
$231$	0.828427	+	4.82843i	0.0545065	+	0.317687i
$232$		0			0
$233$	6.17157	−	6.17157i	0.404313	−	0.404313i	−0.475437	−	0.879750i	$-0.657710\pi$
$233$	6.17157	−	6.17157i	0.404313	−	0.404313i	0.879750	+	0.475437i	$0.157710\pi$
$234$		0			0
$235$	19.2426	−	6.41421i	1.25525	−	0.418417i
$236$		0			0
$237$	−4.82843	+	6.82843i	−0.313640	+	0.443554i
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−11.6569			−0.750884			−0.375442	−	0.926846i	$-0.622509\pi$
$241$	−11.6569			−0.750884			−0.375442	+	0.926846i	$0.622509\pi$
$242$		0			0
$243$	15.5563	−	1.00000i	0.997940	−	0.0641500i
$244$		0			0
$245$	−13.3137	−	6.65685i	−0.850582	−	0.425291i
$246$		0			0
$247$	8.82843	−	8.82843i	0.561739	−	0.561739i
$248$		0			0
$249$	−12.6569	+	2.17157i	−0.802096	+	0.137618i
$250$		0			0
$251$			9.51472i			0.600564i	0.953851	+	0.300282i	$0.0970807\pi$
$251$			9.51472i			0.600564i	−0.953851	+	0.300282i	$0.902919\pi$
$252$		0			0
$253$	−7.65685	−	7.65685i	−0.481382	−	0.481382i
$254$		0			0
$255$	20.0711	+	6.07107i	1.25690	+	0.380185i
$256$		0			0
$257$	−7.48528	−	7.48528i	−0.466919	−	0.466919i	0.433996	−	0.900915i	$-0.357103\pi$
$257$	−7.48528	−	7.48528i	−0.466919	−	0.466919i	−0.900915	+	0.433996i	$0.857103\pi$
$258$		0			0
$259$		−	0.142136i		−	0.00883188i
$260$		0			0
$261$	−7.65685	−	21.6569i	−0.473947	−	1.34053i
$262$		0			0
$263$	−12.8995	+	12.8995i	−0.795417	+	0.795417i	−0.982369	−	0.186952i	$-0.940139\pi$
$263$	−12.8995	+	12.8995i	−0.795417	+	0.795417i	0.186952	+	0.982369i	$0.440139\pi$
$264$		0			0
$265$	−3.00000	−	9.00000i	−0.184289	−	0.552866i
$266$		0			0
$267$	−6.14214	−	4.34315i	−0.375893	−	0.265796i
$268$		0			0
$269$	28.6274			1.74544			0.872722	−	0.488217i	$-0.162353\pi$
$269$	28.6274			1.74544			0.872722	+	0.488217i	$0.162353\pi$
$270$		0			0
$271$	−21.6569			−1.31556			−0.657780	−	0.753210i	$-0.728504\pi$
$271$	−21.6569			−1.31556			−0.657780	+	0.753210i	$0.728504\pi$
$272$		0			0
$273$	−2.14214	−	1.51472i	−0.129648	−	0.0916749i
$274$		0			0
$275$	19.3137	−	14.4853i	1.16466	−	0.873495i
$276$		0			0
$277$	−13.8284	+	13.8284i	−0.830870	+	0.830870i	−0.987636	−	0.156766i	$-0.949893\pi$
$277$	−13.8284	+	13.8284i	−0.830870	+	0.830870i	0.156766	+	0.987636i	$0.449893\pi$
$278$		0			0
$279$	5.65685	+	16.0000i	0.338667	+	0.957895i
$280$		0			0
$281$			5.65685i			0.337460i	0.985662	+	0.168730i	$0.0539665\pi$
$281$			5.65685i			0.337460i	−0.985662	+	0.168730i	$0.946033\pi$
$282$		0			0
$283$	3.24264	+	3.24264i	0.192755	+	0.192755i	0.796885	−	0.604130i	$-0.206479\pi$
$283$	3.24264	+	3.24264i	0.192755	+	0.192755i	−0.604130	+	0.796885i	$0.706479\pi$
$284$		0			0
$285$	8.82843	+	16.4853i	0.522951	+	0.976504i
$286$		0			0
$287$	2.34315	+	2.34315i	0.138312	+	0.138312i
$288$		0			0
$289$			12.3137i			0.724336i
$290$		0			0
$291$	−2.41421	+	0.414214i	−0.141524	+	0.0242816i
$292$		0			0
$293$	−5.34315	+	5.34315i	−0.312150	+	0.312150i	−0.845742	−	0.533592i	$-0.820842\pi$
$293$	−5.34315	+	5.34315i	−0.312150	+	0.312150i	0.533592	+	0.845742i	$0.320842\pi$
$294$		0			0
$295$	−4.00000	+	8.00000i	−0.232889	+	0.465778i
$296$		0			0
$297$	24.1421	+	6.82843i	1.40087	+	0.396226i
$298$		0			0
$299$	5.79899			0.335364
$300$		0			0
$301$	2.00000			0.115278
$302$		0			0
$303$	1.65685	−	2.34315i	0.0951838	−	0.134610i
$304$		0			0
$305$	−11.6569	+	23.3137i	−0.667470	+	1.33494i
$306$		0			0
$307$	−12.8995	+	12.8995i	−0.736213	+	0.736213i	−0.971843	−	0.235630i	$-0.924285\pi$
$307$	−12.8995	+	12.8995i	−0.736213	+	0.736213i	0.235630	+	0.971843i	$0.424285\pi$
$308$		0			0
$309$	−3.48528	−	20.3137i	−0.198271	−	1.15561i
$310$		0			0
$311$			22.4853i			1.27502i	0.770441	+	0.637512i	$0.220036\pi$
$311$			22.4853i			1.27502i	−0.770441	+	0.637512i	$0.779964\pi$
$312$		0			0
$313$	20.3137	+	20.3137i	1.14820	+	1.14820i	0.986907	+	0.161292i	$0.0515661\pi$
$313$	20.3137	+	20.3137i	1.14820	+	1.14820i	0.161292	+	0.986907i	$0.448434\pi$
$314$		0			0
$315$	3.10051	−	2.41421i	0.174694	−	0.136026i
$316$		0			0
$317$	6.65685	+	6.65685i	0.373886	+	0.373886i	0.868891	−	0.495004i	$-0.164834\pi$
$317$	6.65685	+	6.65685i	0.373886	+	0.373886i	−0.495004	+	0.868891i	$0.664834\pi$
$318$		0			0
$319$		−	36.9706i		−	2.06995i
$320$		0			0
$321$	−5.14214	−	29.9706i	−0.287006	−	1.67279i
$322$		0			0
$323$	−18.4853	+	18.4853i	−1.02855	+	1.02855i
$324$		0			0
$325$	−1.82843	+	12.7990i	−0.101423	+	0.709960i
$326$		0			0
$327$	−4.00000	+	5.65685i	−0.221201	+	0.312825i
$328$		0			0
$329$	5.31371			0.292954
$330$		0			0
$331$	−1.65685			−0.0910689			−0.0455345	−	0.998963i	$-0.514499\pi$
$331$	−1.65685			−0.0910689			−0.0455345	+	0.998963i	$0.514499\pi$
$332$		0			0
$333$	−0.656854	−	0.313708i	−0.0359954	−	0.0171911i
$334$		0			0
$335$	4.07107	+	12.2132i	0.222426	+	0.667279i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$	18.0711	−	3.10051i	0.981486	−	0.168396i
$340$		0			0
$341$			27.3137i			1.47912i
$342$		0			0
$343$	−5.65685	−	5.65685i	−0.305441	−	0.305441i
$344$		0			0
$345$	−2.51472	+	8.31371i	−0.135388	+	0.447595i
$346$		0			0
$347$	2.07107	+	2.07107i	0.111181	+	0.111181i	0.760509	−	0.649328i	$-0.224950\pi$
$347$	2.07107	+	2.07107i	0.111181	+	0.111181i	−0.649328	+	0.760509i	$0.724950\pi$
$348$		0			0
$349$		−	1.65685i		−	0.0886894i	−0.999016	−	0.0443447i	$-0.985880\pi$
$349$		−	1.65685i		−	0.0886894i	0.999016	−	0.0443447i	$-0.0141200\pi$
$350$		0			0
$351$	−11.7279	+	6.55635i	−0.625990	+	0.349952i
$352$		0			0
$353$	1.48528	−	1.48528i	0.0790536	−	0.0790536i	−0.666474	−	0.745528i	$-0.732197\pi$
$353$	1.48528	−	1.48528i	0.0790536	−	0.0790536i	0.745528	+	0.666474i	$0.232197\pi$
$354$		0			0
$355$	−12.9706	−	6.48528i	−0.688406	−	0.344203i
$356$		0			0
$357$	4.48528	+	3.17157i	0.237386	+	0.167857i
$358$		0			0
$359$	12.6863			0.669557			0.334778	−	0.942297i	$-0.391339\pi$
$359$	12.6863			0.669557			0.334778	+	0.942297i	$0.391339\pi$
$360$		0			0
$361$	−4.31371			−0.227037
$362$		0			0
$363$	17.4142	+	12.3137i	0.914009	+	0.646302i
$364$		0			0
$365$	−19.9706	+	6.65685i	−1.04531	+	0.348436i
$366$		0			0
$367$	13.2426	−	13.2426i	0.691260	−	0.691260i	−0.271249	−	0.962509i	$-0.587437\pi$
$367$	13.2426	−	13.2426i	0.691260	−	0.691260i	0.962509	+	0.271249i	$0.0874367\pi$
$368$		0			0
$369$	16.0000	−	5.65685i	0.832927	−	0.294484i
$370$		0			0
$371$		−	2.48528i		−	0.129029i
$372$		0			0
$373$	17.4853	+	17.4853i	0.905354	+	0.905354i	0.995893	−	0.0905393i	$-0.0288591\pi$
$373$	17.4853	+	17.4853i	0.905354	+	0.905354i	−0.0905393	+	0.995893i	$0.528859\pi$
$374$		0			0
$375$	−17.5563	−	8.17157i	−0.906606	−	0.421978i
$376$		0			0
$377$	14.0000	+	14.0000i	0.721037	+	0.721037i
$378$		0			0
$379$		−	9.79899i		−	0.503340i	−0.967813	−	0.251670i	$-0.919020\pi$
$379$		−	9.79899i		−	0.503340i	0.967813	−	0.251670i	$-0.0809798\pi$
$380$		0			0
$381$	20.3137	−	3.48528i	1.04070	−	0.178556i
$382$		0			0
$383$	−9.58579	+	9.58579i	−0.489811	+	0.489811i	−0.908246	−	0.418436i	$-0.862579\pi$
$383$	−9.58579	+	9.58579i	−0.489811	+	0.489811i	0.418436	+	0.908246i	$0.362579\pi$
$384$		0			0
$385$	6.00000	−	2.00000i	0.305788	−	0.101929i
$386$		0			0
$387$	4.41421	−	9.24264i	0.224387	−	0.469830i
$388$		0			0
$389$	−29.3137			−1.48626			−0.743132	−	0.669145i	$-0.766661\pi$
$389$	−29.3137			−1.48626			−0.743132	+	0.669145i	$0.766661\pi$
$390$		0			0
$391$	−12.1421			−0.614054
$392$		0			0
$393$	−3.17157	+	4.48528i	−0.159985	+	0.226253i
$394$		0			0
$395$	9.65685	+	4.82843i	0.485889	+	0.242945i
$396$		0			0
$397$	2.17157	−	2.17157i	0.108988	−	0.108988i	−0.650510	−	0.759498i	$-0.725445\pi$
$397$	2.17157	−	2.17157i	0.108988	−	0.108988i	0.759498	+	0.650510i	$0.225445\pi$
$398$		0			0
$399$	0.828427	+	4.82843i	0.0414732	+	0.241724i
$400$		0			0
$401$			16.0000i			0.799002i	0.916733	+	0.399501i	$0.130817\pi$
$401$			16.0000i			0.799002i	−0.916733	+	0.399501i	$0.869183\pi$
$402$		0			0
$403$	−10.3431	−	10.3431i	−0.515229	−	0.515229i
$404$		0			0
$405$	−4.31371	−	19.6569i	−0.214350	−	0.976757i
$406$		0			0
$407$	−0.828427	−	0.828427i	−0.0410636	−	0.0410636i
$408$		0			0
$409$		−	10.3431i		−	0.511436i	−0.966751	−	0.255718i	$-0.917688\pi$
$409$		−	10.3431i		−	0.511436i	0.966751	−	0.255718i	$-0.0823118\pi$
$410$		0			0
$411$	1.72792	+	10.0711i	0.0852321	+	0.496769i
$412$		0			0
$413$	−1.65685	+	1.65685i	−0.0815285	+	0.0815285i
$414$		0			0
$415$	5.24264	+	15.7279i	0.257351	+	0.772053i
$416$		0			0
$417$	−3.17157	+	4.48528i	−0.155313	+	0.219645i
$418$		0			0
$419$	−37.9411			−1.85355			−0.926773	−	0.375623i	$-0.877429\pi$
$419$	−37.9411			−1.85355			−0.926773	+	0.375623i	$0.877429\pi$
$420$		0			0
$421$	−2.97056			−0.144776			−0.0723882	−	0.997377i	$-0.523062\pi$
$421$	−2.97056			−0.144776			−0.0723882	+	0.997377i	$0.523062\pi$
$422$		0			0
$423$	11.7279	−	24.5563i	0.570231	−	1.19397i
$424$		0			0
$425$	3.82843	−	26.7990i	0.185706	−	1.29994i
$426$		0			0
$427$	−4.82843	+	4.82843i	−0.233664	+	0.233664i
$428$		0			0
$429$	−21.3137	+	3.65685i	−1.02904	+	0.176555i
$430$		0			0
$431$		−	8.14214i		−	0.392193i	−0.980585	−	0.196096i	$-0.937173\pi$
$431$		−	8.14214i		−	0.392193i	0.980585	−	0.196096i	$-0.0628266\pi$
$432$		0			0
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	0.247925	−	0.968779i	$-0.420251\pi$
$433$	−15.0000	−	15.0000i	−0.720854	−	0.720854i	−0.968779	+	0.247925i	$0.920251\pi$
$434$		0			0
$435$	−26.1421	+	14.0000i	−1.25342	+	0.671249i
$436$		0			0
$437$	−7.65685	−	7.65685i	−0.366277	−	0.366277i
$438$		0			0
$439$			25.7990i			1.23132i	0.788012	+	0.615659i	$0.211110\pi$
$439$			25.7990i			1.23132i	−0.788012	+	0.615659i	$0.788890\pi$
$440$		0			0
$441$	−18.8284	+	6.65685i	−0.896592	+	0.316993i
$442$		0			0
$443$	−14.0711	+	14.0711i	−0.668537	+	0.668537i	−0.957377	−	0.288841i	$-0.906730\pi$
$443$	−14.0711	+	14.0711i	−0.668537	+	0.668537i	0.288841	+	0.957377i	$0.406730\pi$
$444$		0			0
$445$	−4.34315	+	8.68629i	−0.205885	+	0.411770i
$446$		0			0
$447$	−13.1716	−	9.31371i	−0.622994	−	0.440523i
$448$		0			0
$449$	21.3137			1.00586			0.502928	−	0.864328i	$-0.332256\pi$
$449$	21.3137			1.00586			0.502928	+	0.864328i	$0.332256\pi$
$450$		0			0
$451$	27.3137			1.28615
$452$		0			0
$453$	−3.31371	−	2.34315i	−0.155692	−	0.110091i
$454$		0			0
$455$	−1.51472	+	3.02944i	−0.0710111	+	0.142022i
$456$		0			0
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	−0.683331	−	0.730109i	$-0.739469\pi$
$457$	1.00000	−	1.00000i	0.0467780	−	0.0467780i	0.730109	+	0.683331i	$0.239469\pi$
$458$		0			0
$459$	24.5563	−	13.7279i	1.14619	−	0.640765i
$460$		0			0
$461$			4.97056i			0.231502i	0.993278	+	0.115751i	$0.0369275\pi$
$461$			4.97056i			0.231502i	−0.993278	+	0.115751i	$0.963073\pi$
$462$		0			0
$463$	24.4142	+	24.4142i	1.13462	+	1.13462i	0.989398	+	0.145226i	$0.0463910\pi$
$463$	24.4142	+	24.4142i	1.13462	+	1.13462i	0.145226	+	0.989398i	$0.453609\pi$
$464$		0			0
$465$	19.3137	−	10.3431i	0.895652	−	0.479652i
$466$		0			0
$467$	13.3848	+	13.3848i	0.619374	+	0.619374i	0.945371	−	0.325997i	$-0.105700\pi$
$467$	13.3848	+	13.3848i	0.619374	+	0.619374i	−0.325997	+	0.945371i	$0.605700\pi$
$468$		0			0
$469$			3.37258i			0.155731i
$470$		0			0
$471$	27.7279	−	4.75736i	1.27764	−	0.219208i
$472$		0			0
$473$	11.6569	−	11.6569i	0.535983	−	0.535983i
$474$		0			0
$475$	19.3137	−	14.4853i	0.886174	−	0.664630i
$476$		0			0
$477$	−11.4853	−	5.48528i	−0.525875	−	0.251154i
$478$		0			0
$479$	22.6274			1.03387			0.516937	−	0.856024i	$-0.327072\pi$
$479$	22.6274			1.03387			0.516937	+	0.856024i	$0.327072\pi$
$480$		0			0
$481$	0.627417			0.0286078
$482$		0			0
$483$	−1.31371	+	1.85786i	−0.0597758	+	0.0845358i
$484$		0			0
$485$	1.00000	+	3.00000i	0.0454077	+	0.136223i
$486$		0			0
$487$	16.5563	−	16.5563i	0.750240	−	0.750240i	−0.224284	−	0.974524i	$-0.572004\pi$
$487$	16.5563	−	16.5563i	0.750240	−	0.750240i	0.974524	+	0.224284i	$0.0720043\pi$
$488$		0			0
$489$	1.00000	+	5.82843i	0.0452216	+	0.263571i
$490$		0			0
$491$		−	38.4853i		−	1.73682i	−0.495850	−	0.868408i	$-0.665143\pi$
$491$		−	38.4853i		−	1.73682i	0.495850	−	0.868408i	$-0.334857\pi$
$492$		0			0
$493$	−29.3137	−	29.3137i	−1.32022	−	1.32022i
$494$		0			0
$495$	4.00000	−	32.1421i	0.179787	−	1.44468i
$496$		0			0
$497$	−2.68629	−	2.68629i	−0.120497	−	0.120497i
$498$		0			0
$499$			38.7696i			1.73556i	0.496945	+	0.867782i	$0.334455\pi$
$499$			38.7696i			1.73556i	−0.496945	+	0.867782i	$0.665545\pi$
$500$		0			0
$501$	0.313708	+	1.82843i	0.0140155	+	0.0816881i
$502$		0			0
$503$	20.0711	−	20.0711i	0.894925	−	0.894925i	−0.100057	−	0.994982i	$-0.531903\pi$
$503$	20.0711	−	20.0711i	0.894925	−	0.894925i	0.994982	+	0.100057i	$0.0319025\pi$
$504$		0			0
$505$	−3.31371	−	1.65685i	−0.147458	−	0.0737290i
$506$		0			0
$507$	−6.31371	+	8.92893i	−0.280402	+	0.396548i
$508$		0			0
$509$	−7.65685			−0.339384			−0.169692	−	0.985497i	$-0.554277\pi$
$509$	−7.65685			−0.339384			−0.169692	+	0.985497i	$0.554277\pi$
$510$		0			0
$511$	−5.51472			−0.243957
$512$		0			0
$513$	24.1421	+	6.82843i	1.06590	+	0.301482i
$514$		0			0
$515$	−25.2426	+	8.41421i	−1.11232	+	0.370775i
$516$		0			0
$517$	30.9706	−	30.9706i	1.36208	−	1.36208i
$518$		0			0
$519$	−25.7279	+	4.41421i	−1.12933	+	0.193762i
$520$		0			0
$521$		−	24.0000i		−	1.05146i	−0.850652	−	0.525730i	$-0.823792\pi$
$521$		−	24.0000i		−	1.05146i	0.850652	−	0.525730i	$-0.176208\pi$
$522$		0			0
$523$	−7.10051	−	7.10051i	−0.310483	−	0.310483i	0.534613	−	0.845097i	$-0.320457\pi$
$523$	−7.10051	−	7.10051i	−0.310483	−	0.310483i	−0.845097	+	0.534613i	$0.820457\pi$
$524$		0			0
$525$	−3.68629	−	3.48528i	−0.160883	−	0.152110i
$526$		0			0
$527$	21.6569	+	21.6569i	0.943387	+	0.943387i
$528$		0			0
$529$			17.9706i			0.781329i
$530$		0			0
$531$	4.00000	+	11.3137i	0.173585	+	0.490973i
$532$		0			0
$533$	−10.3431	+	10.3431i	−0.448011	+	0.448011i
$534$		0			0
$535$	−37.2426	+	12.4142i	−1.61014	+	0.536713i
$536$		0			0
$537$	−16.9706	−	12.0000i	−0.732334	−	0.517838i
$538$		0			0
$539$	−32.1421			−1.38446
$540$		0			0
$541$	−6.68629			−0.287466			−0.143733	−	0.989616i	$-0.545911\pi$
$541$	−6.68629			−0.287466			−0.143733	+	0.989616i	$0.545911\pi$
$542$		0			0
$543$	−24.4853	−	17.3137i	−1.05076	−	0.743002i
$544$		0			0
$545$	8.00000	+	4.00000i	0.342682	+	0.171341i
$546$		0			0
$547$	9.72792	−	9.72792i	0.415936	−	0.415936i	−0.467864	−	0.883800i	$-0.654976\pi$
$547$	9.72792	−	9.72792i	0.415936	−	0.415936i	0.883800	+	0.467864i	$0.154976\pi$
$548$		0			0
$549$	11.6569	+	32.9706i	0.497502	+	1.40715i
$550$		0			0
$551$		−	36.9706i		−	1.57500i
$552$		0			0
$553$	2.00000	+	2.00000i	0.0850487	+	0.0850487i
$554$		0			0
$555$	−0.272078	+	0.899495i	−0.0115491	+	0.0381814i
$556$		0			0
$557$	−29.6274	−	29.6274i	−1.25535	−	1.25535i	−0.953287	−	0.302067i	$-0.902323\pi$
$557$	−29.6274	−	29.6274i	−1.25535	−	1.25535i	−0.302067	−	0.953287i	$-0.597677\pi$
$558$		0			0
$559$			8.82843i			0.373403i
$560$		0			0
$561$	44.6274	−	7.65685i	1.88417	−	0.323273i
$562$		0			0
$563$	32.5563	−	32.5563i	1.37209	−	1.37209i	0.514740	−	0.857346i	$-0.327888\pi$
$563$	32.5563	−	32.5563i	1.37209	−	1.37209i	0.857346	−	0.514740i	$-0.172112\pi$
$564$		0			0
$565$	−7.48528	−	22.4558i	−0.314908	−	0.944724i
$566$		0			0
$567$	0.556349	−	5.24264i	0.0233645	−	0.220170i
$568$		0			0
$569$	22.6863			0.951059			0.475529	−	0.879700i	$-0.342257\pi$
$569$	22.6863			0.951059			0.475529	+	0.879700i	$0.342257\pi$
$570$		0			0
$571$	−28.9706			−1.21238			−0.606190	−	0.795320i	$-0.707303\pi$
$571$	−28.9706			−1.21238			−0.606190	+	0.795320i	$0.707303\pi$
$572$		0			0
$573$	−24.1421	+	34.1421i	−1.00855	+	1.42631i
$574$		0			0
$575$	11.1005	+	1.58579i	0.462923	+	0.0661319i
$576$		0			0
$577$	3.34315	−	3.34315i	0.139177	−	0.139177i	−0.634086	−	0.773263i	$-0.718623\pi$
$577$	3.34315	−	3.34315i	0.139177	−	0.139177i	0.773263	+	0.634086i	$0.218623\pi$
$578$		0			0
$579$	−1.38478	−	8.07107i	−0.0575493	−	0.335422i
$580$		0			0
$581$			4.34315i			0.180184i
$582$		0			0
$583$	−14.4853	−	14.4853i	−0.599919	−	0.599919i
$584$		0			0
$585$	10.6569	+	13.6863i	0.440607	+	0.565859i
$586$		0			0
$587$	−20.5563	−	20.5563i	−0.848451	−	0.848451i	0.141489	−	0.989940i	$-0.454811\pi$
$587$	−20.5563	−	20.5563i	−0.848451	−	0.848451i	−0.989940	+	0.141489i	$0.954811\pi$
$588$		0			0
$589$			27.3137i			1.12544i
$590$		0			0
$591$	−1.38478	−	8.07107i	−0.0569621	−	0.331999i
$592$		0			0
$593$	1.48528	−	1.48528i	0.0609932	−	0.0609932i	−0.675952	−	0.736945i	$-0.736267\pi$
$593$	1.48528	−	1.48528i	0.0609932	−	0.0609932i	0.736945	+	0.675952i	$0.236267\pi$
$594$		0			0
$595$	3.17157	−	6.34315i	0.130022	−	0.260044i
$596$		0			0
$597$	−1.51472	+	2.14214i	−0.0619933	+	0.0876718i
$598$		0			0
$599$	−25.9411			−1.05993			−0.529963	−	0.848021i	$-0.677794\pi$
$599$	−25.9411			−1.05993			−0.529963	+	0.848021i	$0.677794\pi$
$600$		0			0
$601$	18.9706			0.773825			0.386913	−	0.922116i	$-0.373541\pi$
$601$	18.9706			0.773825			0.386913	+	0.922116i	$0.373541\pi$
$602$		0			0
$603$	15.5858	+	7.44365i	0.634702	+	0.303129i
$604$		0			0
$605$	12.3137	−	24.6274i	0.500623	−	1.00125i
$606$		0			0
$607$	−15.0416	+	15.0416i	−0.610521	+	0.610521i	−0.943082	−	0.332561i	$-0.892087\pi$
$607$	−15.0416	+	15.0416i	−0.610521	+	0.610521i	0.332561	+	0.943082i	$0.392087\pi$
$608$		0			0
$609$	−7.65685	+	1.31371i	−0.310271	+	0.0532342i
$610$		0			0
$611$			23.4558i			0.948922i
$612$		0			0
$613$	−7.48528	−	7.48528i	−0.302328	−	0.302328i	0.539596	−	0.841924i	$-0.318577\pi$
$613$	−7.48528	−	7.48528i	−0.302328	−	0.302328i	−0.841924	+	0.539596i	$0.818577\pi$
$614$		0			0
$615$	−10.3431	−	19.3137i	−0.417076	−	0.778804i
$616$		0			0
$617$	−17.8284	−	17.8284i	−0.717745	−	0.717745i	0.250398	−	0.968143i	$-0.419439\pi$
$617$	−17.8284	−	17.8284i	−0.717745	−	0.717745i	−0.968143	+	0.250398i	$0.919439\pi$
$618$		0			0
$619$			8.14214i			0.327260i	0.986522	+	0.163630i	$0.0523203\pi$
$619$			8.14214i			0.327260i	−0.986522	+	0.163630i	$0.947680\pi$
$620$		0			0
$621$	5.68629	+	10.1716i	0.228183	+	0.408171i
$622$		0			0
$623$	−1.79899	+	1.79899i	−0.0720750	+	0.0720750i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$	32.9706	+	23.3137i	1.31672	+	0.931060i
$628$		0			0
$629$	−1.31371			−0.0523810
$630$		0			0
$631$	47.5980			1.89485			0.947423	−	0.319984i	$-0.103678\pi$
$631$	47.5980			1.89485			0.947423	+	0.319984i	$0.103678\pi$
$632$		0			0
$633$	−18.3431	−	12.9706i	−0.729075	−	0.515534i
$634$		0			0
$635$	−8.41421	−	25.2426i	−0.333908	−	1.00172i
$636$		0			0
$637$	12.1716	−	12.1716i	0.482255	−	0.482255i
$638$		0			0
$639$	−18.3431	+	6.48528i	−0.725644	+	0.256554i
$640$		0			0
$641$			36.2843i			1.43314i	0.697514	+	0.716571i	$0.254290\pi$
$641$			36.2843i			1.43314i	−0.697514	+	0.716571i	$0.745710\pi$
$642$		0			0
$643$	−30.6985	−	30.6985i	−1.21063	−	1.21063i	−0.970820	−	0.239810i	$-0.922915\pi$
$643$	−30.6985	−	30.6985i	−1.21063	−	1.21063i	−0.239810	−	0.970820i	$-0.577085\pi$
$644$		0			0
$645$	−12.6569	−	3.82843i	−0.498363	−	0.150744i
$646$		0			0
$647$	16.2132	+	16.2132i	0.637407	+	0.637407i	0.949915	−	0.312508i	$-0.101169\pi$
$647$	16.2132	+	16.2132i	0.637407	+	0.637407i	−0.312508	+	0.949915i	$0.601169\pi$
$648$		0			0
$649$			19.3137i			0.758129i
$650$		0			0
$651$	5.65685	−	0.970563i	0.221710	−	0.0380394i
$652$		0			0
$653$	15.3431	−	15.3431i	0.600424	−	0.600424i	−0.340001	−	0.940425i	$-0.610428\pi$
$653$	15.3431	−	15.3431i	0.600424	−	0.600424i	0.940425	+	0.340001i	$0.110428\pi$
$654$		0			0
$655$	6.34315	+	3.17157i	0.247847	+	0.123924i
$656$		0			0
$657$	−12.1716	+	25.4853i	−0.474858	+	0.994276i
$658$		0			0
$659$	34.6274			1.34889			0.674446	−	0.738324i	$-0.264382\pi$
$659$	34.6274			1.34889			0.674446	+	0.738324i	$0.264382\pi$
$660$		0			0
$661$	3.65685			0.142235			0.0711176	−	0.997468i	$-0.477343\pi$
$661$	3.65685			0.142235			0.0711176	+	0.997468i	$0.477343\pi$
$662$		0			0
$663$	−14.0000	+	19.7990i	−0.543715	+	0.768929i
$664$		0			0
$665$	6.00000	−	2.00000i	0.232670	−	0.0775567i
$666$		0			0
$667$	12.1421	−	12.1421i	0.470145	−	0.470145i
$668$		0			0
$669$	−3.48528	−	20.3137i	−0.134749	−	0.785373i
$670$		0			0
$671$			56.2843i			2.17283i
$672$		0			0
$673$	−26.3137	−	26.3137i	−1.01432	−	1.01432i	−0.999896	−	0.0144229i	$-0.995409\pi$
$673$	−26.3137	−	26.3137i	−1.01432	−	1.01432i	−0.0144229	−	0.999896i	$-0.504591\pi$
$674$		0			0
$675$	−24.2426	+	9.34315i	−0.933100	+	0.359618i
$676$		0			0
$677$	21.2843	+	21.2843i	0.818021	+	0.818021i	0.985821	−	0.167800i	$-0.0536663\pi$
$677$	21.2843	+	21.2843i	0.818021	+	0.818021i	−0.167800	+	0.985821i	$0.553666\pi$
$678$		0			0
$679$			0.828427i			0.0317921i
$680$		0			0
$681$	6.17157	+	35.9706i	0.236495	+	1.37839i
$682$		0			0
$683$	8.55635	−	8.55635i	0.327400	−	0.327400i	−0.524197	−	0.851597i	$-0.675635\pi$
$683$	8.55635	−	8.55635i	0.327400	−	0.327400i	0.851597	+	0.524197i	$0.175635\pi$
$684$		0			0
$685$	12.5147	−	4.17157i	0.478163	−	0.159388i
$686$		0			0
$687$	−25.6569	+	36.2843i	−0.978870	+	1.38433i
$688$		0			0
$689$	10.9706			0.417945
$690$		0			0
$691$	22.3431			0.849973			0.424987	−	0.905200i	$-0.360279\pi$
$691$	22.3431			0.849973			0.424987	+	0.905200i	$0.360279\pi$
$692$		0			0
$693$	3.65685	−	7.65685i	0.138912	−	0.290860i
$694$		0			0
$695$	6.34315	+	3.17157i	0.240609	+	0.120305i
$696$		0			0
$697$	21.6569	−	21.6569i	0.820312	−	0.820312i
$698$		0			0
$699$	−14.8995	+	2.55635i	−0.563551	+	0.0966900i
$700$		0			0
$701$		−	4.00000i		−	0.151078i	−0.997143	−	0.0755390i	$-0.975932\pi$
$701$		−	4.00000i		−	0.151078i	0.997143	−	0.0755390i	$-0.0240677\pi$
$702$		0			0
$703$	−0.828427	−	0.828427i	−0.0312447	−	0.0312447i
$704$		0			0
$705$	−33.6274	−	10.1716i	−1.26648	−	0.383084i
$706$		0			0
$707$	−0.686292	−	0.686292i	−0.0258106	−	0.0258106i
$708$		0			0
$709$			24.2843i			0.912015i	0.889976	+	0.456007i	$0.150721\pi$
$709$			24.2843i			0.912015i	−0.889976	+	0.456007i	$0.849279\pi$
$710$		0			0
$711$	13.6569	−	4.82843i	0.512172	−	0.181080i
$712$		0			0
$713$	−8.97056	+	8.97056i	−0.335950	+	0.335950i
$714$		0			0
$715$	8.82843	+	26.4853i	0.330164	+	0.990493i
$716$		0			0
$717$	22.6274	+	16.0000i	0.845036	+	0.597531i
$718$		0			0
$719$	16.0000			0.596699			0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000			0.596699			0.298350	+	0.954457i	$0.403564\pi$
$720$		0			0
$721$	−6.97056			−0.259597
$722$		0			0
$723$	16.4853	+	11.6569i	0.613094	+	0.433523i
$724$		0			0
$725$	22.9706	+	30.6274i	0.853105	+	1.13747i
$726$		0			0
$727$	21.2426	−	21.2426i	0.787846	−	0.787846i	−0.193295	−	0.981141i	$-0.561917\pi$
$727$	21.2426	−	21.2426i	0.787846	−	0.787846i	0.981141	+	0.193295i	$0.0619174\pi$
$728$		0			0
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$		0			0
$731$		−	18.4853i		−	0.683703i
$732$		0			0
$733$	23.1421	+	23.1421i	0.854774	+	0.854774i	0.990717	−	0.135942i	$-0.0434062\pi$
$733$	23.1421	+	23.1421i	0.854774	+	0.854774i	−0.135942	+	0.990717i	$0.543406\pi$
$734$		0			0
$735$	12.1716	+	22.7279i	0.448955	+	0.838332i
$736$		0			0
$737$	19.6569	+	19.6569i	0.724070	+	0.724070i
$738$		0			0
$739$			52.8284i			1.94333i	0.236372	+	0.971663i	$0.424041\pi$
$739$			52.8284i			1.94333i	−0.236372	+	0.971663i	$0.575959\pi$
$740$		0			0
$741$	−21.3137	+	3.65685i	−0.782979	+	0.134338i
$742$		0			0
$743$	−0.615224	+	0.615224i	−0.0225704	+	0.0225704i	−0.718302	−	0.695732i	$-0.755080\pi$
$743$	−0.615224	+	0.615224i	−0.0225704	+	0.0225704i	0.695732	+	0.718302i	$0.255080\pi$
$744$		0			0
$745$	−9.31371	+	18.6274i	−0.341228	+	0.682456i
$746$		0			0
$747$	20.0711	+	9.58579i	0.734362	+	0.350726i
$748$		0			0
$749$	−10.2843			−0.375779
$750$		0			0
$751$	−44.2843			−1.61596			−0.807978	−	0.589213i	$-0.799438\pi$
$751$	−44.2843			−1.61596			−0.807978	+	0.589213i	$0.799438\pi$
$752$		0			0
$753$	9.51472	−	13.4558i	0.346736	−	0.490358i
$754$		0			0
$755$	−2.34315	+	4.68629i	−0.0852758	+	0.170552i
$756$		0			0
$757$	−36.4558	+	36.4558i	−1.32501	+	1.32501i	−0.415347	+	0.909663i	$0.636340\pi$
$757$	−36.4558	+	36.4558i	−1.32501	+	1.32501i	−0.909663	+	0.415347i	$0.863660\pi$
$758$		0			0
$759$	3.17157	+	18.4853i	0.115121	+	0.670973i
$760$		0			0
$761$		−	35.3137i		−	1.28012i	−0.768325	−	0.640060i	$-0.778909\pi$
$761$		−	35.3137i		−	1.28012i	0.768325	−	0.640060i	$-0.221091\pi$
$762$		0			0
$763$	1.65685	+	1.65685i	0.0599822	+	0.0599822i
$764$		0			0
$765$	−22.3137	−	28.6569i	−0.806754	−	1.03609i
$766$		0			0
$767$	−7.31371	−	7.31371i	−0.264083	−	0.264083i
$768$		0			0
$769$		−	17.9411i		−	0.646974i	−0.946233	−	0.323487i	$-0.895145\pi$
$769$		−	17.9411i		−	0.646974i	0.946233	−	0.323487i	$-0.104855\pi$
$770$		0			0
$771$	3.10051	+	18.0711i	0.111662	+	0.650814i
$772$		0			0
$773$	−0.656854	+	0.656854i	−0.0236254	+	0.0236254i	−0.718821	−	0.695195i	$-0.755318\pi$
$773$	−0.656854	+	0.656854i	−0.0236254	+	0.0236254i	0.695195	+	0.718821i	$0.255318\pi$
$774$		0			0
$775$	−16.9706	−	22.6274i	−0.609601	−	0.812801i
$776$		0			0
$777$	−0.142136	+	0.201010i	−0.00509909	+	0.00721120i
$778$		0			0
$779$	27.3137			0.978615
$780$		0			0
$781$	−31.3137			−1.12049
$782$		0			0
$783$	−10.8284	+	38.2843i	−0.386976	+	1.36817i
$784$		0			0
$785$	−11.4853	−	34.4558i	−0.409927	−	1.22978i
$786$		0			0
$787$	30.4142	−	30.4142i	1.08415	−	1.08415i	0.0880320	−	0.996118i	$-0.471942\pi$
$787$	30.4142	−	30.4142i	1.08415	−	1.08415i	0.996118	−	0.0880320i	$-0.0280578\pi$
$788$		0			0
$789$	31.1421	−	5.34315i	1.10869	−	0.190221i
$790$		0			0
$791$		−	6.20101i		−	0.220483i
$792$		0			0
$793$	−21.3137	−	21.3137i	−0.756872	−	0.756872i
$794$		0			0
$795$	−4.75736	+	15.7279i	−0.168726	+	0.557812i
$796$		0			0
$797$	6.65685	+	6.65685i	0.235798	+	0.235798i	0.815108	−	0.579310i	$-0.196678\pi$
$797$	6.65685	+	6.65685i	0.235798	+	0.235798i	−0.579310	+	0.815108i	$0.696678\pi$
$798$		0			0
$799$		−	49.1127i		−	1.73748i
$800$		0			0
$801$	4.34315	+	12.2843i	0.153458	+	0.434043i
$802$		0			0
$803$	−32.1421	+	32.1421i	−1.13427	+	1.13427i
$804$		0			0
$805$	2.62742	+	1.31371i	0.0926043	+	0.0463021i
$806$		0			0
$807$	−40.4853	−	28.6274i	−1.42515	−	1.00773i
$808$		0			0
$809$	−43.6569			−1.53489			−0.767447	−	0.641113i	$-0.778473\pi$
$809$	−43.6569			−1.53489			−0.767447	+	0.641113i	$0.778473\pi$
$810$		0			0
$811$	−22.3431			−0.784574			−0.392287	−	0.919843i	$-0.628316\pi$
$811$	−22.3431			−0.784574			−0.392287	+	0.919843i	$0.628316\pi$
$812$		0			0
$813$	30.6274	+	21.6569i	1.07415	+	0.759539i
$814$		0			0
$815$	7.24264	−	2.41421i	0.253699	−	0.0845662i
$816$		0			0
$817$	11.6569	−	11.6569i	0.407822	−	0.407822i
$818$		0			0
$819$	1.51472	+	4.28427i	0.0529286	+	0.149705i
$820$		0			0
$821$		−	29.9411i		−	1.04495i	−0.852654	−	0.522476i	$-0.825008\pi$
$821$		−	29.9411i		−	1.04495i	0.852654	−	0.522476i	$-0.174992\pi$
$822$		0			0
$823$	19.7279	+	19.7279i	0.687672	+	0.687672i	0.961717	−	0.274045i	$-0.0883617\pi$
$823$	19.7279	+	19.7279i	0.687672	+	0.687672i	−0.274045	+	0.961717i	$0.588362\pi$
$824$		0			0
$825$	−41.7990	+	1.17157i	−1.45525	+	0.0407889i
$826$		0			0
$827$	−37.5269	−	37.5269i	−1.30494	−	1.30494i	−0.925020	−	0.379919i	$-0.875952\pi$
$827$	−37.5269	−	37.5269i	−1.30494	−	1.30494i	−0.379919	−	0.925020i	$-0.624048\pi$
$828$		0			0
$829$			7.31371i			0.254016i	0.991902	+	0.127008i	$0.0405373\pi$
$829$			7.31371i			0.254016i	−0.991902	+	0.127008i	$0.959463\pi$
$830$		0			0
$831$	33.3848	−	5.72792i	1.15811	−	0.198699i
$832$		0			0
$833$	−25.4853	+	25.4853i	−0.883013	+	0.883013i
$834$		0			0
$835$	2.27208	−	0.757359i	0.0786285	−	0.0262095i
$836$		0			0
$837$	8.00000	−	28.2843i	0.276520	−	0.977647i
$838$		0			0
$839$	35.3137			1.21916			0.609582	−	0.792723i	$-0.291337\pi$
$839$	35.3137			1.21916			0.609582	+	0.792723i	$0.291337\pi$
$840$		0			0
$841$	29.6274			1.02164
$842$		0			0
$843$	5.65685	−	8.00000i	0.194832	−	0.275535i
$844$		0			0
$845$	12.6274	+	6.31371i	0.434396	+	0.217198i
$846$		0			0
$847$	5.10051	−	5.10051i	0.175255	−	0.175255i
$848$		0			0
$849$	−1.34315	−	7.82843i	−0.0460966	−	0.268671i
$850$		0			0
$851$		−	0.544156i		−	0.0186534i
$852$		0			0
$853$	26.4558	+	26.4558i	0.905831	+	0.905831i	0.995933	−	0.0901017i	$-0.0287192\pi$
$853$	26.4558	+	26.4558i	0.905831	+	0.905831i	−0.0901017	+	0.995933i	$0.528719\pi$
$854$		0			0
$855$	4.00000	−	32.1421i	0.136797	−	1.09924i
$856$		0			0
$857$	16.5147	+	16.5147i	0.564132	+	0.564132i	0.930479	−	0.366346i	$-0.119392\pi$
$857$	16.5147	+	16.5147i	0.564132	+	0.564132i	−0.366346	+	0.930479i	$0.619392\pi$
$858$		0			0
$859$		−	32.4264i		−	1.10637i	−0.833057	−	0.553187i	$-0.813411\pi$
$859$		−	32.4264i		−	1.10637i	0.833057	−	0.553187i	$-0.186589\pi$
$860$		0			0
$861$	−0.970563	−	5.65685i	−0.0330767	−	0.192785i
$862$		0			0
$863$	6.41421	−	6.41421i	0.218342	−	0.218342i	−0.589457	−	0.807800i	$-0.700658\pi$
$863$	6.41421	−	6.41421i	0.218342	−	0.218342i	0.807800	+	0.589457i	$0.200658\pi$
$864$		0			0
$865$	10.6569	+	31.9706i	0.362344	+	1.08703i
$866$		0			0
$867$	12.3137	−	17.4142i	0.418195	−	0.591418i
$868$		0			0
$869$	23.3137			0.790863
$870$		0			0
$871$	−14.8873			−0.504437
$872$		0			0
$873$	3.82843	+	1.82843i	0.129573	+	0.0618829i
$874$		0			0
$875$	−3.72792	+	5.38478i	−0.126027	+	0.182039i
$876$		0			0
$877$	38.4558	−	38.4558i	1.29856	−	1.29856i	0.369219	−	0.929342i	$-0.379625\pi$
$877$	38.4558	−	38.4558i	1.29856	−	1.29856i	0.929342	−	0.369219i	$-0.120375\pi$
$878$		0			0
$879$	12.8995	−	2.21320i	0.435089	−	0.0746495i
$880$		0			0
$881$		−	24.9706i		−	0.841280i	−0.907228	−	0.420640i	$-0.861806\pi$
$881$		−	24.9706i		−	0.841280i	0.907228	−	0.420640i	$-0.138194\pi$
$882$		0			0
$883$	−34.4142	−	34.4142i	−1.15813	−	1.15813i	−0.984877	−	0.173253i	$-0.944572\pi$
$883$	−34.4142	−	34.4142i	−1.15813	−	1.15813i	−0.173253	−	0.984877i	$-0.555428\pi$
$884$		0			0
$885$	13.6569	−	7.31371i	0.459070	−	0.245848i
$886$		0			0
$887$	−17.7279	−	17.7279i	−0.595245	−	0.595245i	0.343798	−	0.939044i	$-0.388286\pi$
$887$	−17.7279	−	17.7279i	−0.595245	−	0.595245i	−0.939044	+	0.343798i	$0.888286\pi$
$888$		0			0
$889$		−	6.97056i		−	0.233785i
$890$		0			0
$891$	−27.3137	−	33.7990i	−0.915044	−	1.13231i
$892$		0			0
$893$	30.9706	−	30.9706i	1.03639	−	1.03639i
$894$		0			0
$895$	−12.0000	+	24.0000i	−0.401116	+	0.802232i
$896$		0			0
$897$	−8.20101	−	5.79899i	−0.273824	−	0.193623i
$898$		0			0
$899$	−43.3137			−1.44459
$900$		0			0
$901$	−22.9706			−0.765260
$902$		0			0
$903$	−2.82843	−	2.00000i	−0.0941242	−	0.0665558i
$904$		0			0
$905$	−17.3137	+	34.6274i	−0.575527	+	1.15105i
$906$		0			0
$907$	−25.5858	+	25.5858i	−0.849562	+	0.849562i	−0.990078	−	0.140516i	$-0.955124\pi$
$907$	−25.5858	+	25.5858i	−0.849562	+	0.849562i	0.140516	+	0.990078i	$0.455124\pi$
$908$		0			0
$909$	−4.68629	+	1.65685i	−0.155434	+	0.0549544i
$910$		0			0
$911$			35.1716i			1.16529i	0.812728	+	0.582643i	$0.197981\pi$
$911$			35.1716i			1.16529i	−0.812728	+	0.582643i	$0.802019\pi$
$912$		0			0
$913$	25.3137	+	25.3137i	0.837761	+	0.837761i
$914$		0			0
$915$	39.7990	−	21.3137i	1.31571	−	0.704609i
$916$		0			0
$917$	1.31371	+	1.31371i	0.0433825	+	0.0433825i
$918$		0			0
$919$			3.17157i			0.104621i	0.998631	+	0.0523103i	$0.0166585\pi$
$919$			3.17157i			0.104621i	−0.998631	+	0.0523103i	$0.983342\pi$
$920$		0			0
$921$	31.1421	−	5.34315i	1.02617	−	0.176063i
$922$		0			0
$923$	11.8579	−	11.8579i	0.390306	−	0.390306i
$924$		0			0
$925$	1.20101	+	0.171573i	0.0394890	+	0.00564128i
$926$		0			0
$927$	−15.3848	+	32.2132i	−0.505302	+	1.05802i
$928$		0			0
$929$	−55.9411			−1.83537			−0.917684	−	0.397310i	$-0.869944\pi$
$929$	−55.9411			−1.83537			−0.917684	+	0.397310i	$0.869944\pi$
$930$		0			0
$931$	−32.1421			−1.05342
$932$		0			0
$933$	22.4853	−	31.7990i	0.736135	−	1.04105i
$934$		0			0
$935$	−18.4853	−	55.4558i	−0.604533	−	1.81360i
$936$		0			0
$937$	−31.0000	+	31.0000i	−1.01273	+	1.01273i	−0.0128079	+	0.999918i	$0.504077\pi$
$937$	−31.0000	+	31.0000i	−1.01273	+	1.01273i	−0.999918	+	0.0128079i	$0.995923\pi$
$938$		0			0
$939$	−8.41421	−	49.0416i	−0.274587	−	1.60041i
$940$		0			0
$941$		−	35.5980i		−	1.16046i	−0.814452	−	0.580230i	$-0.802962\pi$
$941$		−	35.5980i		−	1.16046i	0.814452	−	0.580230i	$-0.197038\pi$
$942$		0			0
$943$	8.97056	+	8.97056i	0.292122	+	0.292122i
$944$		0			0
$945$	−6.79899	+	0.313708i	−0.221171	+	0.0102049i
$946$		0			0
$947$	23.7279	+	23.7279i	0.771054	+	0.771054i	0.978291	−	0.207237i	$-0.0664471\pi$
$947$	23.7279	+	23.7279i	0.771054	+	0.771054i	−0.207237	+	0.978291i	$0.566447\pi$
$948$		0			0
$949$		−	24.3431i		−	0.790212i
$950$		0			0
$951$	−2.75736	−	16.0711i	−0.0894135	−	0.521140i
$952$		0			0
$953$	1.48528	−	1.48528i	0.0481130	−	0.0481130i	−0.682641	−	0.730754i	$-0.739169\pi$
$953$	1.48528	−	1.48528i	0.0481130	−	0.0481130i	0.730754	+	0.682641i	$0.239169\pi$
$954$		0			0
$955$	48.2843	+	24.1421i	1.56244	+	0.781221i
$956$		0			0
$957$	−36.9706	+	52.2843i	−1.19509	+	1.69011i
$958$		0			0
$959$	3.45584			0.111595
$960$		0			0
$961$	1.00000			0.0322581
$962$		0			0
$963$	−22.6985	+	47.5269i	−0.731448	+	1.53153i
$964$		0			0
$965$	−10.0294	+	3.34315i	−0.322859	+	0.107620i
$966$		0			0
$967$	15.5858	−	15.5858i	0.501205	−	0.501205i	−0.410607	−	0.911812i	$-0.634683\pi$
$967$	15.5858	−	15.5858i	0.501205	−	0.501205i	0.911812	+	0.410607i	$0.134683\pi$
$968$		0			0
$969$	44.6274	−	7.65685i	1.43364	−	0.245974i
$970$		0			0
$971$			25.5147i			0.818806i	0.912354	+	0.409403i	$0.134263\pi$
$971$			25.5147i			0.818806i	−0.912354	+	0.409403i	$0.865737\pi$
$972$		0			0
$973$	1.31371	+	1.31371i	0.0421156	+	0.0421156i
$974$		0			0
$975$	15.3848	−	16.2721i	0.492707	−	0.521124i
$976$		0			0
$977$	−5.14214	−	5.14214i	−0.164511	−	0.164511i	0.620050	−	0.784562i	$-0.287112\pi$
$977$	−5.14214	−	5.14214i	−0.164511	−	0.164511i	−0.784562	+	0.620050i	$0.787112\pi$
$978$		0			0
$979$			20.9706i			0.670222i
$980$		0			0
$981$	11.3137	−	4.00000i	0.361219	−	0.127710i
$982$		0			0
$983$	26.6985	−	26.6985i	0.851549	−	0.851549i	−0.138775	−	0.990324i	$-0.544316\pi$
$983$	26.6985	−	26.6985i	0.851549	−	0.851549i	0.990324	+	0.138775i	$0.0443163\pi$
$984$		0			0
$985$	−10.0294	+	3.34315i	−0.319564	+	0.106521i
$986$		0			0
$987$	−7.51472	−	5.31371i	−0.239196	−	0.169137i
$988$		0			0
$989$	7.65685			0.243474
$990$		0			0
$991$	15.0294			0.477426			0.238713	−	0.971090i	$-0.423275\pi$
$991$	15.0294			0.477426			0.238713	+	0.971090i	$0.423275\pi$
$992$		0			0
$993$	2.34315	+	1.65685i	0.0743575	+	0.0525787i
$994$		0			0
$995$	3.02944	+	1.51472i	0.0960396	+	0.0480198i
$996$		0			0
$997$	8.79899	−	8.79899i	0.278667	−	0.278667i	−0.553910	−	0.832577i	$-0.686865\pi$
$997$	8.79899	−	8.79899i	0.278667	−	0.278667i	0.832577	+	0.553910i	$0.186865\pi$
$998$		0			0
$999$	0.615224	+	1.10051i	0.0194648	+	0.0348184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.v.c.113.1		4
3.2	odd	2		240.2.v.a.113.1		4
4.3	odd	2		120.2.r.b.113.2	yes	4
5.2	odd	4		240.2.v.a.17.2		4
5.3	odd	4		1200.2.v.j.257.1		4
5.4	even	2		1200.2.v.d.593.2		4
8.3	odd	2		960.2.v.f.833.1		4
8.5	even	2		960.2.v.g.833.2		4
12.11	even	2		120.2.r.c.113.2	yes	4
15.2	even	4	inner	240.2.v.c.17.1		4
15.8	even	4		1200.2.v.d.257.2		4
15.14	odd	2		1200.2.v.j.593.2		4
20.3	even	4		600.2.r.b.257.2		4
20.7	even	4		120.2.r.c.17.1	yes	4
20.19	odd	2		600.2.r.c.593.1		4
24.5	odd	2		960.2.v.i.833.2		4
24.11	even	2		960.2.v.a.833.1		4
40.27	even	4		960.2.v.a.257.2		4
40.37	odd	4		960.2.v.i.257.1		4
60.23	odd	4		600.2.r.c.257.1		4
60.47	odd	4		120.2.r.b.17.2	✓	4
60.59	even	2		600.2.r.b.593.1		4
120.77	even	4		960.2.v.g.257.2		4
120.107	odd	4		960.2.v.f.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.r.b.17.2	✓	4	60.47	odd	4
120.2.r.b.113.2	yes	4	4.3	odd	2
120.2.r.c.17.1	yes	4	20.7	even	4
120.2.r.c.113.2	yes	4	12.11	even	2
240.2.v.a.17.2		4	5.2	odd	4
240.2.v.a.113.1		4	3.2	odd	2
240.2.v.c.17.1		4	15.2	even	4	inner
240.2.v.c.113.1		4	1.1	even	1	trivial
600.2.r.b.257.2		4	20.3	even	4
600.2.r.b.593.1		4	60.59	even	2
600.2.r.c.257.1		4	60.23	odd	4
600.2.r.c.593.1		4	20.19	odd	2
960.2.v.a.257.2		4	40.27	even	4
960.2.v.a.833.1		4	24.11	even	2
960.2.v.f.257.1		4	120.107	odd	4
960.2.v.f.833.1		4	8.3	odd	2
960.2.v.g.257.2		4	120.77	even	4
960.2.v.g.833.2		4	8.5	even	2
960.2.v.i.257.1		4	40.37	odd	4
960.2.v.i.833.2		4	24.5	odd	2
1200.2.v.d.257.2		4	15.8	even	4
1200.2.v.d.593.2		4	5.4	even	2
1200.2.v.j.257.1		4	5.3	odd	4
1200.2.v.j.593.2		4	15.14	odd	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.v (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.414214 + 0.414214i) q^{7} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.00000i) q^{3} +(-1.00000 + 2.00000i) q^{5} +(-0.414214 + 0.414214i) q^{7} +(1.00000 + 2.82843i) q^{9} +4.82843i q^{11} +(-1.82843 - 1.82843i) q^{13} +(3.41421 - 1.82843i) q^{15} +(3.82843 + 3.82843i) q^{17} +4.82843i q^{19} +(1.00000 - 0.171573i) q^{21} +(-1.58579 + 1.58579i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(1.41421 - 5.00000i) q^{27} -7.65685 q^{29} +5.65685 q^{31} +(4.82843 - 6.82843i) q^{33} +(-0.414214 - 1.24264i) q^{35} +(-0.171573 + 0.171573i) q^{37} +(0.757359 + 4.41421i) q^{39} -5.65685i q^{41} +(-2.41421 - 2.41421i) q^{43} +(-6.65685 - 0.828427i) q^{45} +(-6.41421 - 6.41421i) q^{47} +6.65685i q^{49} +(-1.58579 - 9.24264i) q^{51} +(-3.00000 + 3.00000i) q^{53} +(-9.65685 - 4.82843i) q^{55} +(4.82843 - 6.82843i) q^{57} +4.00000 q^{59} +11.6569 q^{61} +(-1.58579 - 0.757359i) q^{63} +(5.48528 - 1.82843i) q^{65} +(4.07107 - 4.07107i) q^{67} +(3.82843 - 0.656854i) q^{69} +6.48528i q^{71} +(6.65685 + 6.65685i) q^{73} +(0.242641 + 8.65685i) q^{75} +(-2.00000 - 2.00000i) q^{77} -4.82843i q^{79} +(-7.00000 + 5.65685i) q^{81} +(5.24264 - 5.24264i) q^{83} +(-11.4853 + 3.82843i) q^{85} +(10.8284 + 7.65685i) q^{87} +4.34315 q^{89} +1.51472 q^{91} +(-8.00000 - 5.65685i) q^{93} +(-9.65685 - 4.82843i) q^{95} +(1.00000 - 1.00000i) q^{97} +(-13.6569 + 4.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^5 + 4 * q^7 + 4 * q^9	\( 4 q - 4 q^{5} + 4 q^{7} + 4 q^{9} + 4 q^{13} + 8 q^{15} + 4 q^{17} + 4 q^{21} - 12 q^{23} - 12 q^{25} - 8 q^{29} + 8 q^{33} + 4 q^{35} - 12 q^{37} + 20 q^{39} - 4 q^{43} - 4 q^{45} - 20 q^{47} - 12 q^{51} - 12 q^{53} - 16 q^{55} + 8 q^{57} + 16 q^{59} + 24 q^{61} - 12 q^{63} - 12 q^{65} - 12 q^{67} + 4 q^{69} + 4 q^{73} - 16 q^{75} - 8 q^{77} - 28 q^{81} + 4 q^{83} - 12 q^{85} + 32 q^{87} + 40 q^{89} + 40 q^{91} - 32 q^{93} - 16 q^{95} + 4 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 + 4 * q^7 + 4 * q^9 + 4 * q^13 + 8 * q^15 + 4 * q^17 + 4 * q^21 - 12 * q^23 - 12 * q^25 - 8 * q^29 + 8 * q^33 + 4 * q^35 - 12 * q^37 + 20 * q^39 - 4 * q^43 - 4 * q^45 - 20 * q^47 - 12 * q^51 - 12 * q^53 - 16 * q^55 + 8 * q^57 + 16 * q^59 + 24 * q^61 - 12 * q^63 - 12 * q^65 - 12 * q^67 + 4 * q^69 + 4 * q^73 - 16 * q^75 - 8 * q^77 - 28 * q^81 + 4 * q^83 - 12 * q^85 + 32 * q^87 + 40 * q^89 + 40 * q^91 - 32 * q^93 - 16 * q^95 + 4 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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